Bayesian longitudinal item response modeling with multivariate asymmetric serial dependencies

José Roberto Silva dos Santos*, Caio Lucidius Naberezny Azevedo, Jean Paul Fox

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


It is usually impossible to impose experimental conditions in large-scale longitudinal (observational) studies in education. This increases the risk of bias due to for instance unobserved heterogeneity, missing background variables, and dropouts. A flexible statistical model is required for the nature of the observational assessment data and to account for the unexplained heterogeneity. A general class of longitudinal item response theory (IRT) models is proposed, where growth in performance can be monitored using a skewed multivariate normal distribution for the latent variables. Change in performance and unexplained heterogeneity is addressed through structured covariance patterns and skewed multivariate latent variable distributions. The Cholesky decomposition of the covariance matrix is considered to model the dependence structure. A novel multivariate skew-normal distribution is defined by the antedependence model with centered skew-normal distributed errors. A hybrid MCMC approach is developed for parameter estimation, model-fit assessment, and model comparison. Results of simulation studies show good parameter recovery. A longitudinal assessment study by the Brazilian federal government is considered to show the performance of the general LIRT model.

Original languageEnglish
JournalJournal of Statistical Computation and Simulation
Publication statusE-pub ahead of print/First online - 19 Aug 2021


  • antedependence models
  • Bayesian inference
  • Cholesky decomposition
  • Longitudinal IRT
  • MCMC algorithms


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