We present a method for Bayesian structural equation modeling of sample correlation matrices as correlation structures. The method transforms the sample correlation matrix to an unbounded vector using the matrix logarithm function. Bayesian inference about the unbounded vector is performed assuming a multivariate-normal likelihood, with a mean…

A frequent criticism of exploratory factor analysis (EFA) is that it does not allow correlated residuals to be modelled, while they can be routinely specified in the confirmatory (CFA) model. In this article, we propose an EFA approach in which both the common factor solution and the residual matrix are unrestricted (i.e., the correlated residuals…

The partial correlation coefficient (PCC) is used to quantify the linear relationship between two variables while taking into account/controlling for other variables. Researchers frequently synthesize PCCs in a meta-analysis, but two of the assumptions of the common equal-effect and random-effects meta-analysis model are by definition violated.…

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite requirement on correlation matrices, from sign indeterminacy of factor loadings, and from order constraints on…

An interaction in a fixed effects (FE) regression is usually specified by demeaning the product term. However, algebraic transformations reveal that this strategy does not yield a within-unit estimator. Instead, the standard FE interaction estimator reflects unit-level differences of the interacted variables. This property allows interactions of a…

Accounting for model misspecification in Bayesian structural equation models is an active area of research. We present a uniquely Bayesian approach to misspecification that models the degree of misspecification as a parameter--a parameter akin to the correlation root mean squared residual. The misspecification parameter can be interpreted on its…

Effect sizes are important because they are an accessible way to indicate the practical importance of observed associations or differences. Standardized mean difference (SMD) effect sizes, such as Cohen's d, are widely used in education and the social sciences -- in part because they are relatively easy to calculate. However, SMD effect sizes…

Effect modification (EM) may cause bias in network meta-analysis (NMA). Existing population adjustment NMA methods use individual patient data to adjust for EM but disregard available subgroup information from aggregated data in the evidence network. Additionally, these methods often rely on the shared effect modification (SEM) assumption. In this…

The standard methodology for many large-scale assessments in education involves regressing latent variables on numerous contextual variables to estimate proficiency distributions. To reduce the number of contextual variables used in the regression and improve estimation, we propose and evaluate principal component analysis on the covariance matrix…

When fitting unidimensional item response theory (IRT) models, the population distribution of the latent trait ([theta]) is often assumed to be normally distributed. However, some psychological theories would suggest a nonnormal [theta]. For example, some clinical traits (e.g., alcoholism, depression) are believed to follow a positively skewed…

Methods to generate random correlation matrices have been proposed in the literature, but very few instances exist where these correlation matrices are structured or where the statistical properties of the algorithms are known. By relying on the tetrad relation discovered by Spearman and the properties of the beta distribution, an algorithm is…

Bayesian structural equation modeling (BSEM) is a flexible tool for the exploration and estimation of sparse factor loading structures; that is, most cross-loading entries are zero and only a few important cross-loadings are nonzero. The current investigation was focused on the BSEM with small-variance normal distribution priors (BSEM-N) for both…

A procedure for evaluation of validity related coefficients and their differences is discussed, which is applicable when one or more frequently used assumptions in empirical educational, behavioral and social research are violated. The method is developed within the framework of the latent variable modeling methodology and accomplishes point and…

In real-world situations, multidimensional data may appear on large-scale tests or attitudinal surveys. A simple structure, multidimensional model may be used to evaluate the items, ignoring the cross-loading of some items on the secondary dimension. The purpose of this study was to investigate the influence of structure complexity magnitude of…

This study explored the use of stealth assessments within a digital game to assess second language (L2) Chinese learners' reading comprehension. Log data tracking learners' in-game behaviors from a game designed for Chinese dual language immersion classrooms (Poole et al., 2022) were used to construct Bayesian Belief Networks to model reading…