Longitudinal Measurement Noninvariance with Ordered-Categorical Indicators: How Are the Parameters in Second-Order Latent Growth Model Affected?

Researchers who conduct longitudinal studies are inherently interested in studying individual and population changes over time (e.g., mathematics achievement, subjective well-being). To answer such research questions, models of change (e.g., growth models) make the assumption of longitudinal measurement invariance, i.e., the same construct is measured on the same scale over all time points under study. In many applied situations, key constructs are measured by a collection of ordered-categorical indicators (e.g., Likert scale items). To evaluate longitudinal measurement invariance with ordered-categorical indicators, a set of hierarchical models can be sequentially tested and compared. If the statistical tests of measurement invariance fail to be supported for one of the models, it is useful to have a method with which to gauge the practical significance of the differences in measurement model parameters over time. Using second-order latent growth curve models for ordered-categorical indicators, this study proposes a sensitivity analysis that compares the growth parameter estimates from a model assuming the highest achieved level of measurement invariance to those from a model assuming a higher, incorrect level of measurement invariance as a measure of practical significance. A simulation study investigated the practical significance of non-invariance of ordinal measures in different locations (loadings, thresholds, uniquenesses), measured as the changes in the estimated growth parameters in second-order latent linear growth models assuming a correct versus an incorrect level of measurement invariance. Results suggest that in second-order latent linear growth models, the mean linear slope was affected by non-invariance in the loadings and thresholds, the intercept variance was affected by non-invariance in the uniquenesses, and the slope variance and intercept-slope covariance were affected by non-invariance in all three locations. The influences of a number of other factors were also examined, including the magnitude of non-invariance, the number of non-invariant indicators, the number of non-invariant occasions, and the number of response categories in the indicators. Researchers commonly fit linear growth models to Likert and other ordinal types of items so the simulation results have practical relevance. Extensions of the proposed sensitivity analysis to second-order latent growth curve models with other functional forms of growth and to other models of change were also discussed.