An Essay on Measurement and Factorial Invariance

Analysis of subgroups such as different ethnic, language, or education groups selected from among a parent population is common in health disparities research. One goal of such analyses is to examine measurement equivalence, which includes both qualitative review of the meaning of items as well as quantitative examination of different levels of factorial invariance and differential item functioning.

The purpose of this essay is to review the definitions and assumptions associated with factorial invariance, placing this formulation in the context of bias, fairness, and equity. The connection between the concepts of factorial invariance and item bias (differential item functioning) using a variant of item response theory is discussed. The situations under which different forms of invariance (weak, strong, and strict) are required are discussed.