The Schmid-Leiman (J. Schmid and J. M. Leiman, 1957) decomposition of a hierarchical factor model converts the model to a constrained case of a bifactor model with orthogonal common factors that is equivalent to the hierarchical model. This article discusses the equivalence of the hierarchical and bifactor models. (Author/SLD)

Discusses techniques to account for unmeasured third variables in longitudinal designs, introducing a series of less restrictive synchronous common factor models as an extension of the synchronous common factor model. Recommends the use of such models, which can be tested by structural equation modeling, when possible third variables might have…

Simulation results show that the power to detect small mean differences when fitting a model with free residual variances across groups decreases as the difference in R squared increases. This decrease is more pronounced in the presence of correlated errors and if group sample sizes differ. (SLD)

Explores the four-step procedure for testing structural equation models and outlines some problems with the approach advocated by L. Hayduk and D. Glaser (2000) and S. Mulaik and R. Milsap (2000). Questions the idea that there is a "correct" number of constructs for a given phenomenon. (SLD)

Used simulation to study the effects of the practice of item parceling. Results indicate that certain types of item parceling can obfuscate a multidimensional factor structure in a way that acceptable values of fit indexes are found for a misspecified solution. Discusses why the use of parceling cannot be recommended when items are…

Focuses on the four-step method (four nested models) of structural equation modeling advocated by S. Mulaik (1997, 1998), discussing the limitations of the approach and considering the tests and criteria to be used in moving among the four steps. (SLD)

Defends the four-step approach to structural equation modeling based on testing sequences of models and points out misunderstandings of opponents of the approach. The four-step approach allows the separation of respective constraints within a structural equation model. (SLD)

Neither the four-step model nor the one-step procedure can actually tell whether the researcher has the right number of factors in structural equation modeling. In fact, for reasons discussed, a simple formulaic approach to the correct specification of models does not yet exist. (SLD)

Replies to commentaries on the four-step approach to structural equation modeling, pointing out the strengths and weaknesses of each argument and ultimately concluding that the four-step model is subject to criticisms that can be addressed to factor analysis as well. (SLD)

Information fit indexes such as Akaike Information Criterion, Consistent Akaike Information Criterion, Bayesian Information Criterion, and the expected cross validation index can be valuable in assessing the relative fit of structural equation models that differ regarding restrictiveness. In cases in which models without mean restrictions (i.e.,…

Treating Likert rating scale data as continuous outcomes in confirmatory factor analysis violates the assumption of multivariate normality. Given certain requirements pertaining to the number of categories, skewness, size of the factor loadings, and so forth, it seems nevertheless possible to recover true parameter values if the data stem from a…

A validation study of the Child Sex Abuse Attitude Scale (CSAAS) used confirmatory factor analysis to examine factor structure. Results from a sample of 215 school psychologists supported the hypothesized factor structure of the CSAAS, indicating the plausibility of a four-factor first-order and a single-factor higher order structure for the…

Used nine different confirmatory factor analysis models to test the factorial structure of Rosenberg's (M. Rosenberg, 1965) self-esteem scale with a sample of 430 crack-cocaine users. Results partly support earlier research to show a single global self-esteem factor underlying responses to the Rosenberg scale, method effects associated with item…

Examines some positions in various arguments related to the proper number of factors and proper number of steps when using structural equation models. Defines the issue in estimating structural equation models as a problem of specifying a model appropriately based on theoretical concerns and then diagnosing ills in the model as well as possible.…

Conducted simultaneous group confirmatory factor analyses of the Psychopathy Checklist-Revised (PCL-R)(R. Hare, 1991) with 740 alcoholic inpatients. Results provide general support for the use of the PCL-R with alcoholic inpatients, although there was substantial intercorrelation for the factors of Personality and Behavioral Features. (SLD)