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

IF 1.5 3区心理学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS British Journal of Mathematical & Statistical Psychology Pub Date : 2024-02-21 DOI:10.1111/bmsp.12339

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

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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.

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使用后验预测模型检查法评估时变动态部分信贷模型的拟合度。

最近，有人提出了几种基于项目反应理论的新模型来分析密集的纵向数据。其中一个新模型是时变动态部分学分模型（TV-DPCM；Castro-Alvarez 等人，《多变量行为研究》，2023 年第 1 期），它是部分学分模型和时变自回归模型的结合。该模型可以研究项目的心理测量特性，并在潜态水平上建立非线性趋势模型。然而，目前严重缺乏评估 TV-DPCM 拟合度的工具。在本文中，我们基于后验预测模型检查（PPMC）方法（PPMC; Rubin, The Annals of Statistics, 1984, 12, 1151）提出并开发了几种测试统计量和差异测量方法，用于评估 TV-DPCM 的拟合度。模拟数据和经验数据用于研究 PPMC 方法的性能并说明其有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

British Journal of Mathematical & Statistical Psychology 医学-数学跨学科应用

CiteScore

5.00

自引率

3.80%

发文量

审稿时长

>12 weeks

期刊介绍： The British Journal of Mathematical and Statistical Psychology publishes articles relating to areas of psychology which have a greater mathematical or statistical aspect of their argument than is usually acceptable to other journals including: • mathematical psychology • statistics • psychometrics • decision making • psychophysics • classification • relevant areas of mathematics, computing and computer software These include articles that address substantitive psychological issues or that develop and extend techniques useful to psychologists. New models for psychological processes, new approaches to existing data, critiques of existing models and improved algorithms for estimating the parameters of a model are examples of articles which may be favoured.