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

Many key aspects in the social sciences (e.g. attitudes, values, utility, beliefs, per­sonality traits, cognitive competencies) are not directly observable.1 Rather, they are conceptualized as latent constructs, measured indirectly via a set of manifest or observed indicators (Bollen, 2002). Learning a latent variable's distribution from the observed data presupposes a formal measurement model that postulates how-in mathematical terms-the latent and manifest variables are related. Such models can be derived from test or measurement theories, such as classical test theory (CTT; Lord and Novick, 1968) or item response theory (IRT; Lord, 1980). Because the relations between manifest indicators and latent variables are not seen as definitions but rather as hypotheses, it is important to formulate the model (with all the imposed restrictions) based on theoretical reasoning. For a further discussion of the topic with a philosophy of science background see Fetzer (2001).