Robust Measurement Invariance Testing

Classic measurement invariance tests assume data follow a multivariate normal distribution. Real survey data — Likert items, attitude scales, clinical ratings — rarely do. When normality is violated, ordinary chi-square statistics are inflated, leading researchers to reject perfectly adequate models. Robust measurement invariance testing corrects for this inflation using a scaling factor estimated from the data's actual kurtosis. The logic of the invariance hierarchy (configural, metric, scalar) stays exactly the same; only the test statistic and the way differences between nested models are computed change. The result is a trustworthy verdict on whether item properties are group-invariant even when the data are messy.