Detecting Misspecification in Mean Structures for Growth Curve Models: Performance of Pseudo R²s and Concordance Correlation Coefficients

Abstract

This study examined the performance of 4 correlation-based fit indexes (marginal and conditional pseudo R ²s; average and conditional concordance correlations) in detecting misspecification in mean structures in growth curve models. Their performance was also compared to that of 4 traditional SEM fit indexes. We found that the marginal pseudo R ² and average concordance correlation were able to detect misspecification in the marginal mean structure (average change trajectory). The conditional pseudo R ² and concordance correlation could detect misspecification when it occurred in the conditional mean structure (individual change trajectory) or in both mean structures. Compared to the SEM fit indexes, the correlation-based fit indexes were more robust to sample size but were less robust to data properties such as magnitude of population mean and measurement error. Theoretical and practical implications of the results and directions for future research are discussed.

Keywords:

• concordance correlation
• growth curve model
• mean structure
• model fit
• pseudo R square

Notes

¹In the SEM framework, up to T – 2 (here three) of the T loadings can potentially be freely estimated in the level and shape model (McArdle, 1988; Meredith & Tisak, 1990).

²Note that EBLUP can be only used when the growth curve models are linear in their parameters (i.e., where the outcome is a linear combination of the parameters). The growth curve models with this property include linear and curvilinear models.