Longitudinal measurement (non)invariance in latent constructs: conceptual insights, model specifications and testing strategies

The chapter discusses the basic principles and core problems of latent variable panel modelling, with a focus on the specification of error structures and (the evaluation of) longitudinal measurement invariance. We address alternative specifications of autocorrelative error structures, and demonstrate how to decompose the indicators’ residual variances into indicator-specific and random error components. Furthermore, besides describing the conventional global testing strategy for measurement (non)invariance, we contribute to the literature by integrating theoretical and analytical elements not yet extensively discussed outside the respective disciplines. We (i) introduce response shift theory as viable theoretical basis for the occurrence of noninvariance across time; (ii) provide a detailed description of model and scale identification strategies, accompanied by a critical reflection of their potential to adequately detect noninvariant parameters; and (iii) discuss the concepts of partial and approximate measurement invariance as well as the decomposition of response shifts and true change as different strategies of how to deal with measurement noninvariance.