Does measurement invariance hold for the official Mexican multidimensional poverty measure? A state-level analysis 2012

One of the main goals in poverty measurement is making comparisons of prevalence and severity across geographical units. This is attained by merely disaggregating the index in question. The underlying assumption is that comparisons across units are tenable, inasmuch as the same indicators are utilised for constructing the index. Nonetheless, in practice, this assumption is very rarely tested. From the statistical perspective, measurement invariance (MI) must hold for comparisons to be valid, and violations thereof indicate that a given poverty index measures different things across different countries, states, counties, etc. Consequently, differentials in severity and prevalence cannot be attributed exclusively to the underlying construct (i.e. poverty) but to factors not considered in the measure. This article tests whether MI holds for two indexes: the Mexican official multidimensional measure (MPM) and an adjusted multidimensional measure (MPM-A) that uses less severe thresholds. The analysis is conducted using a novel method called the 'alignment method'. It uses these two measures and the method as an illustration of why it is vital to introduce MI tests into poverty measurement. The results suggest that partial strong MI holds for the official measure and MI is violated when the thresholds are adjusted. Partial strong MI guarantees making valid comparisons across the 32 states. Should the official measure requires to be updated with other thresholds, it would be necessary to adjust the threshold or drop the indicator for water deprivation.