Abstract

Recent technological advancements have enabled the collection of intensive longitudinal data (ILD), consisting of repeated measurements from the same individual. The threshold autoregressive (TAR) model is often used to capture the dynamic outcome process in ILD, with autoregressive parameters varying based on outcome variable levels. For ILD from multiple individuals, multilevel TAR (ML-TAR) models have been proposed, with Bayesian approaches typically used for parameter estimation. However, fitting ML-TAR models can be computationally challenging. This study introduces a mean-field variational Bayes (MFVB) algorithm as an alternative to traditional Bayesian inference. By optimizing to approximate posterior densities, variational Bayes aims to find the best approximation within a defined set of distributions. Simulation results demonstrate that our MFVB algorithm is significantly faster than the standard Markov chain Monte Carlo (MCMC) approach. Moreover, increasing the number of individuals or time points enhances the accuracy of the parameter estimates using MFVB, suggesting that sufficient data are crucial for accurate estimation in complex models like ML-TAR models. When applied to real-world data, the MFVB algorithm was significantly more efficient than MCMC and maintained similar accuracy. Thus, the MFVB algorithm is a faster and more consistent alternative to MCMC for large-scale inference in ILD models.

Abstract

In various areas of science, researchers try to gain insight into important processes by jointly analysing different datasets containing information regarding common aspects of these processes. For example, to explain individual differences in personality, researchers collect, for the same set of persons, data regarding behavioural signatures (i.e., the reaction profile of a person across different situations), on the one hand, and traits or dispositions, on the other hand. To uncover the processes underlying such coupled data, to all N-way N$$ N $$-mode data blocks simultaneously a global model is fitted, in which each data block is represented by an N$$ N $$-way N$$ N $$-mode decomposition model (e.g., principal component analysis [PCA], Parafac, Tucker3) and the parameters underlying the common mode are required to be the same for all data blocks this mode belongs to. To estimate the parameters underlying the common mode, a simultaneous strategy is used that pools the information present in all data blocks (i.e., data fusion). In this paper, we propose the T3–PCA model, which represents three- and two-way data with Tucker3 and PCA respectively. This model is less restrictive than the already proposed LMPCA model in which the three-way data block is decomposed according to a Parafac model. To estimate the T3–PCA model parameters, an alternating least-squares algorithm is proposed. The superior performance of the simultaneous T3–PCA strategy over a sequential strategy (i.e., estimating common parameters using information from the three-way data block only) is demonstrated in an extensive simulation study and an application to empirical coupled anxiety data.

Abstract

This paper provides a literature review of assessment of fit of item response theory models. Various types of fit procedures for item response theory models are reviewed, with a focus on their advantages and disadvantages. Real data examples are used to demonstrate some of the fit procedures. Recommendations are provided for researchers and practitioners who are interested in assessing the fit of item response theory models.

British Journal of Mathematical and Statistical Psychology, Volume 78, Issue 1, Page i-iv, February 2025.