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The use of sampling weights in M ‐quantile random‐effects regression: an application to Programme for International Student Assessment mathematics scores
Author(s) -
Spagnolo Francesco Schirripa,
Salvati Nicola,
D’Agostino Antonella,
Nicaise Ides
Publication year - 2020
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/rssc.12418
Subject(s) - quantile regression , quantile , multilevel model , sampling (signal processing) , econometrics , statistics , stratified sampling , robustification , mathematics , conditional probability distribution , regression analysis , regression , computer science , filter (signal processing) , computer vision , outlier
Summary M ‐quantile random‐effects regression represents an interesting approach for modelling multilevel data when the researcher is focused on conditional quantiles. When data are obtained from complex survey designs, sampling weights must be incorporated in the analysis. A robust pseudolikelihood approach for accommodating sampling weights in M ‐quantile random‐effects regression is presented. In particular, the method is based on a robustification of the estimating equations. The methodology proposed is applied to the Italian sample of the Programme for International Student Assessment 2015 survey to study the gender gap in mathematics at various quantiles of the conditional distribution. The findings offer a possible explanation of the low proportion of women in science, technology, engineering and mathematics sectors.