An Essay on Measurement and Factorial Invariance

Abstract

Invariance of factor loadings across studied groups is required for valid comparisons of scale score or latent variable means. Strong and strict invariance may be less important in the context of basic research in which group differences in specific factors are indicative of individual differences that are important for scientific exploration. However, for most applications in which the aim is to ensure fairness and equity, strict factorial invariance is required. Health disparities research often focuses on self-reported clinical outcomes such as quality of life that are not observed directly. Latent variable models such as factor analyses are central to establishing valid assessment of such outcomes.

Properties of Swedish posttraumatic stress measures after a disaster

“…were evaluated (e.g., Meredith & Teresi, 2006). Tests of invariance evaluate whether the item-to-factor relationships are consistent across groups or assessments.…”

Are Autistic Traits Measured Equivalently in Individuals With and Without An Autism Spectrum Disorder? An Invariance Analysis of the Autism Spectrum Quotient Short Form

“…In addition, in combined analyses of two groups measured by a test that does not exhibit metric invariance across these groups, differences in factor loadings can result in the appearance of additional non-substantive factors (Meredith and Teresi 2006). This has the potential to confuse attempts to identify the dimensionality of autistic traits and any putative correlates of identified dimensions.…”

“…Finally, any aggregated factor analyses of scores of those with and without ASD in which scalar invariance does not hold can result in additional factors appearing due to the differences in thresholds across the groups (Meredith and Teresi 2006). Again, where the dimensionality of ASD traits may be of interest, this could produce misleading results.…”

Externalizing Behavior Problems

“…Structural and measurement residuals were not invariant. Requiring structural and measurement residuals to be equal across groups is a strict level of invariance (Meredith & Teresi, 2006). Thus, for the purposes of this research study, the calibration and validation samples are considered to demonstrate acceptable levels of invariance.…”