Multivariate Linear Mixed Models with Maximum Likelihood Method in Analyzing Indonesian PISA Data Vera Maya Santi (a*), Irsyad Hasari (a), Dian Handayani (a), Widyanti Rahayu (a)
a) Program Studi Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Negeri Jakarta, Jl. Rawamangun Muka, Kota Jakarta Timur, DKI Jakarta, 13220, Indonesia
*vmsanti[at]unj.ac.id
Abstract
Multiple linear regression is usually used to analyze data with a normal distribution response variable. The results of the PISA survey have several numerical responses so as to form a multivariate data structure. The complexity of PISA data increases when it involves random effect within the model. Multivariate mixed linear models is a model that can be used in multivariate data structures with random effects. Quantitative analysis of PISA data, especially multivariate analysis, is still very rarely studied. This article proposes to analyze the data from the PISA survey using the Maximum Likelihood parameter estimation method with the Newthon Raphson algorithm within the framework of a multivariate mixed linear models. The results of the analysis show that the level of education, parental education, internet access, cellphones, books and e-books, student behavior, kindergarten entry age, and class stay during elementary school are factors that affect the scores of mathematical literacy, reading literacy and science literacy simultaneously. Random effect also exert significant effect based on model diagnostic criteria including multivariate normal residual and heteroscedasticity
Keywords: Diagnostic model- PISA score- Multivariate Linear Mixed Models- Newthon-Raphson- random effect
