Longitudinal stability of latent means and individual differences: A unified approach

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Abstract
We examined the stability of responses to a multi‐item self‐esteem scale collected on five occasions over an 8‐year period. A wide variety of approaches were critically examined that considered the stability of means, individual differences (i.e., test‐retest correlations), and factor structures using traditional approaches (e.g., ANOVA and correlations) and structural equation models. Structural equation models based on multiple indicators provided a unified analytic approach for evaluating different aspects of stability and offered important advantages over traditional approaches. We describe a hierarchy of invariances and the nature of interpretations that are justified by different patterns of factor structure invariance associated with each level. We conclude that the assumptions underlying the typical repeated‐measures ANOVA approach to testing mean differences in longitudinal data are far more restrictive, less easily tested, and less likely to be met than those in the structural equation modeling approach advocated here, and that the use of ANOVA for this purpose requires a huge leap of faith that can rarely be justified on logical or empirical grounds.