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betafunctions

Functions for two- and four-parameter Beta distributions and for estimating the accuracy and consistency of classifications based on test scores.

Installation

install.packages("betafunctions")

# Development version:
# install.packages("remotes")
remotes::install_github("HaakonEidemHaakstad/betafunctions")

Classification accuracy and consistency

Three single-administration approaches are implemented. Each has a function for one cut-point (.CA), one for several cut-points (.CA.MC), and an ROC function (.ROC):

Approach	Functions	Input	Model
Livingston and Lewis (1995)	`LL.CA()`, `LL.CA.MC()`, `LL.ROC()`	Total scores and a reliability coefficient	Four- (or two-) parameter Beta true scores, Binomial errors on the effective-test-length scale
Hanson and Brennan (Hanson, 1991)	`HB.CA()`, `HB.CA.MC()`, `HB.ROC()`	Sum scores, test length and a reliability coefficient	Four- (or two-) parameter Beta true scores, Lord’s two-term compound-Binomial errors
Multinomial / compound multinomial (Lee, 2007; Lee, Brennan & Wan, 2009)	`MN.CA()`, `MN.CA.MC()`, `MN.ROC()`	Item scores, optionally in weighted item sets	Examinee-level multinomial errors; no true-score distribution

library(betafunctions)

# 1000 examinees, 20 dichotomous items.
set.seed(1234)
p <- rBeta.4P(1000, 0.15, 0.85, 6, 4)
items <- sapply(1:20, function(i) rbinom(1000, 1, p))
scores <- rowSums(items)

# Livingston and Lewis, with coefficient alpha as the reliability estimate.
LL.CA(scores, reliability = cba(items), cut = 10, min = 0, max = 20)

# Hanson and Brennan, three categories, with results conditional on each score.
HB.CA.MC(scores, reliability = cba(items), cut = c(8, 12), testlength = 20,
         conditional = TRUE)

# Compound multinomial (MULT-CLASS), with Brennan and Lee's bias correction.
MN.CA(items, cut = 10)

# Category-specific indices in one table.
MC.out.tabular(MN.CA.MC(items, cut = c(8, 12)))

The .CA functions return the confusion matrix and accuracy statistics (sensitivity, specificity, predictive values, Youden’s J, accuracy) and the consistency matrix with agreement, chance agreement and Kappa. The LL and HB functions also report a chi-square test of model fit. mdlfit.gfx() plots observed against expected frequencies.

Distributions and estimation

Four-parameter Beta distribution: dBeta.4P(), pBeta.4P(), qBeta.4P(), rBeta.4P(), and the mean-variance parameterization dBetaMS(), pBetaMS(), qBetaMS(), rBetaMS().
Beta-Binomial distribution: dBetaBinom(), pBetaBinom(), rBetaBinom().
Lord’s two-term compound Binomial: dcBinom(), pcBinom(), rcBinom(), dBetacBinom(), rBetacBinom().
Moments: betamoments(), binomialmoments(), betabinomialmoments(), observedmoments().
Fitting: Beta.4p.fit(), Beta.2p.fit(), and true-score fits Beta.tp.fit() (LL) and HB.beta.tp.fit() (HB).
Reliability: Cronbach’s alpha (cba()) and McDonald’s omega (mdo(), maximum likelihood by default); effective test length (ETL()) and Lord’s k (Lords.k()).

Functions deprecated in version 2.0.0 are listed in ?"betafunctions-deprecated".

References

Hanson, B. A. (1991). Method of moments estimates for the four-parameter beta compound binomial model and the calculation of classification consistency indexes. ACT Research Report Series.
Lee, W.-C. (2007). Multinomial and compound multinomial error models for tests with complex item scoring. Applied Psychological Measurement, 31(4), 255–274.
Lee, W.-C., Brennan, R. L., & Wan, L. (2009). Classification consistency and accuracy for complex assessments under the compound multinomial model. Applied Psychological Measurement, 33(5), 374–390.
Livingston, S. A., & Lewis, C. (1995). Estimating the consistency and accuracy of classifications based on test scores. Journal of Educational Measurement, 32(2), 179–197.
Lord, F. M. (1965). A strong true-score theory, with applications. Psychometrika, 30(3), 239–270.

License

CC0. Bug reports and suggestions: https://github.com/HaakonEidemHaakstad/betafunctions/issues.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.