A generalized linear mixed model for understanding determinant factors of student's interest in pursuing bachelor's degree at Universitas Syiah Kuala

Abstract

Generalized Linear Mixed Model (GLMM) is a framework that has a response variable, fixed effects, and random effects. The response variable comes from an exponential family, whereas random effects have a normal distribution. Estimating parameters can be calculated using the maximum likelihood method using the Laplace approach or the Gauss-Hermite Quadrature (GHQ) approach. The purpose of this study was to identify factors that trigger student's interest to continue studying at Universitas Syiah Kuala (USK) using both techniques. The GLMM is suitable for the data because the variable response has a Bernoulli distribution, and the random effects are assumed to be having a normal distribution. Also, the model helps identify the relationship between the dependent variable and the predictors. This study utilizes data from six high schools in Banda Aceh city drawn using a two-stage sampling technique. Stage 1, we randomly chose six out of sixteen public senior high schools in Banda Aceh. Stage 2, we selected students from each school from four different major classes. The GLMM model includes one binary response variable, five numerical fixed-effects, and two random effects. The response variable is the interest of high school students to continue study at USK (yes or no). The five fixed effects in the model including scores of collaboration (C), Action (A), Emotion (E), Purposes (P), and Hope (H). Finally, the random effects are schools (S) and majors (M). In this study, both Laplace and GHQ techniques produce identical results. The predictors that can explain student interest are A, E, and H. These predictors have a positive effect. The random effects of schools and majors are not significantly different from zero. The model with three significant predictors is better than the complete predictor model.

Copula-Based Prediction of Small Area Estimation for Youth Mean Years of Schooling in West Java Province

“…The application of small area estimation models in this research, namely nested error regression compared to the exchangeable copula model in the case of the response variable for the youth mean years of schooling in West Java Province, produces the best model, namely the nested error regression model. This result is different from the previous research results, which state that the exchangeable copula model has better performance than the nested error regression model [2] [3] [17]. The difference in the results of this study is likely due to differences in the distribution of the response variables in the research that had a symmetrical normal distribution, whereas, in the three previous studies, the response variable was a normal distribution with a skewness.…”