GSCA Pro is free, user-friendly software for generalized structured component analysis structural equation modeling (GSCA-SEM), which implements three statistical methods for estimating models with factors only, models with components only, and models with both factors and components. This tutorial aims to provide step-by-step illustrations of how…

Mediation is usually assessed by a regression-based or structural equation modeling (SEM) approach that we refer to as the classical approach. This approach relies on the assumption that there are no confounders that influence both the mediator, "M", and the outcome, "Y". This assumption holds if individuals are randomly…

Simulation researchers are sometimes faced with the need to use multiple statistical software packages in the process of conducting their research, potentially having to go between software packages manually. This can be a tedious and time-consuming process that generally motivates researchers to use fewer replications in their simulations than…

Researchers using structural equation modeling (SEM) aspire to learn about the world by seeking models with causal specifications that match the causal forces extant in the world. This quest for a model matching existing worldly causal forces constitutes an ontology that orients, or perhaps reorients, thinking about measurement validity. This…

In the exploratory factor analysis, when the number of factors exceeds the true number of factors, the likelihood ratio test statistic no longer follows the chi-square distribution due to a problem of rank deficiency and nonidentifiability of model parameters. As a result, decisions regarding the number of factors may be incorrect. Several…

In testing factorial invariance, researchers have often used a reference variable strategy in which the factor loading for a variable (i.e., reference variable) is fixed to 1 for identification. This commonly used method can be misleading if the chosen reference variable is actually a noninvariant item. This simulation study suggests an…

Both structural equation modeling (SEM) and item response theory (IRT) can be used for factor analysis of dichotomous item responses. In this case, the measurement models of both approaches are formally equivalent. They were refined within and across different disciplines, and make complementary contributions to central measurement problems…