Empirical distribution conditional on group.

Background
Composite multidimensional indices are broadly used to measure child poverty and social exclusion. Many of such indices are based on EU-SILC data or similar large scale complex sampling surveys, with the household as unit of analysis. Indicators related to households with or without children may quantify the intended attribute differently depending on the household structure and characteristics of individuals, potentially compromising the assessment.
Methods
We conducted statistical modelling and hypotheses tests using a two-parameter logistic item response model (IRM) and the likelihood-ratio test for DIF verification. Methods were applied to 2020 EU-SILC Portuguese data comprising 11,367 households representing a population of 4,099,052. Statistical analysis have allowed for the survey sampling design.
Conclusion
Our findings demonstrate differential item functioning in the assessment material deprivation in households with or without children.