The ForceChoice package provides a unified framework for fitting, simulating, and evaluating forced-choice and traditional item response models. It supports eight model families spanning dominance, ideal-point/unfolding, and diagnostic classification paradigms, with both full Bayesian estimation (Stan/HMC) and a fast iterative stochastic EM (iStEM) algorithm. FCGDINA also provides a deterministic EM estimator.
The model descriptions below distinguish the package's implemented parameterizations from the broader source literature. Core references are given with DOI links where available so that the modeling assumptions, response-process assumptions, and goodness-of-fit framework can be traced back to peer-reviewed sources.
- Eight model families: MIRT, MGPCM, MGGUM, FCMIRT, FCGGUM, TIRT, FCDCM, FCGDINA
- Estimation backends: Stan (full Bayesian HMC), iStEM (fast stochastic EM for large data), and deterministic EM for FCGDINA
- Comprehensive goodness-of-fit: Limited-information M2, RMSEA, CFI, TLI, SRMSR, pseudo-R^2^, Yen's Q3, posterior diagnostics
- Forced-choice response types: Full ranking (RANK), most-least (MOLE), and best-only (PICK)
- Consistent S3 interface:
coef(),fitted(),logLik(),plot(),predict(),print(),residuals(),summary(),update(),vcov(),confint()
You can install the development version from GitHub:
# install.packages("remotes")
remotes::install_github("Naidantu/ForceChoice")library(ForceChoice)
# Simulate binary response data from a 2-dimensional 2PL model
sim <- sim.data.MIRT(N = 20, I = 6, D = 2, model = "2PL")
# Fit via iStEM (fast, scalable to large datasets)
fit <- fit.MIRT(sim$data, model = "2PL", D = 2, method = "iStEM",
control.method = list(
vis = FALSE, seed = 123,
M = 2, B = 2, burnin.maxitr = 2,
maxitr = 3, eps1 = 10, eps2 = 10,
estimate.se = FALSE))
# Examine results
print(fit)
summary(fit)
# Item parameter estimates
head(coef(fit))
# Person trait estimates
head(fit$theta$est)
# Factor correlation
fit$Corr$est
# Goodness-of-fit evaluation
gof <- get.fit.index(fit)
summary(gof)# Simulate forced-choice ranking data
sim <- sim.data.FCMIRT(N.person = 20, N.block = 3, I.block = 2,
D = 2, model = "2PL", fc.type = "RANK")
# The block.items and fc.type are auto-detected from the data
fit <- fit.FCMIRT(sim$data, model = "2PL", D = 2,
method = "iStEM",
control.method = list(
vis = FALSE, seed = 123,
M = 2, B = 2, burnin.maxitr = 2,
maxitr = 3, eps1 = 10, eps2 = 10,
estimate.se = FALSE))
# Trait recovery: correlation between estimates and true values
diag(cor(fit$theta$est, sim$theta))
# Goodness-of-fit for forced-choice data
gof <- get.fit.index(fit)
summary(gof)# Simulate forced-choice data for TIRT
sim <- sim.data.TIRT(N.person = 20, N.block = 3, I.block = 2,
D = 2, fc.type = "RANK")
fit <- fit.TIRT(sim$data, Q.matrix = sim$Q.matrix,
block.items = sim$block.items,
method = "iStEM",
control.method = list(
vis = FALSE, seed = 123,
M = 2, B = 2, burnin.maxitr = 2,
maxitr = 3, eps1 = 10, eps2 = 10,
estimate.se = FALSE))
# Trait recovery
cor(fit$theta$est, sim$theta)# Simulate paired-comparison data with DINA condensation rule
sim <- sim.data.FCDCM(N.person = 20, N.block = 3, D = 2,
dcm.type = "DINA")
# Fit
fit <- fit.FCDCM(sim$data, Q.matrix = sim$Q.matrix,
block.items = sim$block.items,
method = "iStEM",
control.method = list(
vis = FALSE, seed = 123,
M = 2, B = 2, burnin.maxitr = 2,
maxitr = 3, eps1 = 10, eps2 = 10,
estimate.se = FALSE))
# Posterior attribute mastery profiles
head(fit$alpha$est)
# Attribute mastery proportions
colMeans(fit$alpha$est > 0.5)# Simulate forced-choice diagnostic data under a CDM item model
sim <- sim.data.FCGDINA(N.person = 20, N.block = 2, I.block = 2,
D = 2, model = "GDINA", fc.type = "RANK")
# Fit with deterministic EM for a reproducible baseline
fit <- fit.FCGDINA(sim$data, Q.matrix = sim$Q.matrix,
block.items = sim$block.items, model = "GDINA",
fc.type = sim$fc.type, method = "EM",
control.method = list(vis = FALSE, seed = 123,
maxitr = 2,
estimate.se = FALSE))
head(fit$alpha$est)| Function | Model | Response Type | Key Reference |
|---|---|---|---|
fit.MIRT() |
Multidimensional IRT (1PL--4PL) | Binary | Reckase (2009) |
fit.MGPCM() |
Generalized Partial Credit | Polytomous | Muraki (1992) |
fit.MGGUM() |
Generalized Graded Unfolding | Polytomous | Roberts et al. (2000) |
fit.FCMIRT() |
Forced-Choice MIRT | Ranking/MOLE/PICK | Zheng et al. (2024); Luce (1959); Plackett (1975) |
fit.FCGGUM() |
Forced-Choice GGUM | Ranking/MOLE/PICK | Lee et al. (2018); Roberts et al. (2000) |
fit.TIRT() |
Thurstonian IRT | Ranking/MOLE/PICK | Brown & Maydeu-Olivares (2011) |
fit.FCDCM() |
Forced-Choice DCM | Paired comparison | Huang (2022) |
fit.FCGDINA() |
Forced-Choice GDINA | Ranking/MOLE/PICK | de la Torre (2011); Luce (1959); Plackett (1975) |
Full Bayesian inference via Hamiltonian Monte Carlo (NUTS). Provides posterior means, standard deviations, and R-hat convergence diagnostics. Recommended for final inference and small-to-moderate datasets.
# stan code, long time
fit <- fit.MIRT(data, model = "2PL", D = 2, method = "stan",
control.method = list(chains = 1, iter = 200,
warmup = 100, cores = 1,
seed = 123))Iterative Stochastic EM with Metropolis-within-Gibbs person sampling and L-BFGS-B item optimization. Scales to large datasets. Convergence monitored via Geweke diagnostics and batch-means Monte Carlo error.
fit <- fit.MIRT(data, model = "2PL", D = 2, method = "iStEM",
control.method = list(
vis = FALSE, seed = 123,
M = 2, B = 2, burnin.maxitr = 2,
maxitr = 3, eps1 = 10, eps2 = 10,
estimate.se = FALSE))Deterministic posterior-weight EM is available for FCGDINA. It provides a fast, reproducible point-estimation baseline without MCMC sampling.
All fitted models support comprehensive fit evaluation via get.fit.index():
gof <- get.fit.index(fit)
summary(gof)Fit indices reported:
- Information criteria: AIC, AICc, BIC, CAIC, SABIC, HQIC
- Absolute fit: M2, RMSEA (with 90% CI), SRMSR
- Comparative fit: CFI, TLI, IFI
- Pseudo-R2: McFadden, Cox--Snell, Nagelkerke, and others
- Local dependence: Yen's Q3
- Classification: Posterior entropy, mean max posterior
Brown, A., & Maydeu-Olivares, A. (2011). Item response modeling of forced-choice questionnaires. Educational and Psychological Measurement, 71(3), 460--502. https://doi.org/10.1177/0013164410375112
de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76(2), 179--199. https://doi.org/10.1007/s11336-011-9207-7
Huang, H.-Y. (2022). Diagnostic classification model for forced-choice items and noncognitive tests. Educational and Psychological Measurement, 83(1), 146--180. https://doi.org/10.1177/00131644211069906
Lee, P., Joo, S.-H., Stark, S., & Chernyshenko, O. S. (2018). GGUM-RANK statement and person parameter estimation with multidimensional forced choice triplets. Applied Psychological Measurement, 43(3), 226--240. https://doi.org/10.1177/0146621618768294
Luce, R. D. (1959). Individual choice behavior: A theoretical analysis. Wiley.
Maydeu-Olivares, A., & Joe, H. (2005). Limited- and full-information estimation and goodness-of-fit testing in 2^n contingency tables: A unified framework. Journal of the American Statistical Association, 100(471), 1009--1020. https://doi.org/10.1198/016214504000002069
Maydeu-Olivares, A., & Joe, H. (2006). Limited information goodness-of-fit testing in multidimensional contingency tables. Psychometrika, 71(4), 713--732. https://doi.org/10.1007/s11336-005-1295-9
Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159--176. https://doi.org/10.1177/014662169201600206
Plackett, R. L. (1975). The analysis of permutations. Journal of the Royal Statistical Society: Series C (Applied Statistics), 24(2), 193--202. https://doi.org/10.2307/2346567
Reckase, M. D. (2009). Multidimensional Item Response Theory. Springer. https://doi.org/10.1007/978-0-387-89976-3
Roberts, J. S., Donoghue, J. R., & Laughlin, J. E. (2000). A general item response theory model for unfolding unidimensional polytomous responses. Applied Psychological Measurement, 24(1), 3--32. https://doi.org/10.1177/01466216000241001
Tu, N., Zhang, B., Angrave, L., Sun, T., & Neuman, M. (2023). Estimating the multidimensional generalized graded unfolding model with covariates using a Bayesian approach. Journal of Intelligence, 11(8), 163. https://doi.org/10.3390/jintelligence11080163
Zheng, C., Liu, J., Li, Y., Xu, P., Zhang, B., Wei, R., Zhang, W., Liu, B., & Huang, J. (2024). A 2PLM-RANK multidimensional forced-choice model and its fast estimation algorithm. Behavior Research Methods, 56(6), 6363--6388. https://doi.org/10.3758/s13428-023-02315-x
Zhu, Y.-A., Xu, J., Wang, D., Li, X., Cai, Y., & Tu, D. (2024). A ranking forced choice diagnostic classification model for psychological assessment using forced choice questionnaires. British Journal of Mathematical and Statistical Psychology, 78(2), 617--646. https://doi.org/10.1111/bmsp.12376
GPL (>= 3)