Assumptions of the Two-Step Approach to Latent Variable Modeling

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Abstract
Although methods for latent variable modeling that allow a joint analysis of measurement and theory have become popular, they are not without difficulties. As these difficulties have become more apparent, several researchers have recently called for a “two-step approach” to latent variable modeling in which measurement is evaluated separately from theory. This implies that programs for covariance structure analysis are not needed because factor analysis and regressions would suffice for analysis. Before a return to earlier practice using seemingly simpler analysis tools can be recommended, it seems prudent to consider the assumptions underlying a two-step approach. At least four implicit assumptions can be identified: (a) theory and measurement are independent, (b) results of factor analysis specifications can be generalized to other specifications, (c) the estimators have desirable statistical properties, and (d) the statistical test in one step is independent of the test in the other. The authors show that these assumptions cannot be met in general and that some of them are logically inconsistent. Thus any wholesale adoption of a two-step approach could have serious consequences.