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)

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)

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)

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…

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.…

We illustrate testing measurement invariance in a second-order factor model using a quality of life dataset (n = 924). Measurement invariance was tested across 2 groups at a set of hierarchically structured levels: (a) configural invariance, (b) first-order factor loadings, (c) second-order factor loadings, (d) intercepts of measured variables,…

This simulation investigates bias in trait factor loadings and intercorrelations when analyzing multitrait-multimethod (MTMM) data using the correlated uniqueness (CU) confirmatory factor analysis (CFA) model. A theoretical weakness of the CU model is the assumption of uncorrelated methods. However, previous simulation studies have shown little…

Discusses issues related to model evaluation in structural equation modeling. Supports nested model comparisons via sequential chi-square difference tests as consistent with the four-step approach to model evaluation when models of the factor analytic simultaneous equation type are entertained. (Author/SLD)

Demonstrates empirically a structural equation modeling technique for group comparison of reliability and validity. Data, which are from a study of 495 mothers' attitudes toward pregnancy, have a one-factor measurement model and three sets of subpopulation comparisons. (SLD)

Data from the General Social Survey for 1977 (n=1,303) and 1991 (n=430) are used to examine the stability of attitudes toward abortion and women's roles. Findings support the hypothesis that public attitudes toward discretionary abortion and nontraditional sex roles are discrete but correlated sets of attitudes that remained stable from 1977 to…

The Rasch item fit approach for detecting multidimensionality in response data is compared with principal component analysis without rotation using simulated data. Results indicate that both approaches work in a variety of multidimensional data structures, but the Rasch item fit is better under some circumstances, as discussed. (SLD)