Model Geographically Weighted Multivariate t Regression GWMtR)(Studi Kasus: Pemodelan Kemampuan Belajar Mahasiswa Statistika FMIPA Universitas Terbuka)

Abstract

Model regresi linear multivariat biasa digunakan untuk menjelaskan hubungan antara dua atau lebih variabel respon dan satu atau lebih variabel bebas dengan asumsi variabel respon berdistribusi normal. Jika variabel respon berdistribusi t multivariat, maka digunakan model regresi linear t multivariat (MtR). Model MtR perlu dikembangkan untuk data spasial hasil pengukuran yang memuat informasi lokasi geografis (heterogenitas spasial), yakni model Geographically Weighted Multivariate t Regression (GWMtR). Penaksiran parameter model GWMtR dilakukan dengan metode Maximum Likelihood Estimation (MLE) yakni dengan cara memaksimumkan fungsi local ln likelihood dengan pendekatan algoritma Expectation Maximization (EM). Pengujian hipotesis dalam pemodelan GWMtR meliputi uji kesamaan model GWMtR dengan model MtR, uji parameter model secara serentak, dan uji parameter secara parsial yang dilakukan dengan metode Likelihood Ratio Test (LRT). Selain diterapkan pada data simulasi, model GWMtR juga diaplikasikan untuk mengetahui faktor-faktor yang mempengaruhi kemampuan belajar mahasiswa Statistika FMIPA Universitas Terbuka (UT). Hasil penelitian menunjukkan bahwa penaksir parameter model GWMtR dapat diperoleh menggunakan metode MLE dengan pendekatan algoritma EM. Pemodelan kemampuan belajar mahasiswa Statistika FMIPA-UT dengan menggunakan model regresi t multivariat menunjukkan bahwa rata-rata Usia, rata-rata IP Semester 1, rata-rata IP Semester 2, rata-rata SKS Semester 1, dan rata-rata SKS Semester 2 mempunyai pengaruh yang signifikan terhadap rata-rata lama studi, rata-rata IPK, dan rata-rata nilai Tugas Akhir Program (TAP). Hasil yang berbeda diberikan oleh model GWMtR, dimana variabel yang signifikan berbeda untuk masing-masing UPBJJ-UT. ================================================================================================================== Multivariate linear regression models are often used to explain the relationship between two or more response variables and one or more independent variables assuming the response variables follow a normal distribution. If the response variables follow multivariate t distribution, then the multivariate t regression model (MtR) can be used to explain the relationship between two or more response variables and one or more independent variables. If the MtR model is applied to the spatial data of measurement results containing geographic location information (spatial heterogeneity), a Geographically Weighted Multivariate t Regression (GWMtR) model should be developed. Estimation of GWMtR model parameters can be done by Maximum Likelihood Estimation (MLE) method i.e maximizing local ln likelihood function with Expectation Maximization (EM) algorithm approach. Hypothesis testing in GWMtR modeling includes equation test of GWMtR model with MtR model, simultaneous parameter test, and partial parameter test that can be done by Likelihood Ratio Test (LRT) method. While applied to simulation data, GWMtR model also applied to know the factors that influence learning achievement of Statistics Departement's student, Universitas Terbuka (UT). The results showed that the estimator of GWMtR model parameters can be obtained by using MLE method with EM algorithm approach. Modeling of learning achievement of Statistics Department's student using MtR model shows that the independent variables i.e the average age, the average of GPA on first semester, the average of GPA on second semester, the average of study load on first semester, and the average of study load on second semester have significantly influence against the average length of study, the average GPA, and the average of Final Program score (TAP). The GWMtR model shows there are several significant variables for each the local Universitas Terbuka Distance Learning Program Unit (UPBJJ-UT)