The Use of Sampling Weights inM-Quantile Random-Effects Regression: An Application to Programme for International Student Assessment Mathematics Scores

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.

Studying the relationship between anxiety and school achievement: evidence from PISA data

“…This exploratory-correlational study conducted with data from PISA 2015 and based on the W-MQRE regression model proposed by Schirripa Spagnolo et al (2020) used student performance as the response variable and anxiety index as the main explanatory variable. Other individual and school characteristics are used as control factors in the econometric model.…”

“…In other words, classical multilevel models allow us to estimate only the average effect of anxiety on students' achievement in math, literature and science. For this reason, in this paper, we use the M-quantile random effects regression model (MQRE-2L) proposed by Tzavidis et al (2016) and adapted to complex survey designs by Schirripa Spagnolo et al (2020), henceforth model W-MQRE. This approach focuses on the estimation of the regression parameters at different points of the conditional distribution of the outcome variable given the set of regressors.…”

“…(4) and (5) are solved iteratively using the fixed-point iterative method for getting the estimates of the school-and student-level variance, respectively. The variance of the regression parameters is obtained using a sandwich estimator (Schirripa Spagnolo et al 2020). The model has been fitted using a specific function in the statistical programming environment R (R Core Team 2020).…”

“…Robust prediction of random effects at the school level was proposed in Schirripa Spagnolo et al (2020) following the idea of Tzavidis et al (2016) based on the modified Fellner equation Fellner (1986). The estimation of the random-effects is performed separately at each quantile, therefore the vector of school-random effects depends on the q.…”

Studying the relationship between anxiety and school achievement: evidence from PISA data

“…Robust prediction of random eects at the school level was proposed in Schirripa Spagnolo et al (2020) following the idea of Tzavidis et al (2016) based on the modied Fellner equation Fellner (1986).…”