When comparing relations and means of latent variables, it is important to establish measurement invariance (MI). Most methods to assess MI are based on confirmatory factor analysis (CFA). Recently, new methods have been developed based on exploratory factor analysis (EFA); most notably, as extensions of multi-group EFA, researchers introduced…

Bifactor latent structures were introduced over 70 years ago, but only recently has bifactor modeling been rediscovered as an effective approach to modeling "construct-relevant" multidimensionality in a set of ordered categorical item responses. I begin by describing the Schmid-Leiman bifactor procedure (Schmid & Leiman, 1957) and highlight its…

In a recent article, A. Maydeu-Olivares and D. L. Coffman (2006, see EJ751121) presented a random intercept factor approach for modeling idiosyncratic response styles in questionnaire data and compared this approach with competing confirmatory factor analysis models. Among the competing models was the CT-C(M-1) model (M. Eid, 2000). In an…

In the exploratory factor analysis, when the number of factors exceeds the true number of factors, the likelihood ratio test statistic no longer follows the chi-square distribution due to a problem of rank deficiency and nonidentifiability of model parameters. As a result, decisions regarding the number of factors may be incorrect. Several…

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…

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)

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.…

This article is concerned with the seemingly simple problem of testing whether latent factors are perfectly correlated (i.e., statistically indistinct). In recent literature, researchers have used different approaches, which are not always correct or complete. We discuss the parameter constraints required to obtain such perfectly correlated latent…

The Penn State Worry Questionnaire (PSWQ) was originally designed as a unifactorial measure of pathological trait worry. However, recent studies supported a two-factor solution with positively worded items loading on the first factor and reverse-scored items loading on a second factor. The current study compared this two-factor model to a negative…

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)

This study explored the factorial structure of the Parental Bonding Instrument (PBI) in the Japanese population. Several differences between the structure model in the current study and Parker et al.'s original model were identified. We also examined the adaptability of the inventory to children currently being raised by parents. We also developed…