Affiliation:
1. Department of Psychometrics and Statistics, Faculty of Behavioural and Social Sciences University of Groningen Groningen The Netherlands
2. Department of Human Ecology University of California Davis California USA
3. Educational Testing Service Princeton New Jersey USA
4. Office of Research and Academia‐Government‐Community Collaboration, Education Research Center for Artificial Intelligence and Data Innovation Hiroshima University Higashihiroshima Japan
Abstract
AbstractSeveral 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.