Fully Gibbs Sampling Algorithms for Bayesian Variable Selection in Latent Regression Models

This study proposed efficient Gibbs sampling algorithms for variable selection in a latent regression model under a unidimensional two-parameter logistic item response theory model. Three types of shrinkage priors were employed to obtain shrinkage estimates: double-exponential (i.e., Laplace), horseshoe, and horseshoe+ priors. These shrinkage priors were compared to a uniform prior case in both simulation and real data analysis. The simulation study revealed that two types of horseshoe priors had a smaller root mean square errors and shorter 95% credible interval lengths than double-exponential or uniform priors. In addition, the horseshoe prior+ was slightly more stable than the horseshoe prior. The real data example successfully proved the utility of horseshoe and horseshoe+ priors in selecting effective predictive covariates for math achievement. In the final section, we discuss the benefits and limitations of the three types of Bayesian variable selection methods.

Personality and psychosocial functioning in early adolescence: Age-differential associations from the self- and parent perspective

Although psychosocial functioning and personality are indisputably interrelated in adulthood, much less is known about these associations in early adolescence. Accordingly, the goal of the current study was twofold. First, we investigated associations between adolescents’ personality and three broad indicators of psychosocial functioning: academic achievement, social relationships, and psychosocial adjustment. Second, we tested differential effects by comparing these associations across three different cohorts (Grades 5, 7, and 9) and across two raters of adolescents’ personality: self- and parent reports. Our sample consisted of N = 2667 students and their parents. According to latent regression models, adolescents’ personality traits showed significant associations with all psychosocial functioning variables: Achievement was most consistently associated with emotional stability, openness, and conscientiousness; social relationships were most consistently associated with agreeableness and conscientiousness; and psychosocial adjustment was related to all of the Big Five traits. Most associations did not vary across grades, whereas self-reported extraversion showed lower associations in later grades. Looking at rater-specific effects, we found fewer and usually smaller associations with parent- than with self-rated personality, again with the most significant differences with extraversion. We discuss the consistent interrelatedness between adolescents’ personality and psychosocial functioning but also highlight important exceptions in grade- and rater-specificities.

Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation

The estimation of high-dimensional latent regression item response theory (IRT) models is difficult because of the need to approximate integrals in the likelihood function. Proposed solutions in the literature include using stochastic approximations, adaptive quadrature, and Laplace approximations. We propose using a second-order Laplace approximation of the likelihood to estimate IRT latent regression models with categorical observed variables and fixed covariates where all parameters are estimated simultaneously. The method applies when the IRT model has a simple structure, meaning that each observed variable loads on only one latent variable. Through simulations using a latent regression model with binary and ordinal observed variables, we show that the proposed method is a substantial improvement over the first-order Laplace approximation with respect to the bias. In addition, the approach is equally or more precise to alternative methods for estimation of multidimensional IRT models when the number of items per dimension is moderately high. Simultaneously, the method is highly computationally efficient in the high-dimensional settings investigated. The results imply that estimation of simple-structure IRT models with very high dimensions is feasible in practice and that the direct estimation of high-dimensional latent regression IRT models is tractable even with large sample sizes and large numbers of items.

Developments in Psychometric Population Models for Technology-Based Large-Scale Assessments: An Overview of Challenges and Opportunities

International large-scale assessments (ILSAs) transitioned from paper-based assessments to computer-based assessments (CBAs) facilitating the use of new item types and more effective data collection tools. This allows implementation of more complex test designs and to collect process and response time (RT) data. These new data types can be used to improve data quality and the accuracy of test scores obtained through latent regression (population) models. However, the move to a CBA also poses challenges for comparability and trend measurement, one of the major goals in ISLAs. We provide an overview of current methods used in ILSAs to examine and assure the comparability of data across different assessment modes and methods that improve the accuracy of test scores by making use of new data types provided by a CBA.

A Simple Diffusion Model for Psychometric Analyses

The emergence of computer-based assessments has made response times, in addition to response accuracies, available as a source of information about test takers’ latent abilities. The predominant approach to jointly account for response times and accuracies are statistical models. Substantive approaches such as the diffusion model, on the other hand, have been slow to gain traction due to their unwieldy functional form. In the present work we show how a single simplifying assumption yields a highly tractable diffusion model. This simple diffusion model is straightforward to analyse using Gibbs sampling and can be readily extended with a latent regression framework. We demonstrate the superior computational efficiency of our model compared to the standard diffusion model in a simulation study and showcase the theoretical merit of our model in an example application.