In the past decade, moderated mediation analysis has been extensively and increasingly employed in social and behavioral sciences. With its widespread use, it is particularly important to ensure the moderated mediation analysis will not bring spurious results. Spurious effects have been studied in both mediation and moderation analysis, but this…

Linear factor analysis (FA) models can be reliably tested using test statistics based on residual covariances. We show that the same statistics can be used to reliably test the fit of item response theory (IRT) models for ordinal data (under some conditions). Hence, the fit of an FA model and of an IRT model to the same data set can now be…

A readily implemented procedure is discussed for interval estimation of indexes of interrelationship between items from multiple-component measuring instruments as well as between items and total composite scores. The method is applicable with categorical (ordinal) observed variables, and can be widely used in the process of scale construction,…

Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics. Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors for rotated solutions, although these have still not made…

Amos 5.0 (Arbuckle, 2003) permits exploratory specification searches for the best theoretical model given an initial model using the following fit function criteria: chi-square (C), chi-square--df (C--df), Akaike Information Criteria (AIC), Browne-Cudeck criterion (BCC), Bayes Information Criterion (BIC) , chi-square divided by the degrees of…

This article discusses 5 approaches that secondary researchers might use to obtain robust estimates in structural equation modeling analyses when using data that come from large survey programs. These survey programs usually collect data using complex sampling designs and estimates obtained from conventional analyses that ignore the dependencies…

Multilevel structural equation modeling (MSEM) has been proposed as an extension to structural equation modeling for analyzing data with nested structure. We have begun to see a few applications in cross-cultural research in which MSEM fits well as the statistical model. However, given that cross-cultural studies can only afford collecting data…