Assessing Factorial Invariance in Cross-Sectional and Longitudinal Studies
Daniel E. Bontempo, Scott M. Hofer · 2006
Abstract The issue of factorial invariance (FI), or more specifically the subset of FI tests that pertain to measurement equivalence, is in essence an issue of construct validity. At the conceptual level, a measure is valid when it accurately operationalizes the construct it purports to measure. The operationalization calibrates manifest indicators to theoretical constructs, which are latent in the sense that they are not directly observed. When a construct is used across multiple groups of individuals or on multiple occasions for the same individuals, the construct’s measurement is invariant (and scores may be quantitatively compared) only when the construct’s operationalization functions equivalently for each group or occasion. This is defined as measurement invariance, and multigroup requirements can be mathematically formulated (Meredith, 1993). In practice, invariance of measurements obtained in different groups is often assumed without formal test. This occurs when scale items are summed (i.e., unit-weighted) or latent factor scores (a loading-weighted sum of scale items) are calculated across groups or occasions without first establishing that the score’s meaning is invariant for each group or across occasions. For a construct operationalized as the common factor of a set of manifest indicators, measurement invariance can be demonstrated by testing a sequence of invariance hypotheses focusing on the loadings, intercepts, specific factors, and some structural elements of the common-factor measurement model. These hypotheses provide evidence for the validity of subsequent score comparisons across groups or occasions.