The procedures of carrying out factorial invariance to validate a construct were well developed to ensure the reliability of the construct that can be used across groups for comparison and analysis, yet mainly restricted to the frequentist approach. This motivates an update to incorporate the growing Bayesian approach for carrying out the Bayesian…

In this article, the authors suggest a profile-likelihood approach for estimating complex models by maximum likelihood (ML) using standard software and minimal programming. The method works whenever setting some of the parameters of the model to known constants turns the model into a standard model. An important class of models that can be…

Following an exploratory factor analysis, factor scores may be computed and used in subsequent analyses. Factor scores are composite variables which provide information about an individual's placement on the factor(s). This article discusses popular methods to create factor scores under two different classes: refined and non-refined. Strengths and…

Summarizes the problem of factorial invariance in between-group difference studies, proposes a simplified notation intended to facilitate discussion of the problem, and suggests a structured approach for testing large models. Two computer programs are offered to help with the computation. (SLD)

Many researchers acknowledge the prominent role that factor analysis can play in efforts to establish construct validity. Data can be analyzed with no preconceived ideas about the underlying constructs of structure of the data. This approach is exploratory factor analysis, Another approach is used when the researcher has an understanding of the…

The central objective of factor analysis is to explain the greatest amount of variance in a data set with the smallest number of factors. Higher-order analysis is an invaluable tool that offers the benefit of parsimony provided by first-order analysis with the opportunity to make data-based generalizations beyond the first-order. Higher-order…

Few methods have been tried and used to graphically represent more than two variables. This poster session showed a new method for representing three continuous variables on a single scatterplot using the THREEDE computer program. Two variables are represented as a normal bivariate distribution. The third variable is represented by a symbol, e.g.…