Generalized Linear Mixed Models by Penalized Lasso in Modeling the Scores of Indonesian Students
Vera Maya Santi(a*), Khairil Anwar Notodiputro(b), Bagus Sartono(b), Widyanti Rahayu(a)

a) Program Studi Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Negeri Jakarta
*vmsanti[at]unj.ac.id
b) Departemen Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Institut Pertanian Bogor

Abstract

The Generalized linear mixed model (GLMM) is an extension of the Generalized linear model by adding random effects to linear predictors to accommodate clustered or overdispersion. Severe computational problems in the GLMM modeling cause its use restricted for only a few predictors. When many predictors are available, the estimators become very unstable. Therefore, the procedure for selecting relevant variables is important in modeling. The use of penalty techniques for selecting variables in mixed models is still rarely applied. In this article, penalized Lasso approach are proposed to handle these kinds of problems. The proposed methods select variables and estimate coefficients simultaneously in GLMM. Based on the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and standard error criteria, it was found that glmmLasso has a better performance than GLMM. For the factors affecting Indonesian’s student scores, where glmmLasso produces three important covariates for the GLMM model while GLMM without penalized Lasso has five covariates which mean that the GLMM model is more complex than glmmLasso. Gender, school quality based on National Examination scores and the opportunity for students to investigate to test their ideas are important covariates as factors that influence the score of Indonesian students.

Keywords: Generalized Linear Mixed Models; glmmLasso; Penalty; Variable Selection;the score of Indonesian students

Topic: Mathematics