Item factor analysis (IFA), also known as Multidimensional Item Response Theory (MIRT), is a general framework for specifying the functional relationship between a respondent's multiple latent traits and their response to assessment items. The key element in MIRT is the relationship between the items and the latent traits, so-called item factor…

This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality…

Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than…

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…

Nonnormality of univariate data has been extensively examined previously (Blanca et al., 2013; Micceri, 1989). However, less is known of the potential nonnormality of multivariate data although multivariate analysis is commonly used in psychological and educational research. Using univariate and multivariate skewness and kurtosis as measures of…

Growth curve modeling provides a general framework for analyzing longitudinal data from social, behavioral, and educational sciences. Bayesian methods have been used to estimate growth curve models, in which priors need to be specified for unknown parameters. For the covariance parameter matrix, the inverse Wishart prior is most commonly used due…

It is common to assume that worker productivity is normally distributed, but this assumption is rarely if ever tested. We estimate the distribution of worker productivity where individual productivity is measured with error, using the productivity of elementary school teachers as an example. Proposals to improve teacher productivity often focus on…

Typically a longitudinal growth modeling based on item response theory (IRT) requires repeated measures data from a single group with the same test design. If operational or item exposure problems are present, the same test may not be employed to collect data for longitudinal analyses and tests at multiple time points are constructed with unique…