Assessment of fit of the time-varying dynamic partial credit model using the posterior predictive model checking method

Sebastian Castro-Alvarez*, Sandip Sinharay, Laura F Bringmann, Rob R Meijer, Jorge N Tendeiro

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Several new models based on item response theory have recently been suggested to analyse intensive longitudinal data. One of these new models is the time-varying dynamic partial credit model (TV-DPCM; Castro-Alvarez et al., Multivariate Behavioral Research, 2023, 1), which is a combination of the partial credit model and the time-varying autoregressive model. The model allows the study of the psychometric properties of the items and the modelling of nonlinear trends at the latent state level. However, there is a severe lack of tools to assess the fit of the TV-DPCM. In this paper, we propose and develop several test statistics and discrepancy measures based on the posterior predictive model checking (PPMC) method (PPMC; Rubin, The Annals of Statistics, 1984, 12, 1151) to assess the fit of the TV-DPCM. Simulated and empirical data are used to study the performance of and illustrate the effectiveness of the PPMC method.

Original languageEnglish
JournalBritish Journal of Mathematical and Statistical Psychology
DOIs
Publication statusE-pub ahead of print - 21-Feb-2024

Keywords

  • autoregressive model
  • model misfit
  • partial credit model
  • posterior predictive model checking
  • psychological time series
  • time-varying dynamic partial credit model

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