Generalized Linear Mixed Models by penalized Lasso in modelling the scores of Indonesian students

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 over dispersion. Severe computational problems in the GLMM modelling 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 essential in modelling. The use of penalty techniques for selecting variables in mixed models is still rarely applied. In this article, the penalized Lasso approach 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 significant covariates for the GLMM model while GLMM without penalized Lasso has five covariates, which means that the GLMM model is more complicated than glmmLasso. Gender, school quality based on National Examination (UN) scores and the opportunity for students to investigate to test their ideas are essential covariates as factors that influence the rating of Indonesian students.

Restricted Maximum Likelihood Estimation for Multivariate Linear Mixed Model in Analyzing Pisa Data for Indonesian Students

“…The results of the chi-square count are 56791.8 with a p-value of 0.00 <0.05, so that it can be said that there is a significant effect of all model parameters simultaneously on the three response variables, including father's education, internet access, facilities at home, and the age of entering kindergarten (TK). These findings are in line with research conducted by Pakpahan [8], Santi et al [9], and Santi et al [10]. Based on Table 4 above, the estimation of the variance of random effects obtained from the three responses, the literacy scores of mathematics, science, and reading are 1548.12, 1359.39, and 1082.48, respectively, which involved a random effect in the form of 389 schools as well as the value of the variance of both the random effect and the residual variance that was not equal to zero indicating a relationship between the three response variables used.…”

“…Meanwhile, Santi et al [9] produced 11 factors that significantly influenced the scientific literacy score. Santi et al [10] modeled PISA data using the Generalized Linear Mixed Model (GLMM) involving random effects on univariate response variables. Until now, studies on quantitative PISA data scores have been extremely rare.…”

Multilevel Regression With Maximum Likelihood and Restricted Maximum Likelihood Method in Analyzing Indonesian Reading Literacy Scores

“…The results of testing the significance of parameters partially using the t-test showed that there are 12 explanatory variables level-1 that significantly affect the reading literacy score of students, namely, gender (X1), grade level (X2), mother education (X3), study desk at home (X5), many mobile phones with internet access at home (X7), many computers at home (X8), many books at home (X9), age of entry to early childhood education (X10), age of entry to elementary school (X11), not listening to teachers (X12), skipping school (X13), and failing grade (X15) and there are 2 explanatory variables level-2 that significantly affect the reading literacy score of students, namely, the type of school (Z1) and the location of school (Z2). Based on the results of this study are in line with research conducted by [12], [13], [14], and [15]. Based on Table 5, estimation variance components for every level in a random intercept model with explanatory variables (model 2), where the estimate of level-1 (students) residual variance shows the diversity of reading literacy scores between students in schools (σ ̂e 2 = 2.757,299), while the estimation level-2 (school) residual variance shows the diversity of the average reading literacy scores between schools (σ ̂uo 2 = 1.270,383).…”

“…The research on PISA survey data that has been carried out by [12], [13], [14], and [15] can only find out the student factors that have a significant effect on PISA scores. So it is necessary to do further analysis to find out not only student factors but also school factors that have a significant effect on PISA scores.…”

Penerapan Regresi Least Absolute Shrinkage And Selection Operator (LASSO) Untuk Mengidentifikasi Variabel Yang Berpengaruh Terhadap Kejadian Stunting di Indonesia

“…Kelebihan dari regresi LASSO, yaitu dapat digunakan untuk menyeleksi variabel bebas dalam model, sehingga hanya variabel berpengaruh yang dimasukkan dalam model dan memudahkan dalam menginterpretasikan model regresi. Penalti yang paling terkenal adalah metode LASSO karena perhitungannya cepat untuk menyelesaikan masalah pengoptimalan kecembungan (Santi et al, 2019). Perhitungan yang tepat dalam metode LASSO untuk menjadi lebih baik adalah menggunakan algoritma LAR.…”