| Type: | Package |
| Title: | Estimation of the Rasch Model for Multistage Tests |
| Version: | 0.3.6-0 |
| Date: | 2025-06-20 |
| Author: | Jan Steinfeld 
[cre, aut],
Alexander Robitzsch
[aut] |
| Maintainer: | Jan Steinfeld <jan.d.steinfeld@gmail.com> |
| URL: | https://jansteinfeld.github.io/tmt/, https://github.com/jansteinfeld/tmt |
| BugReports: | https://github.com/jansteinfeld/tmt/issues |
| Description: | Provides conditional maximum likelihood (CML) item parameter estimation of both sequential and cumulative deterministic multistage designs (Zwitser & Maris, 2015, <doi:10.1007/s11336-013-9369-6>) and probabilistic sequential and cumulative multistage designs (Steinfeld & Robitzsch, 2024, <doi:10.1007/s41237-024-00228-3>). Supports CML item parameter estimation of conventional linear designs and additional functions for the likelihood ratio test (Andersen, 1973, <doi:10.1007/BF02291180>) as well as functions for simulating various types of multistage designs. |
| License: | GPL-3 |
| LazyLoad: | yes |
| VignetteBuilder: | knitr |
| Depends: | R (≥ 3.0) |
| Encoding: | UTF-8 |
| NeedsCompilation: | yes |
| Suggests: | roxygen2, eRm, knitr, prettydoc, psychotools, testthat, rmarkdown |
| Imports: | parallel, ggplot2, Rcpp (≥ 0.12.0), stats, rlang |
| LinkingTo: | Rcpp |
| RoxygenNote: | 7.3.2 |
| Language: | en-US |
| Packaged: | 2025-06-20 13:48:47 UTC; jansteinfeld |
| Repository: | CRAN |
| Date/Publication: | 2025-06-20 14:20:01 UTC |
tmt: Estimation of the Rasch Model for Multistage Tests
Description
Provides conditional maximum likelihood (CML) item parameter estimation of both sequential and cumulative deterministic multistage designs (Zwitser & Maris, 2015, doi:10.1007/s11336-013-9369-6) and probabilistic sequential and cumulative multistage designs (Steinfeld & Robitzsch, 2024, doi:10.1007/s41237-024-00228-3). Supports CML item parameter estimation of conventional linear designs and additional functions for the likelihood ratio test (Andersen, 1973, doi:10.1007/BF02291180) as well as functions for simulating various types of multistage designs.
Details
In multistage tests different groups of items (modules) are presented to persons depending on their response behavior to previous item groups. Multistage testing is thus a simple form of adaptive testing. If data is collected on the basis of such a multistage design and the items are estimated using the Conditional Maximum Likelihood (CML) method, Glas (1989) <doi:10.3102/10769986013001045> has shown, that the item parameters are biased. Zwitser and Maris (2015) <doi:10.1007/s11336-013-9369-6> showed in their work, that taking the applied multistage design in consideration and including it in the estimation of the item parameters, the estimation of item parameters is not biased using the CML method. Their proposed solution is implemented in our package. MST designs with a probabilistic instead of a deterministic routing rule (see, e.g. Chen, Yamamoto, & von Davier, 2014 <doi:10.1201/b16858>) are not estimated with this method, therefore the proposed solouting is again modified by Steinfeld and Robitzsch (2021) <doi:10.31234/osf.io/ew27f> which is also integrated into this package.
An application example can be found in the vignette by using the following command in the R console vignette("introduction_to_tmt")
logo
Author(s)
Maintainer: Jan Steinfeld jan.d.steinfeld@gmail.com (ORCID)
Authors:
Alexander Robitzsch robitzsch@leibniz-ipn.de (ORCID)
References
Andersen, E. B. (1973). A goodness of fit test for the Rasch model. Psychometrika, 38(1), 123-140.
Baker, F. B., & Harwell, M. R. (1996). Computing elementary symmetric functions and their derivatives: A didactic. Applied Psychological Measurement, 20(2), 169-192. Chicago
Baker, F. B., & Kim, S. H. (2004). Item response theory: Parameter estimation techniques. CRC Press.
Chen, H., Yamamoto, K., & von Davier, M. (2014). Controlling multistage testing exposure rates in international large-scale assessments. In A. Yan, A. A. von Davier, & C. Lewis (Eds.), Computerized Multistage Testing: Theory and Applications (pp. 391-409). New York: CRC Press. https://doi.org/10.1201/b16858
Fischer, G. H., & Molenaar, I. W. (Eds.). (2012). Rasch models: Foundations, recent developments, and applications. Springer Science & Business Media.
Formann, A. K. (1986). A note on the computation of the second-order derivatives of the elementary symmetric functions in the Rasch model. Psychometrika, 51(2), 335-339.
Glas, C.A.W. (1988). The Rasch model and multistage testing. Journal of Educational Statistics, 13(1), 45-52.
Glas, C.A.W. (2016). Maximum-Likelihood Estimation. In van der Linden, W.J. (Ed.), Handbook of Item Response Theory: Volume two: Statistical tools. (pp. 197 - 236). New York: CRC Press.
Rasch, G. (1960). Probabalistic models for some intelligence and attainment tests. Danmarks paedagogiske institut.
Steinfeld, J., & Robitzsch, A. (2024). Conditional maximum likelihood estimation in probability-based multistage designs. Behaviormetrika, 51(2), 617-634.
Steinfeld, J., Robitzsch, A. (2023). Estimating item parameters in multistage designs with the tmt package in R. Quantitative and Computational Methods in Behavioral Science, 3, e10087. https://doi.org/10.5964/qcmb.10087
Steinfeld, J., & Robitzsch, A. (2021). Item parameter estimation in multistage designs: A comparison of different estimation approaches for the Rasch model. Psych, 3(3), 279-307. https://doi.org/10.3390/psych3030022
Verhelst, N.D., Glas, C.A.W. und van der Sluis, A. (1984). Estimation Problems in the Rasch-Model: The Basic Symmetric Functions. Computational Statistics Quatarly, 1(3), 245-262.
Zwitser, R. J., & Maris, G. (2015). Conditional statistical inference with multistage testing designs. Psychometrika, 80(1), 65-84.
See Also
Useful links:
Report bugs at https://github.com/jansteinfeld/tmt/issues
Examples
tmt:::tmt_ascii()
## _ _
## | |_ _ __ ___ | |_
## | __| '_ ` _ \| __|
## | |_| | | | | | |_
## \__|_| |_| |_|\__|
Function for the Graphical Model Check
Description
This function performs a so-called graphical model check on the basis of the previously performed Likelihood Ratio Test [tmt::tmt_lrttest()]. The estimated item parameters of the two groups are plotted against each other. There is the possibility in this function to highlight items, to be excluded items from the plot, and to produce confidence-ellipses if desired.
Usage
tmt_gmc(
object,
title = "graphical model check",
xaxis = NULL,
yaxis = NULL,
lim = NULL,
ellipse = FALSE,
drop = NULL,
alpha = 0.05,
legendtitle = "split criteria",
info = NULL
)
Arguments
object |
object of the function [tmt::tmt_lrttest()] |
title |
of the plot |
xaxis |
description of the x-axis |
yaxis |
description of the y-axis |
lim |
of the plot |
ellipse |
should confidence-ellipse be plotted |
drop |
which items should be excluded from the plot |
alpha |
which alpha should be used for the ellipse |
legendtitle |
Title of the Legend |
info |
vector with further information for the Plot with names of submitted items |
Author(s)
Jan Steinfeld
Examples
#############################################################################
# Example of Graphical Model Check
#############################################################################
items <- seq(-3,3,length.out = 16)
names(items) <- paste0("i",1:16)
persons = 500
dat <- tmt:::sim.rm(theta = persons, b = items, seed = 1234)
dat.rm <- tmt_rm(dat)
dat.lrt <- tmt_lrtest(dat.rm, split = "median")
info <- rep(c("group_a","group_b"),each = 8)
names(info) <- paste0("i",1:16)
drop <- c("i1","i18")
#library(ggplot2)
plot <- tmt_gmc(object = dat.lrt,
ellipse = TRUE,
info = info,
drop = drop,
title = "graphical model check",
alpha = 0.05,
legendtitle = "split criteria")
Computation of Andersen's Likelihood-Ratio Test
Description
This function applies the Likelihood Ratio Test of Andersen. Note that all persons with raw score equal to "median" are assigned to the lower group in cases of a median split. Is is also allowed to split after "mean" or submit any dichotomous vector as split criteria.
Usage
tmt_lrtest(object, split = "median", cores = NULL, se = TRUE, ...)
Arguments
object |
it is necessary to submit an object of the function |
split |
default is the split criteria "median" of the raw score, optional are "mean" or any dichotomous vector |
cores |
submit integer of cores you would like to apply |
se |
logical: if true, the standard error is estimated |
... |
further arguments for the |
Value
List with following entries
data_orig |
Submitted data frame with item responses |
betapars_subgroup |
List of item parameters (difficulty) for each subgroup |
se.beta_subgroup |
List of standard errors of the estimated item parameters |
model |
Used model ((mst) for Rasch model with multistage design) |
LRvalue |
LR-value |
df |
Degrees of freedoms for the test statistic |
pvalue |
P-value of the likelihood ratio test |
loglik_subgroup |
Log-likelihoods for the subgroups |
split_subgroup |
List of split vector for each subgroup |
call |
Submitted arguments for the function (matched call) |
fitobj |
List of objects from subgroup estimation |
Author(s)
Jan Steinfeld
References
Andersen, E. B. (1973). A goodness of fit test for the Rasch model. Psychometrika, 38(1), 123-140.
Fischer, G. H., & Molenaar, I. W. (Eds.). (2012). Rasch models: Foundations, recent developments, and applications. Springer Science & Business Media.
See Also
Examples
# example for tmt_lrtest
#############################################################################
# Example Rasch model and Likelihood Ratio Test
#############################################################################
dat <- tmt:::sim.rm(theta = 100, b = 10, seed = 1111)
dat.rm <- tmt_rm(dat = dat)
dat.lrt <- tmt_lrtest(dat.rm)
summary(dat.lrt)
Function to Translate the mstdesign Syntax
Description
This function translates the specified multistage design for different purposes and functions used in this package. It is possible to apply this function on deterministic as well as probabilistic multistage designs with either sequential or cumulative routing. A detailed instruciton of the application can be found in the package vignette.
Usage
tmt_mstdesign(
mstdesign,
options = c("design", "simulation", "modules", "items")
)
Arguments
mstdesign |
definition of desired multistage design |
options |
vector of required output. 'modules' = Matrix with the classification of modules and items. ' simulation' = list of all stages. 'design' = matrix of all branches. 'items' vector of all Items. |
Value
List with following entries
modules |
Matrix which contains each module with its corresponding items |
simulation |
List of the multistage design. Each element within the list contains a matrix for each stage |
design |
Matrix of all possible branches |
items |
Vector of item names |
Author(s)
Jan Steinfeld
Examples
# example for tmt_mstdesign
## Not run:
###################################
# Example-1
###################################
mstdesign <- "
B1 =~ c(i1, i2, i3, i4, i5)
B2 =~ c(i6, i7, i8, i9, i10)
B3 =~ c(i11, i12, i13, i14, i15)
B4 =~ c(i16, i17, i18, i19, i20)
B5 =~ c(i21, i22, i23, i24, i25)
B6 =~ c(i26, i27, i28, i29, i30)
# define branches
b1 := B4(0,2) + B2(0,2) + B1(0,5)
b2 := B4(0,2) + B2(3,5) + B3(0,5)
b3 := B4(3,5) + B5(0,2) + B3(0,5)
b4 := B4(3,5) + B5(3,5) + B6(0,5)
"
# ---------------------------
# for simulation purposes
tmt_mstdesign(mstdesign, options = "simulation")$simulation
# ---------------------------
# summary of the submitted design
tmt_mstdesign(mstdesign, options = "design")$design
# ---------------------------
# matrix of all modules with the containing items
tmt_mstdesign(mstdesign, options = "modules")$modules
# ---------------------------
# vector of all items
tmt_mstdesign(mstdesign, options = "items")$items
# ---------------------------
# list of all four elements
tmt_mstdesign(mstdesign, options = c("design", "simulation", "modules", "items"))
## End(Not run)
###################################
# Example-2
###################################
mstdesign <- "
B1 =~ paste0('i',1:5)
B2 =~ paste0('i',6:10)
B3 =~ paste0('i',11:15)
B4 =~ paste0('i',16:20)
B5 =~ paste0('i',21:25)
B6 =~ paste0('i',26:30)
# define branches
b1 := B4(0,2) + B2(0,2) + B1
b2 := B4(0,2) + B2(3,5) + B3
b3 := B4(3,5) + B5(0,2) + B3
b4 := B4(3,5) + B5(3,5) + B6
"
designelements <- tmt_mstdesign(mstdesign,
options = c("design", "simulation", "modules", "items"))
Function to create a template for the multistage design used in tmt
Description
This function creates a template for the definition of multistage designs as required by the estimation function (in multistage design cases). The defines multistage design is then handed over to the functiontmt_mstdesign. Essentially, these are the modules, rules and path sections. In the formula-based notation, it is also possible to state additional conditions (constraints) that can be found in the data and are reflected in the multistage design.
Usage
tmt_msttemplate(formula = NULL, full = TRUE, eval = TRUE)
Arguments
formula |
formula for the desired template of a multistage design. If formula is leaved empty, a matrix as MST design template is generated. |
full |
logical if the modules and rules sections should also be created |
eval |
logical should the text input be evaluated (e.g. 3:6 = c(3, 4, 5, 6)) |
Author(s)
Jan Steinfeld
Examples
#############################################################################
# create simple template
#############################################################################
formula = "start(start) += S1(B1,B2,B3) += S2(B4,B5,B6,B7)"
tmt_msttemplate(formula, full = TRUE, eval = TRUE)
tmt_msttemplate(formula, full = TRUE, eval = FALSE)
#############################################################################
# create complex template
#############################################################################
formula = "nativ(no,yes) ~ education(low,medium,heigh) ~
CBM(3:6) += S1(B1,B2,B3) += S2(B4,B5,B6,B7)"
tmt_msttemplate(formula, full = TRUE, eval = TRUE)
tmt_msttemplate(formula, full = TRUE, eval = FALSE)
#############################################################################
# create template for the input as matrix
#############################################################################
tmt_msttemplate()
Estimation (CML) ot the Rasch model with or without multistage designs.
Description
The tmt_rm function estimates the Rasch model. If the data are collected based on a multistage design (see Zwitser and Maris, 2015) the specific multistage design mstdesign has to be submitted.
Usage
tmt_rm(
dat,
mstdesign = NULL,
weights = NULL,
start = NULL,
sum0 = TRUE,
se = TRUE,
optimization = "nlminb",
...
)
Arguments
dat |
a matrix of dichotomous (0/1) data or a list of the function |
mstdesign |
Model for the multistage design, if CML estimation without multistage designs is required, than leave the default value |
weights |
is optional for the weights of cases |
start |
Vector of start values. If no vector is provided, the start values will be automatic generated |
sum0 |
logical: If the item parameters should be normed to 'sum = 0' as recommended by Glas (2016, p. 208). Otherwise sum0=FALSE |
se |
logical: should the standard error should be estimated? |
optimization |
character: Per default 'nlminb' is used but 'optim' is also supported. |
... |
optional further arguments for optim and nlminb use control = list() with arguments. |
Details
According to Glas (1988) <doi:10.3102/10769986013001045> CML estimation of item parameters is biased if the data is collected in multistage designs and this design is not considered. Zwitser and Maris (2015) <doi:10.1007/s11336-013-9369-6> propose to use an additional design matrix to fragment the elementary symmetric function. Their approach is implemented in this package. MST designs with a probabilistic instead of a deterministic routing rule (see, e.g. Chen, Yamamoto, & von Davier, 2014 <doi:10.1201/b16858>) are not estimated with this method, therefore the proposed solouting is again modified by Steinfeld and Robitzsch (2021) <doi:10.31234/osf.io/ew27f> which is also integrated into this package.
Value
List with following entries
betapar |
Estimated item difficulty parameters (if sum0=FALSE, than the first item is set to 0) |
se.beta |
Standard errors of the estimated item parameters |
loglik |
Conditional log-likelihood of the model |
df |
Number of estimated parameters |
N |
Number of Persons |
I |
Number of items |
data_orig |
Submitted data frame with item responses |
data |
Used data frame with item responses |
desmat |
Design matrix |
convergence |
Convergence criterion |
iterations |
Number of iterations |
hessian |
Hessian-Matrix |
model |
Used model ((mst) for Rasch model with multistage design) |
call |
Submitted arguments for the function (matched call) |
designelements |
If the multistage version is requested, the preprocessed design is returned, otherwise NULL |
mstdesign |
If the multistage version is requested, the submitted design is returned, otherwise NULL |
Author(s)
Jan Steinfeld
References
Baker, F. B., & Harwell, M. R. (1996). Computing elementary symmetric functions and their derivatives: A didactic. Applied Psychological Measurement, 20(2), 169-192.
Baker, F. B., & Kim, S. H. (2004). Item response theory: Parameter estimation techniques. CRC Press.
Chen, H., Yamamoto, K., & von Davier, M. (2014). Controlling multistage testing exposure rates in international large-scale assessments. In A. Yan, A. A. von Davier, & C. Lewis (Eds.), Computerized Multistage Testing: Theory and Applications (pp. 391-409). New York: CRC Press. https://doi.org/10.1201/b16858
Fischer, G. H., & Molenaar, I. W. (Eds.). (2012). Rasch models: Foundations, recent developments, and applications. Springer Science & Business Media.
Formann, A. K. (1986). A note on the computation of the second-order derivatives of the elementary symmetric functions in the Rasch model. Psychometrika, 51(2), 335-339.
Glas, C.A.W. (1988). The Rasch model and multistage testing. Journal of Educational Statistics, 13(1), 45-52.
Glas, C.A.W. (2016). Maximum-Likelihood Estimation. In van der Linden, W.J. (Ed.), Handbook of Item Response Theory: Volume two: Statistical tools. (pp. 197 - 236). New York: CRC Press.
Rasch, G. (1960). Probabalistic models for some intelligence and attainment tests. Danmarks paedagogiske institut.
Steinfeld, J., & Robitzsch, A. (2024). Conditional maximum likelihood estimation in probability-based multistage designs. Behaviormetrika, 51(2), 617-634.
Steinfeld, J., Robitzsch, A. (2023). Estimating item parameters in multistage designs with the tmt package in R. Quantitative and Computational Methods in Behavioral Science, 3, e10087. https://doi.org/10.5964/qcmb.10087
Steinfeld, J., & Robitzsch, A. (2021). Item parameter estimation in multistage designs: A comparison of different estimation approaches for the Rasch model. Psych, 3(3), 279-307. https://doi.org/10.3390/psych3030022
Verhelst, N.D., Glas, C.A.W., & van der Sluis, A. (1984). Estimation Problems in the Rasch-Model: The Basic Symmetric Functions. Computational Statistics Quarterly, 1(3), 245-262.
Zwitser, R. J., & Maris, G. (2015). Conditional statistical inference with multistage testing designs. Psychometrika, 80(1), 65-84.
See Also
Examples
# example for tmt_rm
#############################################################################
# Example-1 simple Rasch model
#############################################################################
dat <- tmt:::sim.rm(theta = 100, b = 10, seed = 1111)
dat.rm <- tmt_rm(dat = dat)
summary(dat.rm)
#############################################################################
# Example-1 for multistage-design
#############################################################################
mstdesign <- "
M1 =~ c(i1, i2, i3, i4, i5)
M2 =~ c(i6, i7, i8, i9, i10)
M3 =~ c(i11, i12, i13, i14, i15)
# define path
p1 := M2(0,2) + M1
p2 := M2(3,5) + M3
"
items <- seq(-1,1,length.out = 15)
names(items) <- paste0("i",1:15)
persons = 1000
dat <- tmt_sim(mstdesign = mstdesign,
items = items, persons = persons)
dat.rm <- tmt_rm(dat = dat, mstdesign = mstdesign)
summary(dat.rm)
## Not run:
############################################################################
# Example-2 simple Rasch model
############################################################################
dat <- tmt:::sim.rm(theta = 100, b = 10, seed = 1111)
dat.rm <- tmt_rm(dat = dat)
summary(dat.rm)
############################################################################
# Example-2 for multistage-design
############################################################################
# also using 'paste' is possible
mstdesign <- "
M1 =~ paste0('i',1:5)
M2 =~ paste0('i',6:10)
M3 =~ paste0('i',11:15)
M4 =~ paste0('i',16:20)
M5 =~ paste0('i',21:25)
M6 =~ paste0('i',26:30)
# define path
p1 := M4(0,2) + M2(0,2) + M1
p2 := M4(0,2) + M2(3,5) + M3
p3 := M4(3,5) + M5(0,2) + M3
p4 := M4(3,5) + M5(3,5) + M6
"
items <- seq(-1,1,length.out = 30)
names(items) <- paste0("i",1:30)
persons = 1000
dat <- tmt_sim(mstdesign = mstdesign,
items = items, persons = persons)
dat.rm <- tmt_rm(dat = dat, mstdesign = mstdesign)
summary(dat.rm)
############################################################################
# Example-3 for cumulative multistage-design
############################################################################
# also using 'paste' is possible
mstdesign <- "
M1 =~ paste0('i',21:30)
M2 =~ paste0('i',11:20)
M3 =~ paste0('i', 1:10)
M4 =~ paste0('i',31:40)
M5 =~ paste0('i',41:50)
M6 =~ paste0('i',51:60)
# define path
p1 := M1(0, 5) += M2( 0,10) += M3
p2 := M1(0, 5) += M2(11,15) += M4
p3 := M1(6,10) += M5( 6,15) += M4
p4 := M1(6,10) += M5(16,20) += M6
"
items <- seq(-1,1,length.out = 60)
names(items) <- paste0("i",1:60)
persons = 1000
dat <- tmt_sim(mstdesign = mstdesign,
items = items, persons = persons)
dat.rm <- tmt_rm(dat = dat, mstdesign = mstdesign)
summary(dat.rm)
## End(Not run)
Function for the Simulation of Multistage-Designs
Description
This function simulates data according to the specified and submitted multistage design. The persons are drawn from a standard normal distribution if the amount of persons are specified. As an additional argument, a seed can also be set. If requested, it is also possible to submit a vector ore list of person parameters to specify different person distributions.
Usage
tmt_sim(
mstdesign = NULL,
items = NULL,
persons = NULL,
preconditions = NULL,
...
)
Arguments
mstdesign |
definition of desired multistage design |
items |
vector of difficulty parameters for each items |
persons |
amount of persons per starting module |
preconditions |
definition of preconditions can optionally be specified. In the case of probabilistic routing preconditions such as a pre-test, which are taken into account in the MST design. For the specification the correlation with the true person parameter have to be specified. The submitted correlation is adjusted in the function according to Demirtas and Yavuz (2015; <doi:10.1080/10543406.2014.920868>) It is also possible to submit your own vector with integers for the preconditions. |
... |
further optional arguments like setting a |
Value
List with following entries
data |
Matrix with item responses |
data_mst |
Data frame with item responses and additional a vector of used modules per person |
persons |
Generated and used person parameters |
mstdesign |
Submitted multistage design |
Author(s)
Jan Steinfeld
References
Demirtas, H., & Yavuz, Y. (2015). Concurrent Generation of Ordinal and Normal Data. Journal of Biopharmaceutical Statistics, 25(4), 635-650. https://doi.org/10.1080/10543406.2014.920868
Examples
#############################################################################
# translate multistage model 1
#############################################################################
mstdesign <- "
M1 =~ c(i1, i2, i3, i4, i5)
M2 =~ c(i6, i7, i8, i9, i10)
M3 =~ c(i11, i12, i13, i14, i15)
# define branches
p1 := M2(0,2) + M1
p2 := M2(3,5) + M3
"
items <- seq(-3,3,length.out = 15)
names(items) <- paste0("i", seq(items))
data_1 <- tmt_sim(mstdesign = mstdesign,
items = items,
persons = 500,
seed = 1111)
#############################################################################
# translate multistage model 2
#############################################################################
mstdesign <- "
M1 =~ c(i1, i2, i3, i4, i5)
M2 =~ c(i6, i7, i8, i9, i10)
M3 =~ c(i11, i12, i13, i14, i15)
M4 =~ c(i16, i17, i18, i19, i20)
M5 =~ c(i21, i22, i23, i24, i25)
M6 =~ c(i26, i27, i28, i29, i30)
# define branches
p1 := M4(0,2) + M2(0,2) + M1
p2 := M4(0,2) + M2(3,5) + M3
p3 := M4(3,5) + M5(0,2) + M3
p4 := M4(3,5) + M5(3,5) + M6
"
items <- seq(-3,3,length.out = 30)
names(items) <- paste0("i", seq(items))
data_2 <- tmt_sim(mstdesign = mstdesign,
items = items,
persons = 500,
seed = 1111)