Modeling between-group differences in dynamics of psychological constructs in the presence of measurement non-invariance: A stepwise approach

Researchers analyzing intensive longitudinal data often aim to detect between-group differences in dynamics of psychological constructs, such as positive and negative affect. These constructs are usually latent (not directly observable). To validly compare groups of individuals in their dynamic processes, the latent constructs must be measured equally across the individuals. If this is not the case – that is, if measurement invariance is violated for some items – this partial non-invariance must be accounted for. Otherwise, the group-specific estimates of the dynamic process may be biased. To aid researchers in obtaining unbiased group-specific estimates despite partial measurement non-invariance, we present an extension of the Three-Step Latent Vector Autoregression, a novel method that separates the estimation of the measurement model and the structural model. We expand this method to multi-group modeling, where differences in structural parameters (e.g., regression coefficients) are captured by allowing these parameters to vary across the groups of individuals. Measurement heterogeneity between and within these groups is captured by group- or person-specific MM parameters. Through two simulation studies, we demonstrate that the method performs well in obtaining correct estimates of a dynamic process despite the presence of measurement heterogeneity. The method is further illustrated with an empirical example.