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One Possible Approach to Testing for Group Differences in SEM

Newsom, SEM, Winter 2005. One Possible Approach to Testing for Group Differences in SEM. Same Form, Free Across Groups. Consider other Models. Good Fit?. No. Yes. Constrain L,Q,y. Assume Partial Measurement Invariance. Constrain L,Q,y Separately. Good Fit?. No. Yes.

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One Possible Approach to Testing for Group Differences in SEM

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  1. Newsom, SEM, Winter 2005 One Possible Approach to Testing for Group Differences in SEM Same Form, Free Across Groups Consider other Models Good Fit? No Yes Constrain L,Q,y Assume Partial Measurement Invariance Constrain L,Q,y Separately Good Fit? No Yes Assume Measurement Invariance Test Individual Parameters Test Individual Parameters No Good Fit? Constrain B Yes Conclude No Group Differences In Predictive Paths Note: Comparisons are made to the same form/free parameters model or the previously tested model. The basic idea is to isolate portions of the model that may be different across groups by comparing nested models, minimizing the number of tests as much as possible. Differences in loadings across groups is usually considered more serious than differences in error terms (which is fairly common). With partial measurement invariance, one has to interpret differences in structural paths in light of how different the measures are across groups. Suggested Reading Byrne, B.M., Shavelson, R.J., & Muthen, B. (1989). Testing for the equivalence of factorial covariance and mean structures: The issue of partial measurement invariance. PsychologicalBulletin, 105, 456-466. Cheung, G.W. & Rensvold, R.B. (1999). Testing factorial invariance across groups: A reconceptualization and proposed new method. Journal of Management, 25, 1-27. Werts, C.E., Rock, D.A., Linn, R.L., & Joreskog, K.G. (1977). Validating psychometric assumptions within and between severalpopulations. Educational and Psychological Measurement, 37, 863-872. Kim, J. O., & Ferree, G. D., Jr. (1981).  Standardization in causal analysis.  Sociological Methods and Research, 10, 187-210. Kim, J. O., & Mueller, C. W. (1976).  Standardized and unstandardized coefficients in causal analysis:  An expository note.  Sociological Methods and Research, 4, 428-438. Millsap, Roger E; Yun-Tein, Jenn. (2004). Assessing Factorial Invariance in Ordered-Categorical Measures. Multivariate Behavioral Research., 39, 479-515. Millsap, Roger E. (1998). Group differences in regression intercepts: Implications for factorial invariance. Multivariate Behavioral Research, 33, 403-424. Millsap, Roger E. (1997). Invariance in measurement and prediction: Their relationship in the single-factor case. Psychological Methods, 2, 248-260.

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