# The use of sampling weights in the M-quantile random-effects regression: an application to PISA mathematics scores

## TL;DR

This paper introduces a pseudo-likelihood method for incorporating sampling weights into M-quantile random-effects regression, applied to PISA data to analyze gender gaps in mathematics across different score quantiles.

## Contribution

It develops a novel approach to handle sampling weights in M-quantile random-effects models for complex survey data.

## Key findings

- Identified gender gaps in mathematics at various quantiles.
- Provided insights into low female participation in STEM fields.
- Demonstrated the methodology on PISA Italian data.

## Abstract

M-quantile random-effects regression represents an interesting approach for modelling multilevel data when the interest of researchers is focused on the conditional quantiles. When data are based on complex survey designs, sampling weights have to be incorporate in the analysis. A pseudo-likelihood approach for accommodating sampling weights in the M-quantile random-effects regression is presented. The proposed methodology is applied to the Italian sample of the "Program for International Student Assessment 2015" survey in order to study the gender gap in mathematics at various quantiles of the conditional distribution. Findings offer a possible explanation of the low share of females in "Science, Technology, Engineering and Mathematics" sectors.