Type:	Package
Title:	Optimal Test Design Approach to Fixed and Adaptive Test Construction
Version:	1.7.0
Maintainer:	Seung W. Choi <schoi@austin.utexas.edu>
Description:	Uses the optimal test design approach by Birnbaum (1968, ISBN:9781593119348) and van der Linden (2018) <doi:10.1201/9781315117430> to construct fixed, adaptive, and parallel tests. Supports the following mixed-integer programming (MIP) solver packages: 'Rsymphony', 'highs', 'gurobi', 'lpSolve', and 'Rglpk'. The 'gurobi' package is not available from CRAN; see https://www.gurobi.com/downloads/.
URL:	https://choi-phd.github.io/TestDesign/ (documentation)
BugReports:	https://github.com/choi-phd/TestDesign/issues/
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Depends:	R (≥ 4.0)
Imports:	Rcpp (≥ 1.0.0), methods, lpSolve, foreach, logitnorm, crayon
SystemRequirements:	C++17
Suggests:	Rsymphony, highs, gurobi, Rglpk, mirt, mirtCAT, progress, shiny, shinythemes, shinyWidgets, shinyjs, DT, knitr, rmarkdown, kableExtra, testthat (≥ 2.1.0), pkgdown, pkgload
LinkingTo:	Rcpp, RcppArmadillo
RoxygenNote:	7.3.2
Encoding:	UTF-8
LazyData:	true
VignetteBuilder:	knitr
Collate:	'RcppExports.R' 'import.R' 'extensions.R' 'item_class.R' 'calc_prob_functions.r' 'calc_escore_functions.r' 'calc_location_functions.r' 'calc_fisher_functions.r' 'calc_loglikelihood_functions.r' 'calc_jacobian_functions.r' 'calc_hessian_functions.r' 'sim_resp_functions.r' 'loading_functions.R' 'static_class.R' 'shadow_class.R' 'item_pool_operators.R' 'item_attrib_operators.R' 'st_attrib_operators.R' 'constraints_operators.R' 'static_functions.R' 'shadow_functions.R' 'bayes_functions.R' 'calculate_adaptivity_measures.r' 'constraint_functions.R' 'cpp_calc_documents.r' 'cpp_core_documents.r' 'cpp_theta_documents.r' 'datasets.R' 'eligibility_functions.R' 'exposure_control_functions.R' 'solver_functions.R' 'helper_functions.R' 'item_pool_cluster_operators.R' 'other_functions.R' 'partitioning_class.r' 'partitioning_functions.r' 'plot_functions.R' 'summary_class.R' 'print_functions.R' 'runshiny.R' 'shadowtest_functions.R' 'summary_functions.R' 'show_functions.R' 'simulation_data_cache_class.r' 'simulation_data_cache_operators.r' 'theta_functions.R' 'xdata_functions.R'
NeedsCompilation:	yes
Packaged:	2024-08-22 02:27:15 UTC; chois1
Author:	Seung W. Choi [aut, cre], Sangdon Lim [aut]
Repository:	CRAN
Date/Publication:	2024-08-22 10:50:02 UTC

(Internal) Package startup functions

Description

.onAttach is an internal function called when the package is first loaded.

Usage

.onAttach(libname, pkgname)

Arguments

Value

.onAttach does not return anything.

Calculate Relative Errors

Description

Calculate Relative Errors.

Usage

RE(RMSE_foc, RMSE_ref)

Arguments

Calculate Root Mean Squared Error

Description

Calculate Root Mean Squared Error.

Usage

RMSE(x, y, conditional = TRUE)

Arguments

Run adaptive test assembly

Description

Shadow is a test assembly function for performing adaptive test assembly based on the generalized shadow-test framework.

Usage

Shadow(
  config,
  constraints = NULL,
  true_theta = NULL,
  data = NULL,
  prior = NULL,
  prior_par = NULL,
  exclude = NULL,
  include_items_for_estimation = NULL,
  force_solver = FALSE,
  session = NULL,
  seed = NULL,
  cumulative_usage_matrix = NULL
)

## S4 method for signature 'config_Shadow'
Shadow(
  config,
  constraints = NULL,
  true_theta = NULL,
  data = NULL,
  prior = NULL,
  prior_par = NULL,
  exclude = NULL,
  include_items_for_estimation = NULL,
  force_solver = FALSE,
  session = NULL,
  seed = NULL,
  cumulative_usage_matrix = NULL
)

Arguments

Value

Shadow returns an output_Shadow_all object containing assembly results.

References

van der Linden, W. J., Reese, L. M. (1998). A model for optimal constrained adaptive testing. Applied Psychological Measurement, 22, 259-270.

van der Linden, W. J. (1998). Optimal assembly of psychological and educational tests. Applied Psychological Measurement, 22, 195-211.

van der Linden, W. J. (2000). Optimal assembly of tests with item sets. Applied Psychological Measurement, 24, 225-240.

van der Linden, W. J. (2005). Linear models for optimal test design. Springer Science & Business Media.

Examples

config <- createShadowTestConfig()
true_theta <- rnorm(1)
solution <- Shadow(config, constraints_science, true_theta)
solution@output

Split an item pool into partitions

Description

Split is a function for splitting a pool into multiple parallel tests or pools. When constructing parallel tests, each test is constructed to satisfy all constraints. When constructing parallel pools, each pool is constructed so that it contains a test that satisfies all constraints.

Usage

Split(
  config,
  constraints,
  n_partition,
  partition_type,
  partition_size_range = NULL,
  n_maximum_partitions_per_item = 1,
  force_solver = FALSE
)

## S4 method for signature 'config_Static'
Split(
  config,
  constraints,
  n_partition,
  partition_type,
  partition_size_range = NULL,
  n_maximum_partitions_per_item = 1,
  force_solver = FALSE
)

Arguments

Value

Split returns an output_Split object containing item/set indices of created tests/pools.

Examples

## Not run: 
config <- createStaticTestConfig(MIP = list(solver = "RSYMPHONY"))
constraints <- constraints_science[1:10]

solution <- Split(config, constraints, n_partition = 4, partition_type = "test"))
plot(solution)
solution <- Split(config, constraints, n_partition = 4, partition_type = "pool"))
plot(solution)

## End(Not run)

Run fixed-form test assembly

Description

Static is a test assembly function for performing fixed-form test assembly based on the generalized shadow-test framework.

Usage

Static(config, constraints, force_solver = FALSE)

## S4 method for signature 'config_Static'
Static(config, constraints, force_solver = FALSE)

Arguments

Value

Static returns a output_Static object containing the selected items.

References

van der Linden, W. J. (2005). Linear models for optimal test design. Springer Science & Business Media.

Examples

config_science <- createStaticTestConfig(
  list(
    method = "MAXINFO",
    target_location = c(-1, 1)
  )
)
solution <- Static(config_science, constraints_science)

Open TestDesign app

Description

TestDesign is a caller function for opening the Shiny interface of TestDesign package.

Usage

TestDesign()

Examples

## Not run: 
if (interactive()) {
  TestDesign()
}

## End(Not run)

Calculate alpha angles from a-parameters

Description

a_to_alpha is a function for converting an a-parameter vector to an alpha angle vector. The returned values are in the radian metric.

Usage

a_to_alpha(a)

Arguments

Examples

a_to_alpha(c(1, 1))

(Internal) Count number of pool items that match a constraint

Description

addCountsToConstraintData is an internal function for counting the number of items in the pool that match a constraint.

Usage

addCountsToConstraintData(x, attrib)

Arguments

Value

addCountsToConstraintData returns an updated data.frame.

(Internal) Sum scores of items in a solution that match a constraint

Description

addScoreToConstraintData is an internal function for summing the score of items in a solution that match a constraint.

Usage

addScoreToConstraintData(x, attrib, item_idx, item_resp, item_ncat)

Arguments

Value

addScoreToConstraintData returns an updated data.frame.

(Internal) Count number of items in a solution that match a constraint

Description

addSolutionToConstraintData is an internal function for counting the number of items in a solution that match a constraint.

Usage

addSolutionToConstraintData(x, attrib, item_idx, all_values)

Arguments

Value

addSolutionToConstraintData returns an updated data.frame.

(Internal) Apply spike-reduction mechanism on exposure rates

Description

adjustAlphaToReduceSpike is an internal function for applying spike-reduction mechanism on exposure rates.

Usage

adjustAlphaToReduceSpike(
  exposure_record,
  segment_prob_of_final_theta,
  segments_visited,
  eligibility_flag_in_final_theta_segment,
  x,
  simulation_constants
)

Arguments

Value

clipEligibilityRates returns an updated exposure record.

(Internal) Aggregate item usage matrix into exposure rate table

Description

aggregateUsageMatrix is an internal function for aggregating item usage matrix into an exposure rate table.

Usage

aggregateUsageMatrix(usage_matrix, simulation_constants, constraints)

Arguments

Value

aggregateUsageMatrix returns a data.frame containing exposure rates.

Open TestDesign app

Description

app and OAT are aliases of TestDesign.

Usage

app()

OAT()

Details

TestDesign is a caller function for opening the Shiny interface of TestDesign package.

Examples

## Not run: 
if (interactive()) {
  TestDesign()
}

## End(Not run)

(Internal) Append mean information to shadowtest

Description

(Internal) Append mean information to shadowtest

Usage

appendMeanInfo(shadow_test, v, mean_info_name)

Arguments

Value

appendMeanInfo returns an updated shadowtest.

(Internal) Modify item information using eligibility constraints

Description

applyEligibilityConstraintsToInfo is an internal function for modifying item information using eligibility constraints. This is known as the big M method. The function penalizes item information of items that are marked as ineligibile. This leads to those items being deterred from selected in shadowtest assembly, unless necessary.

Usage

applyEligibilityConstraintsToInfo(
  info,
  eligibility_flag_in_current_theta_segment,
  config,
  simulation_constants
)

Arguments

Value

applyEligibilityConstraintsToInfo returns an updated item information vector.

(Internal) Augment constraint matrix-data with eligibility constraints

Description

applyEligibilityConstraintsToXdata is an internal function for augmenting constraint matrix-data with eligibility constraints. The function marks items/sets marked as ineligibile to be formally excluded in the constraint matrix-data.

Usage

applyEligibilityConstraintsToXdata(
  xdata,
  eligibility_flag_in_current_theta_segment,
  simulation_constants,
  constraints
)

Arguments

Value

applyEligibilityConstraintsToXdata returns an updated constriant matrix-data.

(Internal) Apply fading to exposure record

Description

applyFading is an internal function for applying fading to exposure record. Specifically, the following exposure records are multiplied by fading_factor:

• n_k: the number of examinees completed the test so far, at each segment k.

• f_k:

• a_ik: the number of times each item i was administered to examinees, at each segment k

• r_ik:

Usage

applyFading(exposure_record, segments_to_apply, simulation_constants)

Arguments

Value

applyFading returns an updated exposure record.

(Internal) Modify item information using overlap constraints

Description

applyOverlapConstraintsToInfo is an internal function for modifying item information using eligibility constraints. This is known as the big M method. The function penalizes item information of items that have been administered previously (within examinees). This leads to those items being deterred from selected in shadowtest assembly, unless necessary.

Usage

applyOverlapConstraintsToInfo(info, usage_flag, config, simulation_constants)

Arguments

Value

applyEligibilityConstraintsToInfo returns an updated item information vector.

(Internal) Apply shrinkage correction to theta estimate

Description

applyShrinkageCorrection is an internal function for applying shrinkage correction to a theta estimate.

Usage

applyShrinkageCorrection(EAP, config_theta, j)

Arguments

Value

applyShrinkageCorrection returns an updated list containing corrected EAP theta estimate.

(Internal) Thin a MCMC chain

Description

applyThin is an internal function for thinning a Markov chain. Burn-in is also applied.

Usage

applyThin(posterior_sample, bayesian_constants)

Arguments

Value

applyThin returns an updated Markov chain.

(Internal) Assemble a shadowtest

Description

(Internal) Assemble a shadowtest

Usage

assembleShadowTest(
  j,
  position,
  o,
  eligibility_flag,
  exclude_flag,
  usage_flag,
  groupings_record,
  info,
  config,
  simulation_constants,
  constraints
)

Arguments

Value

a named list containing a shadowtest and related data.

• shadow_test a data.frame containing the shadowtest.

• feasible whether the assembly was feasible the first time.

(Internal) Determine if shadowtest assembly was feasible for exposure control purposes

Description

assemblyInFinalThetaSegmentWasFeasibleAtLeastOnceInInterimThetaSegments is an internal function for determining if shadowtest assembly was feasible for exposure control purposes. Specifically, for the segment k the final theta estimate belonged to, it returns TRUE if shadowtest assembly was feasible at any interim theta that also belonged to k, and returns FALSE otherwise.

Usage

assemblyInFinalThetaSegmentWasFeasibleAtLeastOnceInInterimThetaSegments(
  x,
  final_theta_segment
)

Arguments

Details

Example 1:

• Interim theta segments are 1, 2, 3, 4, 5, 1, 2, 3, 4, 5

• Shadowtest feasibility are 1, 1, 1, 0, 0, 1, 0, 0, 0, 0

• Final theta estimate is in segment 3

• From the two vectors, segments where shadowtest assembly was feasible: 1, 2, 3, 1

• Final theta segment 3 is an element of the above vector. Return TRUE

Example 2:

• Interim theta segments are 1, 2, 3, 4, 5, 1, 2, 3, 4, 5

• Shadowtest feasibility are 1, 1, 1, 0, 0, 1, 0, 0, 0, 0

• Final theta estimate is in segment 4

• From the two vectors, segments where shadowtest assembly was feasible: 1, 2, 3, 1

• Final theta segment 4 is not an element of the above vector. Return FALSE

Value

assemblyInFinalThetaSegmentWasFeasibleAtLeastOnceInInterimThetaSegments returns TRUE or FALSE.

Build constraints (shortcut to other loading functions)

Description

buildConstraints is a data loading function for creating a constraints object. buildConstraints is a shortcut that calls other data loading functions. The constraints must be in the expected format; see the vignette in vignette("constraints").

Usage

buildConstraints(object, item_pool, item_attrib, st_attrib = NULL)

Arguments

Value

buildConstraints returns a constraints object. This object is used in Static and Shadow.

Examples

## Read from objects:
constraints_science <- buildConstraints(constraints_science_data,
  itempool_science, itemattrib_science)
constraints_reading <- buildConstraints(constraints_reading_data,
  itempool_reading, itemattrib_reading, stimattrib_reading)

## Read from data.frame:
constraints_science <- buildConstraints(constraints_science_data,
  itempool_science_data, itemattrib_science_data)
constraints_reading <- buildConstraints(constraints_reading_data,
  itempool_reading_data, itemattrib_reading_data, stimattrib_reading_data)

## Read from file: write to tempdir() for illustration and clean afterwards
f1 <- file.path(tempdir(), "constraints_science.csv")
f2 <- file.path(tempdir(), "itempool_science.csv")
f3 <- file.path(tempdir(), "itemattrib_science.csv")
write.csv(constraints_science_data, f1, row.names = FALSE)
write.csv(itempool_science_data   , f2, row.names = FALSE)
write.csv(itemattrib_science_data , f3, row.names = FALSE)
constraints_science <- buildConstraints(f1, f2, f3)
file.remove(f1)
file.remove(f2)
file.remove(f3)

Calculate expected scores

Description

calcEscore is a function for calculating expected scores.

Usage

calcEscore(object, theta)

## S4 method for signature 'item_1PL,numeric'
calcEscore(object, theta)

## S4 method for signature 'item_2PL,numeric'
calcEscore(object, theta)

## S4 method for signature 'item_3PL,numeric'
calcEscore(object, theta)

## S4 method for signature 'item_PC,numeric'
calcEscore(object, theta)

## S4 method for signature 'item_GPC,numeric'
calcEscore(object, theta)

## S4 method for signature 'item_GR,numeric'
calcEscore(object, theta)

## S4 method for signature 'item_pool,numeric'
calcEscore(object, theta)

## S4 method for signature 'item_1PL,matrix'
calcEscore(object, theta)

## S4 method for signature 'item_2PL,matrix'
calcEscore(object, theta)

## S4 method for signature 'item_3PL,matrix'
calcEscore(object, theta)

## S4 method for signature 'item_PC,matrix'
calcEscore(object, theta)

## S4 method for signature 'item_GPC,matrix'
calcEscore(object, theta)

## S4 method for signature 'item_GR,matrix'
calcEscore(object, theta)

## S4 method for signature 'item_pool,matrix'
calcEscore(object, theta)

## S4 method for signature 'item_pool_cluster,numeric'
calcEscore(object, theta)

Arguments

Value

item object:

calcEscore a vector containing expected score of the item at the theta values.

item_pool object:

calcEscore returns a vector containing the pool-level expected score at the theta values.

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

item_1     <- new("item_1PL", difficulty = 0.5)
item_2     <- new("item_2PL", slope = 1.0, difficulty = 0.5)
item_3     <- new("item_3PL", slope = 1.0, difficulty = 0.5, guessing = 0.2)
item_4     <- new("item_PC", threshold = c(-1, 0, 1), ncat = 4)
item_5     <- new("item_GPC", slope = 1.2, threshold = c(-0.8, -1.0, 0.5), ncat = 4)
item_6     <- new("item_GR", slope = 0.9, category = c(-1, 0, 1), ncat = 4)

ICC_item_1 <- calcEscore(item_1, seq(-3, 3, 1))
ICC_item_2 <- calcEscore(item_2, seq(-3, 3, 1))
ICC_item_3 <- calcEscore(item_3, seq(-3, 3, 1))
ICC_item_4 <- calcEscore(item_4, seq(-3, 3, 1))
ICC_item_5 <- calcEscore(item_5, seq(-3, 3, 1))
ICC_item_6 <- calcEscore(item_6, seq(-3, 3, 1))
TCC_pool   <- calcEscore(itempool_science, seq(-3, 3, 1))

Calculate Fisher information

Description

calcFisher is a function for calculating Fisher information.

Usage

calcFisher(object, theta)

## S4 method for signature 'item_1PL,numeric'
calcFisher(object, theta)

## S4 method for signature 'item_2PL,numeric'
calcFisher(object, theta)

## S4 method for signature 'item_3PL,numeric'
calcFisher(object, theta)

## S4 method for signature 'item_PC,numeric'
calcFisher(object, theta)

## S4 method for signature 'item_GPC,numeric'
calcFisher(object, theta)

## S4 method for signature 'item_GR,numeric'
calcFisher(object, theta)

## S4 method for signature 'item_pool,numeric'
calcFisher(object, theta)

## S4 method for signature 'item_1PL,matrix'
calcFisher(object, theta)

## S4 method for signature 'item_2PL,matrix'
calcFisher(object, theta)

## S4 method for signature 'item_3PL,matrix'
calcFisher(object, theta)

## S4 method for signature 'item_PC,matrix'
calcFisher(object, theta)

## S4 method for signature 'item_GPC,matrix'
calcFisher(object, theta)

## S4 method for signature 'item_GR,matrix'
calcFisher(object, theta)

## S4 method for signature 'item_pool,matrix'
calcFisher(object, theta)

## S4 method for signature 'item_pool_cluster,numeric'
calcFisher(object, theta)

Arguments

Value

item object:

calcFisher returns a (nq, 1) matrix of information values.

item_pool object:

calcProb returns a (nq, ni) matrix of information values.

notations

• nq denotes the number of theta values.

• ni denotes the number of items in the item_pool object.

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

item_1      <- new("item_1PL", difficulty = 0.5)
item_2      <- new("item_2PL", slope = 1.0, difficulty = 0.5)
item_3      <- new("item_3PL", slope = 1.0, difficulty = 0.5, guessing = 0.2)
item_4      <- new("item_PC", threshold = c(-1, 0, 1), ncat = 4)
item_5      <- new("item_GPC", slope = 1.2, threshold = c(-0.8, -1.0, 0.5), ncat = 4)
item_6      <- new("item_GR", slope = 0.9, category = c(-1, 0, 1), ncat = 4)

info_item_1 <- calcFisher(item_1, seq(-3, 3, 1))
info_item_2 <- calcFisher(item_2, seq(-3, 3, 1))
info_item_3 <- calcFisher(item_3, seq(-3, 3, 1))
info_item_4 <- calcFisher(item_4, seq(-3, 3, 1))
info_item_5 <- calcFisher(item_5, seq(-3, 3, 1))
info_item_6 <- calcFisher(item_6, seq(-3, 3, 1))
info_pool   <- calcFisher(itempool_science, seq(-3, 3, 1))

Calculate second derivative of log-likelihood

Description

calcHessian is a function for calculating the second derivative of the log-likelihood function.

Usage

calcHessian(object, theta, resp)

## S4 method for signature 'item_1PL,numeric,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_2PL,numeric,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_3PL,numeric,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_PC,numeric,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_GPC,numeric,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_GR,numeric,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_1PL,matrix,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_2PL,matrix,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_3PL,matrix,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_PC,matrix,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_GPC,matrix,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_GR,matrix,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_pool,numeric,numeric'
calcHessian(object, theta, resp)

## S4 method for signature 'item_pool_cluster,numeric,list'
calcHessian(object, theta, resp)

Arguments

Details

notations

• nq denotes the number of theta values.

• ni denotes the number of items in the item_pool object.

Value

item object:

calcHessian returns a length nq vector containing the second derivative of the log-likelihood function, of observing the response at each theta.

item_pool object:

calcHessian returns a (nq, ni) matrix containing the second derivative of the log-likelihood function, of observing the response at each theta.

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

item_1    <- new("item_1PL", difficulty = 0.5)
item_2    <- new("item_2PL", slope = 1.0, difficulty = 0.5)
item_3    <- new("item_3PL", slope = 1.0, difficulty = 0.5, guessing = 0.2)
item_4    <- new("item_PC", threshold = c(-1, 0, 1), ncat = 4)
item_5    <- new("item_GPC", slope = 1.2, threshold = c(-0.8, -1.0, 0.5), ncat = 4)
item_6    <- new("item_GR", slope = 0.9, category = c(-1, 0, 1), ncat = 4)

h_item_1 <- calcHessian(item_1, seq(-3, 3, 1), 0)
h_item_2 <- calcHessian(item_2, seq(-3, 3, 1), 0)
h_item_3 <- calcHessian(item_3, seq(-3, 3, 1), 0)
h_item_4 <- calcHessian(item_4, seq(-3, 3, 1), 0)
h_item_5 <- calcHessian(item_5, seq(-3, 3, 1), 0)
h_item_6 <- calcHessian(item_6, seq(-3, 3, 1), 0)
h_pool   <- calcHessian(
  itempool_science, seq(-3, 3, 1),
  rep(0, itempool_science@ni)
)

Calculate first derivative of log-likelihood

Description

calcJacobian is a function for calculating the first derivative of the log-likelihood function.

Usage

calcJacobian(object, theta, resp)

## S4 method for signature 'item_1PL,numeric,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_2PL,numeric,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_3PL,numeric,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_PC,numeric,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_GPC,numeric,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_GR,numeric,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_1PL,matrix,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_2PL,matrix,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_3PL,matrix,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_PC,matrix,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_GPC,matrix,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_GR,matrix,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_pool,numeric,numeric'
calcJacobian(object, theta, resp)

## S4 method for signature 'item_pool_cluster,numeric,list'
calcJacobian(object, theta, resp)

Arguments

Value

item object:

calcJacobian returns a length nq vector containing the first derivative of the log-likelihood function, of observing the response at each theta.

item_pool object:

calcJacobian returns a (nq, ni) matrix containing the first derivative of the log-likelihood function, of observing the response at each theta.

notations

• nq denotes the number of theta values.

• ni denotes the number of items in the item_pool object.

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

item_1    <- new("item_1PL", difficulty = 0.5)
item_2    <- new("item_2PL", slope = 1.0, difficulty = 0.5)
item_3    <- new("item_3PL", slope = 1.0, difficulty = 0.5, guessing = 0.2)
item_4    <- new("item_PC", threshold = c(-1, 0, 1), ncat = 4)
item_5    <- new("item_GPC", slope = 1.2, threshold = c(-0.8, -1.0, 0.5), ncat = 4)
item_6    <- new("item_GR", slope = 0.9, category = c(-1, 0, 1), ncat = 4)

j_item_1 <- calcJacobian(item_1, seq(-3, 3, 1), 0)
j_item_2 <- calcJacobian(item_2, seq(-3, 3, 1), 0)
j_item_3 <- calcJacobian(item_3, seq(-3, 3, 1), 0)
j_item_4 <- calcJacobian(item_4, seq(-3, 3, 1), 0)
j_item_5 <- calcJacobian(item_5, seq(-3, 3, 1), 0)
j_item_6 <- calcJacobian(item_6, seq(-3, 3, 1), 0)
j_pool   <- calcJacobian(
  itempool_science, seq(-3, 3, 1),
  rep(0, itempool_science@ni)
)

Calculate central location (overall difficulty)

Description

calcLocation is a function for calculating the central location (overall difficulty) of items.

Usage

calcLocation(object)

## S4 method for signature 'item_1PL'
calcLocation(object)

## S4 method for signature 'item_2PL'
calcLocation(object)

## S4 method for signature 'item_3PL'
calcLocation(object)

## S4 method for signature 'item_PC'
calcLocation(object)

## S4 method for signature 'item_GPC'
calcLocation(object)

## S4 method for signature 'item_GR'
calcLocation(object)

## S4 method for signature 'item_pool'
calcLocation(object)

Arguments

Value

item object:

calcLocation returns a theta value representing the central location.

item_pool object:

calcProb returns a length ni list, each containing the central location of the item.

notations

• ni denotes the number of items in the item_pool object.

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

item_1      <- new("item_1PL", difficulty = 0.5)
item_2      <- new("item_2PL", slope = 1.0, difficulty = 0.5)
item_3      <- new("item_3PL", slope = 1.0, difficulty = 0.5, guessing = 0.2)
item_4      <- new("item_PC", threshold = c(-1, 0, 1), ncat = 4)
item_5      <- new("item_GPC", slope = 1.2, threshold = c(-0.8, -1.0, 0.5), ncat = 4)
item_6      <- new("item_GR", slope = 0.9, category = c(-1, 0, 1), ncat = 4)

loc_item_1 <- calcLocation(item_1)
loc_item_2 <- calcLocation(item_2)
loc_item_3 <- calcLocation(item_3)
loc_item_4 <- calcLocation(item_4)
loc_item_5 <- calcLocation(item_5)
loc_item_6 <- calcLocation(item_6)
loc_pool   <- calcLocation(itempool_science)

Calculate log-likelihood

Description

calcLogLikelihood is a function for calculating log-likelihood values.

Usage

calcLogLikelihood(object, theta, resp)

## S4 method for signature 'item_pool,numeric,numeric'
calcLogLikelihood(object, theta, resp)

## S4 method for signature 'item_pool,numeric,matrix'
calcLogLikelihood(object, theta, resp)

## S4 method for signature 'item_pool,matrix,numeric'
calcLogLikelihood(object, theta, resp)

## S4 method for signature 'item_pool,matrix,matrix'
calcLogLikelihood(object, theta, resp)

Arguments

Value

calcLogLikelihood returns values of log-likelihoods.

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

j_pool   <- calcLogLikelihood(itempool_science, seq(-3, 3, 1), 0)

Calculate item response probabilities

Description

calcProb is a function for calculating item response probabilities.

Usage

calcProb(object, theta)

## S4 method for signature 'item_1PL,numeric'
calcProb(object, theta)

## S4 method for signature 'item_2PL,numeric'
calcProb(object, theta)

## S4 method for signature 'item_3PL,numeric'
calcProb(object, theta)

## S4 method for signature 'item_PC,numeric'
calcProb(object, theta)

## S4 method for signature 'item_GPC,numeric'
calcProb(object, theta)

## S4 method for signature 'item_GR,numeric'
calcProb(object, theta)

## S4 method for signature 'item_pool,numeric'
calcProb(object, theta)

## S4 method for signature 'item_1PL,matrix'
calcProb(object, theta)

## S4 method for signature 'item_2PL,matrix'
calcProb(object, theta)

## S4 method for signature 'item_3PL,matrix'
calcProb(object, theta)

## S4 method for signature 'item_PC,matrix'
calcProb(object, theta)

## S4 method for signature 'item_GPC,matrix'
calcProb(object, theta)

## S4 method for signature 'item_GR,matrix'
calcProb(object, theta)

## S4 method for signature 'item_pool,matrix'
calcProb(object, theta)

## S4 method for signature 'item_pool_cluster,numeric'
calcProb(object, theta)

Arguments

Value

item object:

calcProb returns a (nq, ncat) matrix of probability values.

item_pool object:

calcProb returns a length ni list, each containing a matrix of probability values.

notations

• nq denotes the number of theta values.

• ncat denotes the number of response categories.

• ni denotes the number of items in the item_pool object.

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

item_1      <- new("item_1PL", difficulty = 0.5)
item_2      <- new("item_2PL", slope = 1.0, difficulty = 0.5)
item_3      <- new("item_3PL", slope = 1.0, difficulty = 0.5, guessing = 0.2)
item_4      <- new("item_PC", threshold = c(-1, 0, 1), ncat = 4)
item_5      <- new("item_GPC", slope = 1.2, threshold = c(-0.8, -1.0, 0.5), ncat = 4)
item_6      <- new("item_GR", slope = 0.9, category = c(-1, 0, 1), ncat = 4)

prob_item_1 <- calcProb(item_1, seq(-3, 3, 1))
prob_item_2 <- calcProb(item_2, seq(-3, 3, 1))
prob_item_3 <- calcProb(item_3, seq(-3, 3, 1))
prob_item_4 <- calcProb(item_4, seq(-3, 3, 1))
prob_item_5 <- calcProb(item_5, seq(-3, 3, 1))
prob_item_6 <- calcProb(item_6, seq(-3, 3, 1))
prob_pool   <- calcProb(itempool_science, seq(-3, 3, 1))

Calculate the mutual information using full Bayesian

Description

Calculate the mutual information using full Bayesian.

Usage

calc_MI_FB(x, items_list, ncat, model)

Arguments

(C++) For multiple items, calculate Fisher information

Description

calc_info() and calc_info_matrix() are functions for calculating Fisher information. These functions are designed for multiple items.

Usage

calc_info(x, item_parm, ncat, model)

calc_info_matrix(x, item_parm, ncat, model)

Arguments

Details

calc_info() accepts a single theta value, and calc_info_matrix() accepts multiple theta values.

Currently supports unidimensional models.

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

# item parameters
item_parm <- matrix(c(
  1, NA,   NA,
  1,  2,   NA,
  1,  2, 0.25,
  0,  1,   NA,
  2,  0,    1,
  2,  0,    2),
  nrow = 6,
  byrow = TRUE
)

ncat  <- c(2, 2, 2, 3, 3, 3)
model <- c(1, 2, 3, 4, 5, 6)

# single theta example
x <- 0.5
calc_info(x, item_parm, ncat, model)

# multiple thetas example
x <- matrix(seq(0.1, 0.5, 0.1)) # column vector in matrix form
calc_info_matrix(x, item_parm, ncat, model)

Calculate the Fisher information using empirical Bayes

Description

Calculate the Fisher information using empirical Bayes.

Usage

calc_info_EB(x, item_parm, ncat, model)

Arguments

Calculate the Fisher information using full Bayesian

Description

Calculate the Fisher information using full Bayesian.

Usage

calc_info_FB(x, items_list, ncat, model, useEAP = FALSE)

Arguments

(C++) For multiple items, calculate likelihoods

Description

calc_likelihood() and calc_likelihood_function() are functions for calculating likelihoods.

Usage

calc_likelihood(x, item_parm, resp, ncat, model)

calc_likelihood_function(theta_grid, item_parm, resp, ncat, model)

calc_log_likelihood(x, item_parm, resp, ncat, model, prior, prior_parm)

calc_log_likelihood_function(
  theta_grid,
  item_parm,
  resp,
  ncat,
  model,
  prior,
  prior_parm
)

Arguments

Details

calc_log_likelihood() and calc_log_likelihood_function() are functions for calculating log likelihoods.

These functions are designed for multiple items.

calc_*() functions accept a single theta value, and calc_*_function() functions accept multiple theta values.

Currently supports unidimensional models.

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

# item parameters
item_parm <- matrix(c(
  1, NA,   NA,
  1,  2,   NA,
  1,  2, 0.25,
  0,  1,   NA,
  2,  0,    1,
  2,  0,    2),
  nrow = 6,
  byrow = TRUE
)

ncat  <- c(2, 2, 2, 3, 3, 3)
model <- c(1, 2, 3, 4, 5, 6)
resp  <- c(0, 1, 0, 1, 0, 1)

x <- 3
l  <- calc_likelihood(x, item_parm, resp, ncat, model)
ll <- calc_log_likelihood(x, item_parm, resp, ncat, model, 2, NA)
log(l) == ll

x <- matrix(seq(-3, 3, .1))
l  <- calc_likelihood_function(x, item_parm, resp, ncat, model)
ll <- calc_log_likelihood_function(x, item_parm, resp, ncat, model, 2, NA)
all(log(l) == ll)

Calculate a posterior value of theta

Description

Calculate a posterior value of theta.

Usage

calc_posterior(x, item_parm, resp, ncat, model, prior, prior_parm)

Arguments

Calculate a posterior distribution of theta

Description

Calculate a posterior distribution of theta.

Usage

calc_posterior_function(
  theta_grid,
  item_parm,
  resp,
  ncat,
  model,
  prior,
  prior_parm
)

Arguments

Calculate a posterior value of theta for a single item

Description

Calculate a posterior value of theta for a single item.

Usage

calc_posterior_single(x, item_parm, resp, ncat, model, prior, prior_parm)

Arguments

Calculate Adaptivity Measures

Description

calculateAdaptivityMeasures is a function for calculating commonly used adaptivity measures.

Usage

calculateAdaptivityMeasures(x)

Arguments

Value

calculateAdaptivityMeasures returns a named list:

• corr the correlation between final theta estimates and average test locations.

• ratio the ratio of (1) standard deviation of average test locations, versus (2) standard deviation of final theta estimates.

• PRV the proportion of variance reduced, from (1) the variance of item locations of all items in the pool, by (2) the average of test location variances.

• info (1) average information of a test at final theta estimate, relative to (2) best average obtainable from item pool using same test length, adjusting for (3) average information from item pool using random selection.

Check the consistency of constraints and item usage

Description

Check the consistency of constraints and item usage.

Usage

checkConstraints(constraints, usage_matrix, true_theta = NULL)

Arguments

(Internal) Clip eligibility rates into 0-1 bounds

Description

clipEligibilityRates is an internal function for processing eligibility rate updates.

Usage

clipEligibilityRates(exposure_record, simulation_constants)

Arguments

Value

clipEligibilityRates returns an updated exposure record.

(Internal) Combine constraints data

Description

combineConstraintsData is an internal function for combining constraints data. Columns that exist on only one side are filled in with NA values.

Usage

combineConstraintsData(raw1, raw2)

Arguments

Value

combineConstraintsData returns a data.frame containing the combined constraints data. This can be supplied to loadConstraints.

(Internal) Combine item pool data

Description

combineItemPoolData is an internal function for combining item pool data. Columns that exist on only one side are filled in with NA values.

Usage

combineItemPoolData(raw1, raw2, unique)

Arguments

Value

combineItemPoolData returns a data.frame containing the combined item pool data. This can be supplied to loadItemPool.

(Internal) Combine two constraint matrix-data

Description

(Internal) Combine two constraint matrix-data

Usage

combineXdata(x1, x2)

Arguments

Value

combineXdata returns the combined constraint matrix-data.

(Internal) Convert posterior densities into an EAP estimate

Description

computeEAPFromPosterior is an internal function for converting posterior densities into an EAP estimate.

Usage

computeEAPFromPosterior(posterior, theta_grid)

Arguments

Value

computeEAPFromPosterior returns a named list containing an EAP theta estimate.

(Internal) Compute item information at current theta estimate

Description

computeInfoAtCurrentTheta is an internal function for computing item information at current theta estimate.

Usage

computeInfoAtCurrentTheta(
  item_selection,
  j,
  current_theta,
  item_pool,
  model_code,
  info_fixed_theta,
  info_grid,
  item_parameter_sample
)

Arguments

Create a config_Shadow object

Description

createShadowTestConfig is a config function for creating a config_Shadow object for shadowtest assembly. Default values are used for any unspecified parameters/slots.

Usage

createShadowTestConfig(
  item_selection = NULL,
  content_balancing = NULL,
  MIP = NULL,
  MCMC = NULL,
  exclude_policy = NULL,
  refresh_policy = NULL,
  exposure_control = NULL,
  overlap_control = NULL,
  stopping_criterion = NULL,
  interim_theta = NULL,
  final_theta = NULL,
  theta_grid = seq(-4, 4, 0.1)
)

Arguments

Examples

cfg1 <- createShadowTestConfig(refresh_policy = list(
  method = "STIMULUS"
))
cfg2 <- createShadowTestConfig(refresh_policy = list(
  method = "POSITION",
  position = c(1, 5, 9)
))

Create a config_Static object

Description

createStaticTestConfig is a config function for creating a config_Static object for Static (fixed-form) test assembly. Default values are used for any unspecified parameters/slots.

Usage

createStaticTestConfig(item_selection = NULL, MIP = NULL)

Arguments

Value

createStaticTestConfig returns a config_Static object. This object is used in Static.

Examples

cfg1 <- createStaticTestConfig(
  list(
    method = "MAXINFO",
    info_type = "FISHER",
    target_location = c(-1, 0, 1),
    target_weight = c(1, 1, 1)
  )
)

cfg2 <- createStaticTestConfig(
  list(
    method = "TIF",
    info_type = "FISHER",
    target_location = c(-1, 0, 1),
    target_weight = c(1, 1, 1),
    target_value = c(8, 10, 12)
  )
)

cfg3 <- createStaticTestConfig(
  list(
    method = "TCC",
    info_type = "FISHER",
    target_location = c(-1, 0, 1),
    target_weight = c(1, 1, 1),
    target_value = c(10, 15, 20)
  )
)

Class 'constraint': a single constraint

Description

constraint is an S4 class for representing a single constraint.

Slots

constraint

the numeric index of the constraint.

constraint_id

the character ID of the constraint.

nc

the number of MIP-format constraints translated from this constraint.

mat,dir,rhs

these represent MIP-format constraints. A single MIP-format constraint is associated with a row in mat, a value in rhs, and a value in dir.

• the i-th row of mat represents LHS coefficients to use on decision variables in the i-th MIP-format constraint.

• the i-th value of rhs represents RHS values to use in the i-th MIP-format constraint.

• the i-th value of dir represents the imposed constraint between LHS and RHS.

suspend

TRUE if the constraint is not to be imposed.

Class 'constraints': a set of constraints

Description

constraints is an S4 class for representing a set of constraints and its associated objects.

Details

See constraints-operators for object manipulation functions.

Slots

constraints

a data.frame containing the constraint specifications.

list_constraints

a list containing the constraint object representation of each constraint.

pool

the item_pool object associated with the constraints.

item_attrib

the item_attrib object associated with the constraints.

st_attrib

the st_attrib object associated with the constraints.

test_length

the test length specified in the constraints.

nv

the number of decision variables. Equals ni + ns.

ni

the number of items to search from.

ns

the number of stimulus to search from.

id

the item/stimulus ID string of each item/stimulus.

index,mat,dir,rhs

these represent MIP-format constraints. A single MIP-format constraint is associated with a value in index, a row in mat, a value in rhs, and a value in dir.

• the i-th value of index represents which constraint specification in the constraints argument it was translated from.

• the i-th row of mat represents LHS coefficients to use on decision variables in the i-th MIP-format constraint.

• the i-th value of rhs represents RHS values to use in the i-th MIP-format constraint.

• the i-th value of dir represents the imposed constraint between LHS and RHS.

set_based

TRUE if the constraint is set-based. FALSE otherwise.

item_order

the item attribute of each item to use in imposing an item order constraint, if any.

item_order_by

the name of the item attribute to use in imposing an item order constraint, if any.

stim_order

the stimulus attribute of each stimulus to use in imposing a stimulus order constraint, if any.

stim_order_by

the name of the stimulus attribute to use in imposing a stimulus order constraint, if any.

item_index_by_stimulus

a list containing item indices of each stimulus.

stimulus_index_by_item

the stimulus indices of each item.

Basic operators for constraints objects

Description

Create a subset of a constraints object:

• constraints[i]

• subsetConstraints(constraints, 1:10)

Combine two constraints objects:

• c(constraints1, constraints2)

• combineConstraints(constraints1, constraints2)

Usage

subsetConstraints(x, i = NULL)

combineConstraints(x1, x2)

## S4 method for signature 'constraints,numeric'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'constraints'
c(x, ...)

Arguments

Examples

c1 <- constraints_science
c2 <- c1[1:10]
c3 <- c1[c(1, 11:36)] # keep constraint 1 for test length
c4 <- c(c2, c3)

Bayes dataset

Description

Item-based example item pool with standard errors (320 items).

Details

This pool is associated with the following objects:

• itempool_bayes an item_pool object containing 320 items.

• itemattrib_bayes a item_attrib object containing 5 item-level attributes.

• constraints_bayes a constraints object containing 14 constraints.

Also, the following objects are intended for illustrating expected data structures.

• itempool_bayes_data a data.frame containing item parameters.

• itempool_se_bayes_data a data.frame containing item parameter standard errors.

• itemattrib_bayes_data a data.frame containing item attributes.

• constraints_bayes_data a data.frame containing constraint specifications.

Examples

itempool_bayes    <- loadItemPool(itempool_bayes_data, itempool_se_bayes_data)
itemattrib_bayes  <- loadItemAttrib(itemattrib_bayes_data, itempool_bayes)
constraints_bayes <- loadConstraints(constraints_bayes_data,
  itempool_bayes, itemattrib_bayes)

Fatigue dataset

Description

Item-based example pool with item contents (95 items).

Details

This pool is associated with the following objects:

• itempool_fatigue an item_pool object containing 95 items.

• itemattrib_fatigue an item_attrib object containing 7 item-level attributes.

• constraints_fatigue a constraints object containing 111 constraints.

Also, the following objects are intended for illustrating expected data structures.

• itempool_fatigue_data a data.frame containing item parameters.

• itemattrib_fatigue_data a data.frame containing item attributes.

• itemtext_fatigue_data a data.frame containing item texts.

• constraints_fatigue_data a data.frame containing constraint specifications.

• resp_fatigue_data a data.frame containing raw response data.

Examples

itempool_fatigue   <- loadItemPool(itempool_fatigue_data)
itemattrib_fatigue <- loadItemAttrib(itemattrib_fatigue_data, itempool_fatigue)
constraints_fatigue <- loadConstraints(constraints_fatigue_data,
  itempool_fatigue, itemattrib_fatigue)

Reading dataset

Description

Stimulus-based example item pool (303 items, 35 stimuli).

Details

This pool is associated with the following objects:

• itempool_reading an item_pool object containing 303 items.

• itemattrib_reading an item_attrib object containing 12 item-level attributes.

• stimattrib_reading a st_attrib object containing 4 stimulus-level attributes.

• constraints_reading a constraints object containing 18 constraints.

Also, the following objects are intended for illustrating expected data structures.

• itempool_reading_data a data.frame containing item parameters.

• itemattrib_reading_data a data.frame containing item attributes.

• stimattrib_reading_data a data.frame containing stimulus attributes.

• constraints_reading_data a data.frame containing constraint specifications.

Examples

itempool_reading    <- loadItemPool(itempool_reading_data)
itemattrib_reading  <- loadItemAttrib(itemattrib_reading_data, itempool_reading)
stimattrib_reading  <- loadStAttrib(stimattrib_reading_data, itemattrib_reading)
constraints_reading <- loadConstraints(constraints_reading_data,
  itempool_reading, itemattrib_reading, stimattrib_reading)

Science dataset

Description

Item-based example item pool (1000 items).

Details

This pool is associated with the following objects:

• itempool_science an item_pool object containing 1000 items.

• itemattrib_science an item_attrib object containing 9 item-level attributes.

• constraints_science a constraints object containing 36 constraints.

Also, the following objects are intended for illustrating expected data structures.

• itempool_science_data a data.frame containing item parameters.

• itemattrib_science_data a data.frame containing item attributes.

• constraints_science_data a data.frame containing constraint specifications.

Examples

itempool_science    <- loadItemPool(itempool_science_data)
itemattrib_science  <- loadItemAttrib(itemattrib_science_data, itempool_science)
constraints_science <- loadConstraints(constraints_science_data,
  itempool_science, itemattrib_science)

(Internal) Bind matrices diagonally

Description

dbind is an internal function for binding matrices diagonally. This is used for constructing constraint matrix-data in Split.

Usage

dbind(...)

Arguments

Value

dbind returns a matrix.

Detect best solver

Description

Detect best solver

Usage

detectBestSolver()

Value

the package name of the best available solver on the system.

Examples

solver <- detectBestSolver()
cfg <- createStaticTestConfig(MIP = list(solver = solver))
cfg <- createShadowTestConfig(MIP = list(solver = solver))

(Internal) Determine the current theta segment

Description

determineCurrentThetaSegment is an internal function for determining the current theta segment.

Usage

determineCurrentThetaSegment(
  current_theta,
  position,
  exposure_control,
  simulation_constants
)

Arguments

Value

determineCurrentThetaSegment returns a segment index.

(Internal) Perform exposure control

Description

doExposureControl is an internal function for performing exposure control. This is a wrapper function for calling other low-level functions for respective exposure control methods.

Usage

doExposureControl(
  exposure_record,
  segment_record,
  o,
  j,
  current_theta,
  eligibility_flag,
  simulation_constants
)

Arguments

Value

doExposureControl returns an updated list for exposure control records.

(C++) Calculate expected scores

Description

e_*() and array_e_*() are C++ functions for calculating expected scores.

Usage

e_1pl(x, b)

e_2pl(x, a, b)

e_m_2pl(x, a, d)

e_3pl(x, a, b, c)

e_m_3pl(x, a, d, c)

e_pc(x, b)

e_gpc(x, a, b)

e_m_gpc(x, a, d)

e_gr(x, a, b)

e_m_gr(x, a, d)

array_e_1pl(x, b)

array_e_2pl(x, a, b)

array_e_3pl(x, a, b, c)

array_e_pc(x, b)

array_e_gpc(x, a, b)

array_e_gr(x, a, b)

Arguments

Details

e_*() functions accept a single theta value, and array_p_*() functions accept multiple theta values.

Supports unidimensional and multidimensional models.

• e_1pl(), array_e_1pl(): 1PL models

• e_2pl(), array_e_2pl(): 2PL models

• e_3pl(), array_e_3pl(): 3PL models

• e_pc(), array_e_pc(): PC (partial credit) models

• e_gpc(), array_e_gpc(): GPC (generalized partial credit) models

• e_gr(), array_e_gr(): GR (graded response) models

• e_m_2pl(), array_e_m_2pl(): multidimensional 2PL models

• e_m_3pl(), array_e_m_3pl(): multidimensional 3PL models

• e_m_gpc(), array_e_m_gpc(): multidimensional GPC models

• e_m_gr(), array_e_m_gr(): multidimensional GR models

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

x <- 0.5

e_1pl(x, 1)
e_2pl(x, 1, 2)
e_3pl(x, 1, 2, 0.25)
e_pc(x, c(0, 1))
e_gpc(x, 2, c(0, 1))
e_gr(x, 2, c(0, 2))

x <- matrix(seq(-3, 3, 1)) # three theta values, unidimensional

array_e_1pl(x, 1)
array_e_2pl(x, 1, 2)
array_e_3pl(x, 1, 2, 0.25)
array_e_pc(x, c(0, 1))
array_e_gpc(x, 2, c(0, 1))
array_e_gr(x, 2, c(0, 2))

Compute expected a posteriori estimates of theta

Description

eap is a function for computing expected a posteriori estimates of theta.

Usage

eap(
  object,
  select = NULL,
  resp,
  theta_grid = seq(-4, 4, 0.1),
  prior = rep(1/81, 81)
)

## S4 method for signature 'item_pool'
eap(
  object,
  select = NULL,
  resp,
  theta_grid = seq(-4, 4, 0.1),
  prior = rep(1/81, 81)
)

EAP(object, select = NULL, prior, reset_prior = FALSE)

## S4 method for signature 'test'
EAP(object, select = NULL, prior, reset_prior = FALSE)

## S4 method for signature 'test_cluster'
EAP(object, select = NULL, prior, reset_prior = FALSE)

Arguments

Value

eap returns a list containing estimated values.

• th theta value.

• se standard error.

Examples

eap(itempool_fatigue, resp = resp_fatigue_data[10, ])
eap(itempool_fatigue, select = 1:20, resp = resp_fatigue_data[10, 1:20])

(Internal) Estimate final theta

Description

estimateFinalTheta is an internal function for estimating final theta.

Usage

estimateFinalTheta(
  o,
  j,
  position,
  augmented_item_pool,
  model_code,
  augmented_item_index,
  augmented_item_resp,
  include_items_for_estimation,
  item_parameter_sample,
  config,
  simulation_constants,
  bayesian_constants
)

Arguments

Value

estimateFinalTheta returns an updated output_Shadow object.

(Internal) Estimate interim theta

Description

estimateInterimTheta is an internal function for estimating interim theta.

Usage

estimateInterimTheta(
  o,
  j,
  position,
  augmented_current_theta,
  augmented_item_pool,
  model_code,
  augmented_item_index,
  augmented_item_resp,
  include_items_for_estimation,
  item_parameter_sample,
  config,
  simulation_constants,
  bayesian_constants
)

Arguments

Value

estimateInterimTheta returns an updated output_Shadow object.

(C++) Classify theta values into segments using cutpoints

Description

find_segment() is a function for classifying theta values into segments based on supplied cutpoints.

Usage

find_segment(x, segment)

Arguments

Examples

cuts <- c(-Inf, -2, 0, 2, Inf)

find_segment(-3, cuts)
find_segment(-1, cuts)
find_segment(1, cuts)
find_segment(3, cuts)
find_segment(seq(-3, 3, 2), cuts)

(Internal) Update eligibility flags to mark administered items as eligible

Description

flagAdministeredAsEligible is an internal function for updating eligibility flags. Specifically, the function marks items/sets that are already administered to the current examinee as eligible. This is necessary to ensure already administered items/sets are included in the shadowtest.

Usage

flagAdministeredAsEligible(
  eligibility_flag_in_current_theta_segment,
  x,
  position,
  simulation_constants
)

Arguments

Value

flagAdministeredAsEligible returns an updated eligibility flag list.

(Internal) Obtain item/set level eligibility flags

Description

flagIneligible is an internal function for obtaining item/set-level eligibility flags based on segment-wise exposure rates.

Usage

flagIneligible(
  exposure_record,
  simulation_constants,
  item_index_by_stimulus,
  seed,
  j,
  usage_flag = NULL
)

Arguments

Value

flagIneligible returns a named list containing the following:

i

a (n_segment, ni) matrix of 1 and 0 values.

s

a (n_segment, ns) matrix of 1 and 0 values. Only returned when simulation_constants$group_by_stimulus is TRUE.

In each matrix, 1 indicates the item/set is eligible to be selected in a shadowtest, and 0 indicates the item/set is not eligible to be selected in a shadowtest. The higher the observed exposure rate, the more likely the item/set will be flagged as 0. The rows represent theta segments, and the flags in the row corresponding to the examinee's current interim theta estimate is used for the shadowtest assembly.

(Internal) Convert prior parameters to distribution densities

Description

generateDensityFromPriorPar is an internal function for converting prior parameters to distribution densities.

Usage

generateDensityFromPriorPar(config_theta, theta_q)

Arguments

Value

parsePriorParameters returns a named list containing:

prior_dist

the type of distribution. One of NORMAL, UNIFORM, RAW.

prior_par

an examinee-wise list containing prior parameters.

(Internal) Generate item parameter samples for Bayesian purposes

Description

generateItemParameterSample is a function for generating item parameter samples. Used for the FB (full-Bayesian) estimation method.

Usage

generateItemParameterSample(config, item_pool, bayesian_constants)

Arguments

Value

If either the interim or the final theta estimation method is FB, generateItemParameterSample returns a length-ni list of item parameter matrices, with each matrix having n_sample rows. Otherwise, the function returns NULL.

(Internal) Generate random theta samples from prior distribution

Description

generateSampleFromPriorPar is an internal function for generating random theta samples from prior distribution.

Usage

generateSampleFromPriorPar(config_theta, j, bayesian_constants)

Arguments

Value

generateSampleFromPriorPar returns n_sample theta samples.

(Internal) Parse Bayesian-related constants

Description

getBayesianConstants is an internal function for parsing Bayesian-related constants

Usage

getBayesianConstants(config, simulation_constants)

Arguments

Value

getBayesianConstants returns a named list containing:

final_theta_prior_densities

prior densities for final theta estimation for all examinees.

If interim or final theta estimation method is EB or FB, the following are included in the list:

n_sample

the length of MCMC chain for theta estimation.

burn_in

the length of MCMC chain to trim from the start of the chain.

thin

the thinning interval to apply to the chain.

jump_factor

the scaling factor.

(Internal) Parse constants for adaptive test assembly simulation

Description

getConstants is an internal function for parsing constants for adaptive test assembly simulation.

Usage

getConstants(constraints, config, arg_data, true_theta, max_info)

Arguments

Value

getConstants returns a named list containing constants.

(Internal) Make decision variables for selecting an item

Description

getDecisionVariablesOfItemForMultipool is an internal function for making decision variables for selecting a single item, for the purpose of multiple-pool assembly.

Usage

getDecisionVariablesOfItemForMultipool(item_idx, nv_per_bin, n_bins)

Arguments

Value

getDecisionVariablesOfItemForMultipool returns a vector of indices.

(Internal) Make decision variables for selecting a pool

Description

getDecisionVariablesOfPoolForMultipool is an internal function for making decision variables for selecting a single pool, for the purpose of multiple-pool assembly.

Usage

getDecisionVariablesOfPoolForMultipool(pool_idx, ni_per_bin, nv_per_bin)

Arguments

Value

getDecisionVariablesOfPoolForMultipool returns a vector of indices.

(Internal) Parse eligibility flags for a specific theta segment

Description

getEligibilityFlagInSegment is an internal function for obtaining item/set-level eligibility flags for a specific theta segment.

Usage

getEligibilityFlagInSegment(eligiblity_flag, segment, simulation_constants)

Arguments

Value

getEligibilityFlagInSegment returns a named list containing the following:

i

a length-ni) vector of 1 and 0 values.

s

a length-ns) vector of 1 and 0 values. Only returned when simulation_constants$group_by_stimulus is TRUE.

In each vector, 1 indicates the item/set is eligible to be selected in a shadowtest, and 0 indicates the item/set is not eligible to be selected in a shadowtest. The higher the observed exposure rate, the more likely the item/set will be flagged as 0.

(Internal) Convert item IDs to item indices for exclusion

Description

getIndexOfExcludedEntry is an internal function for converting item IDs to item indices for exclusion.

Usage

getIndexOfExcludedEntry(exclude, constraints)

Arguments

Details

Notation:

• nj the number of examinees

Value

getIndexOfExcludedEntry returns a length-nj list in the same structure, with its contents converted to item indices.

(Internal) Precalculate item information for fixed-theta item selection methods

Description

getInfoFixedTheta is an internal function for calculating item information for fixed-theta item selection methods. This is done once at the start of the simulation and cached for speed gain.

Usage

getInfoFixedTheta(item_selection, simulation_constants, item_pool, model)

Arguments

Value

getInfoFixedTheta returns a named list containing item information values at designated thetas for each simulee.

(Internal) Apply information penalty on items to be excluded

Description

(Internal) Apply information penalty on items to be excluded

Usage

getInfoOfExcludedEntry(info, exclude_index, simulation_constants)

Arguments

Value

getInfoOfExcludedEntry returns an updated one-row matrix containing information values.

(Internal) Parse item/stimulus lower/upper bounds from constraints data

Description

getLBUBInConstraintData is an internal function for parsing maximum item/stimulus lower/upper bounds from constraints data.

Usage

getLBUBInConstraintData(
  constants,
  constraints,
  item_constraints,
  stim_constraints
)

Arguments

Value

getLBUBInConstraintData returns an updated list of constants.

Retrieve constraints-related scores from solution

Description

getScoreAttributes is a helper function for retrieving constraints-related scores from a solution.

Usage

getScoreAttributes(constraints, item_idx, item_resp, item_ncat)

Arguments

Examples

item_idx <-
  c( 29,  33,  26,  36,  34,
    295, 289, 296, 291, 126,
    133, 124, 134, 129,  38,
     47,  39,  41,  46,  45,
    167, 166, 170, 168, 113,
    116, 119, 117, 118, 114)

item_resp <-
  c( 1, 0, 1, 1, 0,
     0, 1, 1, 0, 0,
     1, 0, 1, 0, 1,
     1, 1, 1, 0, 1,
     0, 1, 1, 1, 1,
     1, 0, 1, 0, 1)

item_ncat <-
  c( 2, 2, 2, 2, 2,
     2, 2, 2, 2, 2,
     2, 2, 2, 2, 2,
     2, 2, 2, 2, 2,
     2, 2, 2, 2, 2,
     2, 2, 2, 2, 2)

getScoreAttributes(constraints_reading, item_idx, item_resp, item_ncat)

(Internal) Calculate theta segment of a given examinee

Description

getSegmentOf is an internal function for calculating which theta segment an examinee belongs to.

Usage

getSegmentOf(x, simulation_constants)

Arguments

Value

getSegmentOf returns a list containing:

• final_theta_est the theta segment based on final theta estimate.

• true_theta the theta segment based on true theta.

• visited segments the examinee visited.

(Internal) Convert a theta distribution to segment-wise classification probabilities

Description

getSegmentProb is an internal function for converting a theta distribution to segment-wise classification probabilities This is used for BIGM-BAYESIAN exposure control.

Usage

getSegmentProb(posterior_sample, simulation_constants)

Arguments

Value

getSegmentProb returns a vector of segment-wise classification probabilities.

(Internal) Make a vector for segment-dimensioned matrix update

Description

getSegmentsToApply is an internal function for creating a vector for the purpose of updating various matrices that use theta segments as a dimension.

Usage

getSegmentsToApply(n_segment, segments)

Arguments

Value

getSegmentsToApply returns a vector.

Print solution items

Description

Print solution items

Usage

getSolution(object, examinee = NA, position = NA, index_only = TRUE)

## S4 method for signature 'list'
getSolution(object, examinee = NA, position = NA, index_only = TRUE)

## S4 method for signature 'output_Static'
getSolution(object, examinee = NA, position = NA, index_only = TRUE)

Arguments

Value

Item attributes of solution items.

Retrieve constraints-related attributes from solution

Description

getSolutionAttributes is a helper function for retrieving constraints-related attributes from a solution.

Usage

getSolutionAttributes(constraints, item_idx, all_values = FALSE)

Arguments

Value

• If all_values == FALSE, getSolutionAttributes returns a data.frame containing constraints data and their associated attributes.

• If all_values == TRUE, getSolutionAttributes returns a list containing attributes associated to each constraint.

Examples

item_idx <-
  c( 29,  33,  26,  36,  34,
    295, 289, 296, 291, 126,
    133, 124, 134, 129,  38,
     47,  39,  41,  46,  45,
    167, 166, 170, 168, 113,
    116, 119, 117, 118, 114)

getSolutionAttributes(constraints_reading, item_idx, FALSE)
getSolutionAttributes(constraints_reading, item_idx, TRUE)

(Internal) Obtain constraint matrix-data of administered items/sets

Description

getXdataOfAdministered is an internal function for obtaining constraint matrix-data of administered items/sets. Specifically, it returns a constraint matrix-data that tells the solver to include items/sets that are already administered to the current examinee. This is necessary for shadow-test assembly for adaptive test assembly.

Usage

getXdataOfAdministered(
  simulation_constants,
  position,
  x,
  groupings_record,
  constraints
)

Arguments

Value

getXdataOfAdministered returns a constraint matrix-data. A constraint matrix-data is a named list containing the following:

xmat

a (nc, ni) matrix for the left-hand side in a MIP problem.

xdir

a length-nc) vector of relational operators, for comparing the two sides in a MIP problem.

xrhs

a length-nc) vector, for the right-hand side in a MIP problem.

(Internal) Translate item exclusion instructions into a constraint matrix-data

Description

(Internal) Translate item exclusion instructions into a constraint matrix-data

Usage

getXdataOfExcludedEntry(simulation_constants, exclude_index)

Arguments

Value

getXdataOfExcludedEntry returns a named list containing a constraint matrix-data.

• xmat The left-hand side multipliers on decision variables.

• xdir The relation operator.

• xrhs The right-hand side value.

Examples

simulation_constants <- list(
  nv = 5,
  ni = 5,
  group_by_stimulus = FALSE
)
exclude_index <- list(
  i = c(1, 2)
)
## Not run: 
getXdataOfExcludedEntry(simulation_constants, exclude_index)

## End(Not run)

(C++) Calculate second derivative of log-likelihood

Description

h_*() and array_h_*() are C++ functions for calculating the second derivative of the log-likelihood function.

Usage

h_1pl(x, b, u)

h_2pl(x, a, b, u)

h_m_2pl(x, a, d, u)

h_3pl(x, a, b, c, u)

h_m_3pl(x, a, d, c, u)

h_pc(x, b, u)

h_gpc(x, a, b, u)

h_m_gpc(x, a, d, u)

h_gr(x, a, b, u)

h_m_gr(x, a, d, u)

array_h_1pl(x, b, u)

array_h_2pl(x, a, b, u)

array_h_3pl(x, a, b, c, u)

array_h_pc(x, b, u)

array_h_gpc(x, a, b, u)

array_h_gr(x, a, b, u)

Arguments

Details

h_*() functions accept a single theta value, and array_h_*() functions accept multiple theta values.

Supports unidimensional and multidimensional models.

• h_1pl(), array_h_1pl(): 1PL models

• h_2pl(), array_h_2pl(): 2PL models

• h_3pl(), array_h_3pl(): 3PL models

• h_pc(), array_h_pc(): PC (partial credit) models

• h_gpc(), array_h_gpc(): GPC (generalized partial credit) models

• h_gr(), array_h_gr(): GR (graded response) models

• h_m_2pl(), array_h_m_2pl(): multidimensional 2PL models

• h_m_3pl(), array_h_m_3pl(): multidimensional 3PL models

• h_m_gpc(), array_h_m_gpc(): multidimensional GPC models

• h_m_gr(), array_h_m_gr(): multidimensional GR models

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

u <- 1

x <- 0.5
h_1pl(x, 1, u)
h_2pl(x, 1, 2, u)
h_3pl(x, 1, 2, 0.25, u)
h_pc(x, c(0, 1), u)
h_gpc(x, 2, c(0, 1), u)
h_gr(x, 2, c(0, 2), u)

x <- matrix(seq(-3, 3, 1)) # three theta values, unidimensional
array_h_1pl(x, 1, u)
array_h_2pl(x, 1, 2, u)
array_h_3pl(x, 1, 2, 0.25, u)
array_h_pc(x, c(0, 1), u)
array_h_gpc(x, 2, c(0, 1), u)
array_h_gr(x, 2, c(0, 2), u)

(Internal) Increment exposure record variable: alpha

Description

incrementAlpha is an internal function for incrementing an exposure record variable. Specifically, the a_ijk is incremented by one for administered items/sets.

Usage

incrementAlpha(
  exposure_record,
  segments_to_apply,
  segment_prob,
  x,
  simulation_constants
)

Arguments

Value

incrementAlpha returns an updated exposure record.

(Internal) Increment exposure record variable: n

Description

incrementPhi is an internal function for incrementing an exposure record variable. Specifically, the n_k is incremented by one.

Usage

incrementN(
  exposure_record,
  segments_to_apply,
  segment_prob,
  simulation_constants
)

Arguments

Value

incrementN returns an updated exposure record.

(Internal) Increment exposure record variable: phi

Description

incrementPhi is an internal function for incrementing an exposure record variable. Specifically, the f_k is incremented by one if the following conditions are simultaneously met:

• For the final theta segment k, shadowtest assembly was feasible at least one times in any item position while interim theta segment was k.

Usage

incrementPhi(
  exposure_record,
  segments_to_apply,
  segment_prob,
  assembly_was_feasible
)

Arguments

Value

incrementPhi returns an updated exposure record.

(Internal) Increment exposure record variable: rho

Description

incrementRho is an internal function for incrementing an exposure record variable. Specifically, the s_ijk variable is incremented for accounting for infeasible shadowtests.

Usage

incrementRho(
  exposure_record,
  segments_to_apply,
  segment_prob,
  eligibility_flag,
  assembly_was_feasible,
  simulation_constants
)

Arguments

Value

incrementRho returns an updated exposure record.

(C++) Calculate Fisher information

Description

info_*() and array_info_*() are functions for calculating Fisher information.

Usage

info_1pl(x, b)

info_2pl(x, a, b)

info_m_2pl(x, a, d)

dirinfo_m_2pl(x, a, d)

thisdirinfo_m_2pl(x, alpha_vec, a, d)

info_3pl(x, a, b, c)

info_m_3pl(x, a, d, c)

dirinfo_m_3pl(x, a, d, c)

thisdirinfo_m_3pl(x, alpha_vec, a, d, c)

info_pc(x, b)

info_gpc(x, a, b)

info_m_gpc(x, a, d)

dirinfo_m_gpc(x, a, d)

thisdirinfo_m_gpc(x, alpha_vec, a, d)

info_gr(x, a, b)

info_m_gr(x, a, d)

dirinfo_m_gr(x, a, d)

thisdirinfo_m_gr(x, alpha_vec, a, d)

array_info_1pl(x, b)

array_info_2pl(x, a, b)

array_info_m_2pl(x, a, d)

array_dirinfo_m_2pl(x, a, d)

array_thisdirinfo_m_2pl(x, alpha_vec, a, d)

array_info_3pl(x, a, b, c)

array_info_m_3pl(x, a, d, c)

array_dirinfo_m_3pl(x, a, d, c)

array_thisdirinfo_m_3pl(x, alpha_vec, a, d, c)

array_info_pc(x, b)

array_info_gpc(x, a, b)

array_info_m_gpc(x, a, d)

array_dirinfo_m_gpc(x, a, d)

array_thisdirinfo_m_gpc(x, alpha_vec, a, d)

array_info_gr(x, a, b)

array_info_m_gr(x, a, d)

array_dirinfo_m_gr(x, a, d)

array_thisdirinfo_m_gr(x, alpha_vec, a, d)

Arguments

Details

info_*() functions accept a single theta value, and array_info_* functions accept multiple theta values.

Supports unidimensional and multidimensional models.

• info_1pl(), array_info_1pl(): 1PL models

• info_2pl(), array_info_2pl(): 2PL models

• info_3pl(), array_info_3pl(): 3PL models

• info_pc(), array_info_pc(): PC (partial credit) models

• info_gpc(), array_info_gpc(): GPC (generalized partial credit) models

• info_gr(), array_info_gr(): GR (graded response) models

• info_m_2pl(), array_info_m_2pl(): multidimensional 2PL models

• info_m_3pl(), array_info_m_3pl(): multidimensional 3PL models

• info_m_gpc(), array_info_m_gpc(): multidimensional GPC models

• info_m_gr(), array_info_m_gr(): multidimensional GR models

• Directional information for a specific angle

  • thisdirinfo_m_2pl(), array_thisdirinfo_m_2pl(): multidimensional 2PL models

  • thisdirinfo_m_3pl(), array_thisdirinfo_m_3pl(): multidimensional 3PL models

  • thisdirinfo_m_gpc(), array_thisdirinfo_m_gpc(): multidimensional GPC models

  • thisdirinfo_m_gr(), array_thisdirinfo_m_gr(): multidimensional GR models

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

x <- 0.5

info_1pl(x, 1)
info_2pl(x, 1, 2)
info_3pl(x, 1, 2, 0.25)
info_pc(x, c(0, 1))
info_gpc(x, 2, c(0, 1))
info_gr(x, 2, c(0, 2))

x <- matrix(seq(0.1, 0.5, 0.1)) # three theta values, unidimensional

array_info_1pl(x, 1)
array_info_2pl(x, 1, 2)
array_info_3pl(x, 1, 2, 0.25)
array_info_pc(x, c(0, 1))
array_info_gpc(x, 2, c(0, 1))
array_info_gr(x, 2, c(0, 2))

(Internal) Initialize groupings record

Description

initializeCompletedGroupingsRecord is an internal function for creating a new groupings record. Used for keeping track of completed groups such as item sets.

Usage

initializeCompletedGroupingsRecord()

Value

initializeCompletedGroupingsRecord returns a groupings record.

(Internal) Initialize diagnostic exposure record

Description

initializeDiagnosticExposureRecord is an internal function for creating a new diagnostic exposure record.

Usage

initializeDiagnosticExposureRecord(simulation_constants)

Arguments

Value

initializeDiagnosticExposureRecord returns a list containing diagnostic exposure record.

(Internal) Initialize exposure record

Description

initializeExposureRecord is an internal function for creating a new exposure record.

Usage

initializeExposureRecord(exposure_control, simulation_constants)

Arguments

Value

initializeExposureRecord returns a list containing exposure record.

(Internal) Initialize segment record

Description

initializeSegmentRecord is an internal function for creating a new segment record.

Usage

initializeSegmentRecord(simulation_constants)

Arguments

Value

initializeSegmentRecord returns a list containing segment record.

• freq_true is a length-n_segment vector containing the number of times examinees belonged in each theta segment, based on true thetas.

• freq_est is a length-n_segment vector containing the number of times examinees belonged in each theta segment, based on final theta estimates.

• count_true

• count_est

(Internal) Initialize item usage matrix

Description

initializeUsageMatrix is an internal function for creating a new item usage matrix. An item usage matrix is a (nj, nv) matrix with TRUE or FALSE values. The rows represent examinees, and the columns represent decision variables.

Usage

initializeUsageMatrix(simulation_constants)

Arguments

Value

initializeUsageMatrix returns a new item usage matrix.

Generate item parameter samples for Bayesian purposes

Description

iparPosteriorSample is a function for generating item parameter samples. Used for the FB (full-Bayesian) estimation method.

Usage

iparPosteriorSample(pool, n_sample = 500)

Arguments

Value

iparPosteriorSample returns a length-ni list of item parameter matrices, with each matrix having n_sample rows.

Examples

ipar <- iparPosteriorSample(itempool_bayes, 5)
ipar <- iparPosteriorSample(itempool_science, 5) # no variation

(Internal) Check if customized first segments are available

Description

isCustomFirstSegmentAvailable is an internal function for checking if customized first segments are available.

Usage

isCustomFirstSegmentAvailable(available, n_values, position)

Arguments

Value

isCustomFirstSegmentAvailable returns TRUE or FALSE.

(Internal) Check whether solution is optimal

Description

isSolutionOptimal is an internal function for checking whether a solution is optimal.

Usage

isSolutionOptimal(status, solver)

Arguments

Value

isSolutionOptimal returns TRUE or FALSE.

Item classes

Description

• item_1PL class represents a 1PL item.

• item_2PL class represents a 2PL item.

• item_3PL class represents a 3PL item.

• item_PC class represents a partial credit item.

• item_GPC class represents a generalized partial credit item.

• item_GR class represents a graded response item.

Slots

slope

a slope parameter value

difficulty

a difficulty parameter value

guessing

a guessing parameter value

threshold

a vector of threshold parameter values

category

a vector of category boundary values

ncat

the number of response categories

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

item_1 <- new("item_1PL", difficulty = 0.5)
item_2 <- new("item_2PL", slope = 1.0, difficulty = 0.5)
item_3 <- new("item_3PL", slope = 1.0, difficulty = 0.5, guessing = 0.2)
item_4 <- new("item_PC", threshold = c(-0.5, 0.5), ncat = 3)
item_5 <- new("item_GPC", slope = 1.0, threshold = c(-0.5, 0.0, 0.5), ncat = 4)
item_6 <- new("item_GR", slope = 1.0, category = c(-2.0, -1.0, 0, 1.0, 2.0), ncat = 6)

Load item attributes

Description

loadItemAttrib is a data loading function for creating an item_attrib object. loadItemAttrib can read item attributes from a data.frame or a .csv file.

Usage

loadItemAttrib(object, pool)

Arguments

Value

loadItemAttrib returns an item_attrib object.

• data a data.frame containing item attributes.

See Also

dataset_science, dataset_reading, dataset_fatigue, dataset_bayes for examples.

Examples

## Read from data.frame:
itempool_science   <- loadItemPool(itempool_science_data)
itemattrib_science <- loadItemAttrib(itemattrib_science_data, itempool_science)

## Read from file: write to tempdir() for illustration and clean afterwards
f <- file.path(tempdir(), "itemattrib_science.csv")
write.csv(itemattrib_science_data, f, row.names = FALSE)
itemattrib_science <- loadItemAttrib(f, itempool_science)
file.remove(f)

Basic functions for item attribute objects

Description

Basic functions for item attribute objects

Usage

## S4 method for signature 'item_attrib,numeric'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'item_attrib'
dim(x)

## S4 method for signature 'item_attrib'
colnames(x)

## S4 method for signature 'item_attrib'
rownames(x)

## S4 method for signature 'item_attrib'
names(x)

## S4 method for signature 'item_attrib'
as.data.frame(x, row.names = NULL, optional = FALSE, ...)

Arguments

Examples

x <- itemattrib_science
x[1:10]
dim(x)
ncol(x)
nrow(x)
colnames(x)
rownames(x)
names(x)
as.data.frame(x)

Class 'item_pool': an item pool

Description

item_pool is an S4 class for representing an item pool.

Details

See item_pool-operators for object manipulation functions.

Slots

ni

the number of items in the pool.

max_cat

the maximum number of response categories across the pool.

index

the numeric index of each item.

id

the ID string of each item.

model

the item class name of each item. See item-classes.

NCAT

the number of response categories of each item.

parms

a list containing item class objects. See item-classes.

ipar

a matrix containing item parameters.

se

a matrix containing item parameter standard errors.

raw

the raw input data.frame used in loadItemPool to create this object.

raw_se

the raw input data.frame used in loadItemPool to create this object.

unique

whether item IDs must be unique for this object to be a valid object.

Basic operators for item pool objects

Description

Create a subset of an item_pool object:

• pool[i]

• subsetItemPool(pool, i)

Combine two item_pool objects:

• c(pool1, pool2)

• combineItemPool(pool1, pool2)

• pool1 + pool2

pool1 - pool2 excludes items in pool2 from pool1.

pool1 == pool2 tests whether two item_pool objects are identical.

Usage

subsetItemPool(x, i = NULL)

combineItemPool(x1, x2, unique = TRUE, verbose = TRUE)

## S4 method for signature 'item_pool,numeric'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'item_pool'
c(x, ...)

## S3 method for class 'item_pool'
x1 + x2

## S3 method for class 'item_pool'
x1 - x2

## S3 method for class 'item_pool'
x1 == x2

Arguments

Examples

p1 <- itempool_science[1:100]
p2 <- c(itempool_science, itempool_reading)
p3 <- p2 - p1

p1 <- itempool_science[1:500]
p2 <- itempool_science - p1
p3 <- itempool_science[501:1000]
identical(p2, p3)  ## TRUE

p <- p1 + p3
p == itempool_science ## TRUE

Class 'item_pool_cluster': an item pool

Description

item_pool_cluster is an S4 class for representing a group of item pools.

Slots

np

the number of item pools.

pools

a list of item_pool objects.

names

a vector containing item pool names.

(C++) Calculate first derivative of log-likelihood

Description

j_*() and array_j_*() are C++ functions for calculating the first derivative of the log-likelihood function.

Usage

j_1pl(x, b, u)

j_2pl(x, a, b, u)

j_m_2pl(x, a, d, u)

j_3pl(x, a, b, c, u)

j_m_3pl(x, a, d, c, u)

j_pc(x, b, u)

j_gpc(x, a, b, u)

j_m_gpc(x, a, d, u)

j_gr(x, a, b, u)

j_m_gr(x, a, d, u)

array_j_1pl(x, b, u)

array_j_2pl(x, a, b, u)

array_j_3pl(x, a, b, c, u)

array_j_pc(x, b, u)

array_j_gpc(x, a, b, u)

array_j_gr(x, a, b, u)

Arguments

Details

j_*() functions accept a single theta value, and array_j_*() functions accept multiple theta values.

Supports unidimensional and multidimensional models.

• j_1pl(), array_j_1pl(): 1PL models

• j_2pl(), array_j_2pl(): 2PL models

• j_3pl(), array_j_3pl(): 3PL models

• j_pc(), array_j_pc(): PC (partial credit) models

• j_gpc(), array_j_gpc(): GPC (generalized partial credit) models

• j_gr(), array_j_gr(): GR (graded response) models

• j_m_2pl(), array_j_m_2pl(): multidimensional 2PL models

• j_m_3pl(), array_j_m_3pl(): multidimensional 3PL models

• j_m_gpc(), array_j_m_gpc(): multidimensional GPC models

• j_m_gr(), array_j_m_gr(): multidimensional GR models

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

u <- 1

x <- 0.5
j_1pl(x, 1, u)
j_2pl(x, 1, 2, u)
j_3pl(x, 1, 2, 0.25, u)
j_pc(x, c(0, 1), u)
j_gpc(x, 2, c(0, 1), u)
j_gr(x, 2, c(0, 2), u)

x <- matrix(seq(-3, 3, 1)) # three theta values, unidimensional
array_j_1pl(x, 1, u)
array_j_2pl(x, 1, 2, u)
array_j_3pl(x, 1, 2, 0.25, u)
array_j_pc(x, c(0, 1), u)
array_j_gpc(x, 2, c(0, 1), u)
array_j_gr(x, 2, c(0, 2), u)

Convert mean and standard deviation into log-normal distribution parameters

Description

lnHyperPars is a function for calculating parameters for a log-normal distribution, such that the distribution yields desired mean and standard deviation. Used for sampling the a-parameter.

Usage

lnHyperPars(mean, sd)

Arguments

Value

lnHyperPars returns two values. These can be directly supplied to rlnorm.

Examples

pars <- lnHyperPars(2, 4)
x <- rlnorm(1000000, pars[1], pars[2])
mean(x) # close to 2
sd(x)   # close to 4

Load constraints

Description

loadConstraints is a data loading function for creating a constraints object. loadConstraints can read constraints from a data.frame or a .csv file. The contents must be in the expected format; see the vignette in vignette("constraints") for a documentation.

Usage

loadConstraints(object, pool, item_attrib, st_attrib = NULL)

Arguments

Value

loadConstraints returns a constraints object. This object is used in Static and Shadow.

See Also

dataset_science, dataset_reading, dataset_fatigue, dataset_bayes for examples.

Examples

## Read from data.frame:
itempool_science    <- loadItemPool(itempool_science_data)
itemattrib_science  <- loadItemAttrib(itemattrib_science_data, itempool_science)
constraints_science <- loadConstraints(constraints_science_data,
  itempool_science, itemattrib_science)

## Read from file: write to tempdir() for illustration and clean afterwards
f <- file.path(tempdir(), "constraints_science.csv")
write.csv(constraints_science_data, f, row.names = FALSE)
constraints_science <- loadConstraints(f,
  itempool_science, itemattrib_science)
file.remove(f)

Load item pool

Description

loadItemPool is a data loading function for creating an item_pool object. loadItemPool can read item parameters and standard errors from a data.frame or a .csv file.

Usage

loadItemPool(ipar, ipar_se = NULL, unique = FALSE)

Arguments

Value

loadItemPool returns an item_pool object.

• ni the number of items in the pool.

• max_cat the maximum number of response categories across all items in the pool.

• index the numeric item index of each item.

• id the item ID string of each item.

• model the object class names of each item representing an item model type. Can be item_1PL, item_2PL, item_3PL, item_PC, item_GPC, or item_GR.

• NCAT the number of response categories of each item.

• parms a list containing the item object of each item.

• ipar a matrix containing all item parameters.

• se a matrix containing all item parameter standard errors. The values will be 0 if the argument ipar_se was not supplied.

• raw the original input ipar argument used to create this object.

• raw_se the original input ipar_se argument used to create this object. If the argument was not supplied, this will be in the same structure with the ipar argument but the item parameter values will be filled with 0s.

• unique the original input unique argument used to create this object.

See Also

dataset_science, dataset_reading, dataset_fatigue, dataset_bayes for examples.

Examples

## Read from data.frame:
itempool_science <- loadItemPool(itempool_science_data)

## Read from file: write to tempdir() for illustration and clean afterwards
f <- file.path(tempdir(), "itempool_science.csv")
write.csv(itempool_science_data, f, row.names = FALSE)
itempool_science <- loadItemPool(f)
file.remove(f)

Convert mean and standard deviation into logit-normal distribution parameters

Description

logitHyperPars is a function for calculating parameters for a logit-normal distribution, such that the distribution yields desired mean and standard deviation. Used for sampling the c-parameter.

Usage

logitHyperPars(mean, sd)

Arguments

Value

logitHyperPars returns two values. These can be directly supplied to rlogitnorm.

Examples

pars <- logitHyperPars(0.2, 0.1)
x <- logitnorm::rlogitnorm(1000000, pars[1], pars[2])
mean(x) # close to 0.2
sd(x)   # close to 0.1

make constraints objects from Split() solution indices

Description

makeConstraintsByEachPartition is a helper function for making constraints objects from Split solution indices.

Usage

makeConstraintsByEachPartition(constraints, solution_per_bin)

Arguments

Value

makeConstraintsByEachPartition returns a list of constraints objects.

(Internal) Collect diagnostic exposure record

Description

makeDiagnosticExposureRecord is an internal function for collecting diagnostic exposure record.

Usage

makeDiagnosticExposureRecord(
  true_theta,
  segment_record,
  diagnostic_exposure_record,
  config,
  simulation_constants
)

Arguments

Value

makeDiagnosticExposureRecord returns an updated exposure record.

Create an item pool cluster object

Description

Create a item_pool_cluster object.

item_pool_cluster1 == item_pool_cluster2 tests equality of two item_pool_cluster objects.

Usage

makeItemPoolCluster(x, ..., names = NULL)

## S4 method for signature 'item_pool'
makeItemPoolCluster(x, ..., names = NULL)

## S3 method for class 'item_pool_cluster'
item_pool_cluster1 == item_pool_cluster2

Arguments

Examples

cluster <- makeItemPoolCluster(itempool_science, itempool_reading)
cluster1 <- makeItemPoolCluster(itempool_science, itempool_reading)
cluster2 <- makeItemPoolCluster(cluster1@pools[[1]], cluster1@pools[[2]])
cluster1 == cluster2  ## TRUE

(Internal) Make set-based strucutre constraints

Description

makeSetStructureConstraints is an internal function for making the left-hand side matrix of set-based structure constraints.

Usage

makeSetStructureConstraints(constraints)

Arguments

Value

makeSetStructureConstraints returns a matrix.

Create a simulation data cache object

Description

makeSimulationDataCache is a function for creating a simulation_data_cache object. This is used in Shadow to make all necessary data (e.g., item information, response data) prior to the main simulation.

Usage

makeSimulationDataCache(
  item_pool,
  info_type = "FISHER",
  theta_grid = seq(-4, 4, 0.1),
  seed = NULL,
  true_theta = NULL,
  response_data = NULL
)

## S4 method for signature 'item_pool'
makeSimulationDataCache(
  item_pool,
  info_type = "FISHER",
  theta_grid = seq(-4, 4, 0.1),
  seed = NULL,
  true_theta = NULL,
  response_data = NULL
)

Arguments

Create a test object

Description

makeTest is a function for creating a test object. This is used to make all necessary data (e.g., item information, response data) prior to the main simulation. This function is only kept for backwards compatibility. The functionality of this function is superseded by makeSimulationDataCache.

Usage

makeTest(
  object,
  theta = seq(-4, 4, 0.1),
  info_type = "FISHER",
  true_theta = NULL
)

## S4 method for signature 'item_pool'
makeTest(
  object,
  theta = seq(-4, 4, 0.1),
  info_type = "FISHER",
  true_theta = NULL
)

Arguments

Examples

test <- makeTest(itempool_science, seq(-3, 3, 1))

Create a test cluster object

Description

makeTestCluster is a function for creating a test_cluster object. This is used to make all necessary data (e.g., item information, response data) prior to the main simulation. This function is only kept for backwards compatibility.

Usage

makeTestCluster(object, theta, true_theta)

## S4 method for signature 'item_pool_cluster,numeric,numeric'
makeTestCluster(object, theta, true_theta)

## S4 method for signature 'item_pool_cluster,numeric,list'
makeTestCluster(object, theta, true_theta)

Arguments

Compute maximum likelihood estimates of theta

Description

mle is a function for computing maximum likelihood estimates of theta.

Usage

mle(
  object,
  select = NULL,
  resp,
  start_theta = NULL,
  max_iter = 100,
  crit = 0.001,
  truncate = FALSE,
  theta_range = c(-4, 4),
  max_change = 1,
  use_step_size = FALSE,
  step_size = 0.5,
  do_Fisher = TRUE
)

## S4 method for signature 'item_pool'
mle(
  object,
  select = NULL,
  resp,
  start_theta = NULL,
  max_iter = 50,
  crit = 0.005,
  truncate = FALSE,
  theta_range = c(-4, 4),
  max_change = 1,
  use_step_size = FALSE,
  step_size = 0.5,
  do_Fisher = TRUE
)

MLE(
  object,
  select = NULL,
  start_theta = NULL,
  max_iter = 100,
  crit = 0.001,
  theta_range = c(-4, 4),
  truncate = FALSE,
  max_change = 1,
  do_Fisher = TRUE
)

## S4 method for signature 'test'
MLE(
  object,
  select = NULL,
  start_theta = NULL,
  max_iter = 100,
  crit = 0.001,
  theta_range = c(-4, 4),
  truncate = FALSE,
  max_change = 1,
  do_Fisher = TRUE
)

## S4 method for signature 'test_cluster'
MLE(object, select = NULL, start_theta = NULL, max_iter = 100, crit = 0.001)

Arguments

Value

mle returns a list containing estimated values.

• th theta value.

• se standard error.

• conv TRUE if estimation converged.

• trunc TRUE if truncation was applied on th.

Examples

mle(itempool_fatigue, resp = resp_fatigue_data[10, ])
mle(itempool_fatigue, select = 1:20, resp = resp_fatigue_data[10, 1:20])

Compute maximum likelihood estimates of theta using fence items

Description

mlef is a function for computing maximum likelihood estimates of theta using fence items.

Usage

mlef(
  object,
  select = NULL,
  resp,
  fence_slope = 5,
  fence_difficulty = c(-5, 5),
  start_theta = NULL,
  max_iter = 100,
  crit = 0.001,
  truncate = FALSE,
  theta_range = c(-4, 4),
  max_change = 1,
  use_step_size = FALSE,
  step_size = 0.5,
  do_Fisher = TRUE
)

## S4 method for signature 'item_pool'
mlef(
  object,
  select = NULL,
  resp,
  fence_slope = 5,
  fence_difficulty = c(-5, 5),
  start_theta = NULL,
  max_iter = 50,
  crit = 0.005,
  truncate = FALSE,
  theta_range = c(-4, 4),
  max_change = 1,
  use_step_size = FALSE,
  step_size = 0.5,
  do_Fisher = TRUE
)

Arguments

Value

mlef returns a list containing estimated values.

• th theta value.

• se standard error.

• conv TRUE if estimation converged.

• trunc TRUE if truncation was applied on th.

References

Han, K. T. (2016). Maximum likelihood score estimation method with fences for short-length tests and computerized adaptive tests. Applied Psychological Measurement, 40(4), 289-301.

Examples

mlef(itempool_fatigue, resp = resp_fatigue_data[10, ])
mlef(itempool_fatigue, select = 1:20, resp = resp_fatigue_data[10, 1:20])

Class 'output_Shadow': adaptive assembly solution for one simulee

Description

output_Shadow is an S4 class for representing the adaptive assembly solution for one simulee.

Slots

simulee_id

the numeric ID of the simulee.

true_theta

the true theta of the simulee, if was specified.

true_theta_segment

the segment number of the true theta.

final_theta_est

final theta estimate.

final_se_est

the standard error of final_theta_est.

administered_item_index

item IDs administered at each position.

administered_item_resp

item responses from the simulee at each position.

administered_item_ncat

the number of categories of each administered item.

administered_stimulus_index

stimulus IDs administered at each position.

shadow_test_refreshed

TRUE indicates the shadowtest was refreshed for the position.

shadow_test_feasible

TRUE indicates the MIP was feasible with all constraints.

solve_time

elapsed time in running the solver at each position.

initial_theta_est

initial theta estimate.

interim_theta_est

interim theta estimates at each position.

interim_se_est

the standard error of the interim estimate at each position.

theta_segment_index

segment numbers of interim theta estimates.

prior

prior distribution, if was specified.

prior_par

prior parameters, if were specified.

posterior

the posterior distribution after completing test.

posterior_sample

posterior samples of interim theta before the estimation of final theta. mean(posterior_sample) == interim_theta_est[test_length] holds.

likelihood

the likelihood distribution after completing test.

shadow_test

the list containing the item IDs within the shadowtest used in each position.

max_cat_pool

the maximum number of response categories the item pool had.

ni_pool

the total number of items the item pool had.

ns_pool

the total number of stimuli the item pool had.

test_length_constraints

the test length constraint used in assembly.

set_based

whether the item pool was set-based.

item_index_by_stimulus

the list of items by each stimulus the item pool had.

Class 'output_Shadow_all': a set of adaptive assembly solutions

Description

output_Shadow_all is an S4 class for representing a set of adaptive assembly solutions.

Details

notations

• ni denotes the number of items in the item_pool object.

• ns denotes the number of stimuli.

• nj denotes the number of participants.

Slots

call

the function call used for obtaining this object.

output

a length-*nj* list of output_Shadow objects, containing the assembly results for each participant.

final_theta_est

a length-*nj* vector containing final theta estimates for each participant.

final_se_est

a length-*nj* vector standard errors of the final theta estimates for each participant.

exposure_rate

a matrix containing item-level exposure rates of all items in the pool. Also contains stimulus-level exposure rates if the assembly was set-based.

usage_matrix

a *nj* by (*ni* + *ns*) matrix representing whether the item/stimulus was administered to each participant. Stimuli representations are appended to the right side of the matrix.

cumulative_usage_matrix

a *nj* by (*ni* + *ns*) matrix representing the number of times the item/stimulus was administered to each participant over multiple administrations.

true_segment_count

a length-*nj* vector containing the how many examinees are now in their segment based on the true theta. This will tend to increase. This can be reproduced with true theta values alone.

est_segment_count

a length-*nj* vector containing the how many examinees are now in their segment based on the estimated theta. This will tend to increase. This can be reproduced with estimated theta values alone.

eligibility_stats

exposure record for diagnostics.

check_eligibility_stats

detailed segment-wise exposure record for diagnostics. available when config_Shadow@exposure_control$diagnostic_stats is TRUE.

no_fading_eligibility_stats

detailed segment-wise exposure record without fading for diagnostics. available when config_Shadow@exposure_control$diagnostic_stats is TRUE.

freq_infeasible

a table representing the number of times the assembly was initially infeasible.

pool

the item_pool used in the assembly.

config

the config_Shadow used in the assembly.

constraints

the constraints used in the assembly.

true_theta

the true_theta argument used in the assembly.

data

the data argument used in the assembly.

prior

the prior argument used in the assembly.

prior_par

the prior_par argument used in the assembly.

adaptivity

a list of adaptivity indices.

simulation_constants

a list containing simulation constants parsed from input.

Class 'output_Split': partitioning solution

Description

output_Split is an S4 class for representing the partitioning solution of an item pool.

Slots

call

the function call used for obtaining this object.

output

a list containing item/set indices of each partition.

feasible

for partitioning into sub-pools, TRUE indicates the complete assignment problem was feasible.

solve_time

elapsed time in running the solver.

set_based

whether the item pool is set-based.

config

the config_Static used in the assembly.

constraints

the constraints used in the assembly.

partition_size_range

the partition size range for splitting into sub-pools.

partition_type

the partition type. Can be a test or a pool.

constraints_by_each_partition

a list of constraints objects that represent each partition.

Class 'output_Static': fixed-form assembly solution

Description

output_Static is an S4 class for representing a fixed-form assembly solution.

Slots

call

the function call used for obtaining this object.

MIP

a list containing the result from MIP solver.

selected

a data.frame containing the selected items and their attributes.

obj_value

the objective value of the solution.

solve_time

the elapsed time in running the solver.

achieved

a data.frame containing attributes of the assembled test, by each constraint.

pool

the item_pool used in the assembly.

config

the config_Static used in the assembly.

constraints

the constraints used in the assembly.

(C++) Calculate item response probability

Description

p_*() and array_p_*() are C++ functions for calculating item response probability.

Usage

p_1pl(x, b)

p_2pl(x, a, b)

p_m_2pl(x, a, d)

p_3pl(x, a, b, c)

p_m_3pl(x, a, d, c)

p_pc(x, b)

p_gpc(x, a, b)

p_m_gpc(x, a, d)

p_gr(x, a, b)

p_m_gr(x, a, d)

array_p_1pl(x, b)

array_p_2pl(x, a, b)

array_p_m_2pl(x, a, d)

array_p_3pl(x, a, b, c)

array_p_m_3pl(x, a, d, c)

array_p_pc(x, b)

array_p_gpc(x, a, b)

array_p_m_gpc(x, a, d)

array_p_gr(x, a, b)

array_p_m_gr(x, a, d)

Arguments

Details

p_*() functions accept a single theta value, and array_p_*() functions accept multiple theta values.

Supports unidimensional and multidimensional models.

• p_1pl(), array_p_1pl(): 1PL models

• p_2pl(), array_p_2pl(): 2PL models

• p_3pl(), array_p_3pl(): 3PL models

• p_pc(), array_p_pc(): PC (partial credit) models

• p_gpc(), array_p_gpc(): GPC (generalized partial credit) models

• p_gr(), array_p_gr(): GR (graded response) models

• p_m_2pl(), array_p_m_2pl(): multidimensional 2PL models

• p_m_3pl(), array_p_m_3pl(): multidimensional 3PL models

• p_m_gpc(), array_p_m_gpc(): multidimensional GPC models

• p_m_gr(), array_p_m_gr(): multidimensional GR models

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

x <- 0.5

p_1pl(x, 1)
p_2pl(x, 1, 2)
p_3pl(x, 1, 2, 0.25)
p_pc(x, c(0, 1))
p_gpc(x, 2, c(0, 1))
p_gr(x, 2, c(0, 2))

x <- matrix(seq(0.1, 0.5, 0.1)) # three theta values, unidimensional

array_p_1pl(x, 1)
array_p_2pl(x, 1, 2)
array_p_3pl(x, 1, 2, 0.25)
array_p_pc(x, c(0, 1))
array_p_gpc(x, 2, c(0, 1))
array_p_gr(x, 2, c(0, 2))

(Internal) Parse a constraint data into an object

Description

parseConstraintData is an internal function for parsing data for a single constraint.

Usage

parseConstraintData(x, attrib, constants)

Arguments

Value

parseConstraintData returns a constraint object.

(Internal) Parse prior parameters from viable sources

Description

parsePriorParameters is an internal function for parsing prior parameters from viable sources

Usage

parsePriorParameters(
  config_theta,
  simulation_constants,
  prior_density_override,
  prior_par_override
)

Arguments

Value

parsePriorParameters returns a named list containing:

prior_dist

the type of distribution. One of NORMAL, UNIFORM, RAW.

prior_par

an examinee-wise list containing prior parameters.

(Internal) Parse shadowtest refresh schedule

Description

parseShadowTestRefreshSchedule is an internal function for parsing shadowtest refresh schedule from supplied config.

Usage

parseShadowTestRefreshSchedule(simulation_constants, refresh_policy)

Arguments

Value

parseShadowTestRefreshSchedule returns a named list.

Extension of plot() for objects in TestDesign package

Description

Extension of plot() for objects in TestDesign package

Usage

## S4 method for signature 'item_pool'
plot(
  x,
  y,
  type = "info",
  theta = seq(-3, 3, 0.1),
  info_type = "FISHER",
  plot_sum = TRUE,
  select = NULL,
  examinee_id = 1,
  position = NULL,
  theta_range = c(-5, 5),
  ylim = NULL,
  color = "blue",
  z_ci = 1.96,
  simple = TRUE,
  theta_type = "Estimated",
  color_final = "blue",
  color_stim = "red",
  segment = NULL,
  rmse = FALSE,
  use_segment_label = TRUE,
  use_par = TRUE,
  ...
)

## S4 method for signature 'output_Static'
plot(
  x,
  y,
  type = NULL,
  theta = seq(-3, 3, 0.1),
  info_type = "FISHER",
  plot_sum = TRUE,
  select = NULL,
  examinee_id = 1,
  position = NULL,
  theta_range = c(-5, 5),
  ylim = NULL,
  color = "blue",
  z_ci = 1.96,
  simple = TRUE,
  use_par = TRUE,
  ...
)

## S4 method for signature 'constraints'
plot(
  x,
  y,
  type = "info",
  theta = seq(-3, 3, 0.1),
  info_type = "FISHER",
  plot_sum = TRUE,
  select = NULL,
  examinee_id = 1,
  position = NULL,
  theta_range = c(-5, 5),
  ylim = NULL,
  color = "blue",
  z_ci = 1.96,
  simple = TRUE,
  use_par = TRUE,
  ...
)

## S4 method for signature 'output_Shadow'
plot(
  x,
  y,
  type = "audit",
  theta = seq(-3, 3, 0.1),
  info_type = "FISHER",
  plot_sum = TRUE,
  select = NULL,
  examinee_id = 1,
  theta_range = c(-5, 5),
  ylim = NULL,
  color = "blue",
  z_ci = 1.96,
  simple = FALSE,
  theta_type = "Estimated",
  use_par = TRUE,
  ...
)

## S4 method for signature 'output_Shadow_all'
plot(
  x,
  y,
  type = "audit",
  theta = seq(-3, 3, 0.1),
  info_type = "FISHER",
  plot_sum = TRUE,
  select = NULL,
  examinee_id = 1,
  position = NULL,
  theta_range = c(-5, 5),
  ylim = NULL,
  color = "blue",
  z_ci = 1.96,
  simple = FALSE,
  theta_type = "Estimated",
  color_final = "blue",
  color_stim = "red",
  segment = NULL,
  rmse = FALSE,
  use_segment_label = TRUE,
  use_par = TRUE,
  ...
)

## S4 method for signature 'output_Split'
plot(
  x,
  y,
  type = NULL,
  theta = seq(-3, 3, 0.1),
  info_type = "FISHER",
  plot_sum = TRUE,
  select = NULL,
  examinee_id = 1,
  position = NULL,
  theta_range = c(-5, 5),
  ylim = NULL,
  color = "blue",
  z_ci = 1.96,
  simple = TRUE,
  use_par = TRUE,
  ...
)

Arguments

Examples

subitempool <- itempool_science[1:8]

## Plot item information of a pool
plot(subitempool)
plot(itempool_science, select = 1:8)

## Plot expected score of a pool
plot(subitempool, type = "score")
plot(itempool_science, type = "score", select = 1:8)

## Plot assembly results from Static()
cfg <- createStaticTestConfig()
solution <- Static(cfg, constraints_science)
plot(solution)                 # defaults to the objective type
plot(solution, type = "score") # plot expected scores

## Plot attainable information range from constraints
plot(constraints_science)

## Plot assembly results from Shadow()
cfg <- createShadowTestConfig()
set.seed(1)
solution <- Shadow(cfg, constraints_science, true_theta = rnorm(1))
plot(solution, type = 'audit' , examinee_id = 1)
plot(solution, type = 'shadow', examinee_id = 1, simple = TRUE)

## plot(solution, type = 'exposure')
## plot(solution, type = 'overlap')

(Internal) Draw an exposure rate plot

Description

plotExposurePanel is an internal function for drawing an exposure rate plot for a single theta segment.

Usage

plotExposurePanel(
  item_exposure_rate,
  item_exposure_rate_final = NULL,
  stim_exposure_rate = NULL,
  stim_index = NULL,
  max_rate = max_rate,
  title = NULL,
  color = "blue",
  color_final = "yellow",
  color_stim = "red",
  color_threshold = "dark gray",
  simple = FALSE,
  ...
)

Arguments

(Internal) Plot audit trail of a single examinee

Description

plotShadowAudit is an internal function for plotting audit trail of a single examinee, showing interim theta estimates over the course of an adaptive test.

Usage

plotShadowAudit(x, theta_range, z_ci, use_par, ...)

Arguments