Finding invariance when noninvariance is found: An illustrative example of conducting partial measurement invariance testing with the automation of the factor-ratio test and list-and-delete procedure

Abstract

Comparisons between groups are common in human resource development (HRD) studies, yet many researchers neglect a crucial prerequisite step before analyzing and interpreting what group differences might mean. In essence, how can HRD scholars be confident in knowing that mean group differences are attributable to actual differences between groups as opposed to differences in how each group interprets the constructs of interest? Measurement invariance (MI) provides insight into whether a measure or construct has the same meaning between groups or over time and is an important precursor to the evaluation of group differences. While MI testing has gained some traction within HRD studies, steps to take when partial MI testing is needed have received very little attention. The purpose of this article is to encourage HRD researchers and practitioners to embrace and utilize two techniques when partial invariance (i.e., noninvariance) occurs. There are several techniques one could use during partial MI testing; however, the two showcased herein, the factor-ratio test and the list-and-delete procedure, are established, reliable, and proven within the confirmatory factor analysis framework. This article provides an illustrative example of how to use these techniques to identify invariance at the item level when noninvariance is found. Additionally, R syntax is included that allows for the automation of these techniques. The importance to theory and implications to researchers and practitioners of finding noninvariance and then testing for partial MI is also discussed.