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…

Cluster sampling results in response variable variation both among respondents (i.e., within-cluster or Level 1) and among clusters (i.e., between-cluster or Level 2). Properly modeling within- and between-cluster variation could be of substantive interest in numerous settings, but applied researchers typically test only within-cluster (i.e.,…

Two Monte Carlo studies were conducted to examine the sensitivity of goodness of fit indexes to lack of measurement invariance at 3 commonly tested levels: factor loadings, intercepts, and residual variances. Standardized root mean square residual (SRMR) appears to be more sensitive to lack of invariance in factor loadings than in intercepts or…