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Structural Equation Modeling: Applications Using Mplus by Xiaoqian Wang, Jichuan Wang

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3.3 Correcting for Measurement Errors in Single Indicator Variables

In Chapters 1 and 2 we have discussed that the measurement model is designed to handle measurement errors in the observed variables, and at least three indicators per factor are needed in a CFA model. In real research, observed variables are very often treated as either independent or dependent variables in a model assuming no measurement errors. In order to understand how failing to account for measurement errors in a single indicator can result in attenuated parameter estimates, the influence of measurement errors is briefly reviewed in Appendix 3.A.

When measurement errors are ignored in a regression, biased parameter estimates and standard errors can occur (Hayduk, 1987). A variety of statistical methods (both parametric and nonparametric) can be used to correct for measurement errors and to make adjustments for the relations between the flawed variables and others (Allison and Hauser, 1991; Armstrong, Whittemore, and Howe, 1989; Greenland and Kleinbaum, 1983; Marshall and Graham, 1984; Rosner, Spiegelman, and Willett, 1990; Thomas, Stram, and Dwyer 1993). When multiple indicators per latent variable are available, SEM is a powerful approach to mitigate the problems of measurement errors in understanding the relationship among variables in the model. In the case where a single indicator variable is included in a model to predict endogenous variable(s), an appropriate way to adjust for the influence of measurement ...

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