title: Measurement invariance within and between individuals: a distinct problem in testing the equivalence of intra- and inter-individual model structures.
abstract: We address the question of equivalence between modeling results obtained on intra-individual and inter-individual levels of psychometric analysis. Our focus is on the concept of measurement invariance and the role it may play in this context. We discuss this in general against the background of the latent variable paradigm, complemented by an operational demonstration in terms of a linear state-space model, i.e., a time series model with latent variables. Implemented in a multiple-occasion and multiple-subject setting, the model simultaneously accounts for intra-individual and inter-individual differences. We consider the conditions-in terms of invariance constraints-under which modeling results are generalizable (a) over time within subjects, (b) over subjects within occasions, and (c) over time and subjects simultaneously thus implying an equivalence-relationship between both dimensions. Since we distinguish the measurement model from the structural model governing relations between the latent variables of interest, we decompose the invariance constraints into those that involve structural parameters and those that involve measurement parameters and relate to measurement invariance. Within the resulting taxonomy of models, we show that, under the condition of measurement invariance over time and subjects, there exists a form of structural equivalence between levels of analysis that is distinct from full structural equivalence, i.e., ergodicity. We demonstrate how measurement invariance between and within subjects can be tested in the context of high-frequency repeated measures in personality research. Finally, we relate problems of measurement variance to problems of non-ergodicity as currently discussed and approached in the literature.
authors.affiliation: Center for Lifespan Psychology, Max Planck Institute for Human Development Berlin, Germany.
authors.forename: Janne
authors.initials: J
authors.lastname: Adolf
authors.affiliation: Department of Methodology and Statistics, Faculty of Social and Behavioral Sciences, Utrecht University Utrecht, Netherlands.
authors.forename: Noémi K
authors.initials: NK
authors.lastname: Schuurman
authors.affiliation: Personality and Diagnostics Group, Department of Psychology, Faculty of Philosophy I, Martin-Luther-University Halle-Wittenberg Halle, Germany.
authors.forename: Peter
authors.initials: P
authors.lastname: Borkenau
authors.affiliation: Psychological Methods Group, Department of Psychology, Faculty of Social and Behavioral Sciences, University of Amsterdam Amsterdam, Netherlands.
authors.forename: Denny
authors.initials: D
authors.lastname: Borsboom
authors.affiliation: Department of Biological Psychology, Faculty of Psychology and Education, Free University of Amsterdam Amsterdam, Netherlands.
authors.forename: Conor V
authors.initials: CV
authors.lastname: Dolan
keywords: ergodicity; intra-individual level of analysis; latent variables; measurement invariance; state-space modeling