Sugiarti, Harmi (2018) Model Geographically Weighted Multivariate t Regression GWMtR)(Studi Kasus: Pemodelan Kemampuan Belajar Mahasiswa Statistika FMIPA Universitas Terbuka). Doctoral thesis, Institut Teknologi Sepuluh Nopember.
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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).
| Item Type: | Thesis (Doctoral) |
|---|---|
| Additional Information: | RDSt 519.535 Sug m |
| Uncontrolled Keywords: | regresi t multivariat; spasial heterogenitas; GWtR; GWMtR; Multivariate t regression; spatial heterogeneity |
| Subjects: | Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression Q Science > QA Mathematics > QA278 Cluster Analysis. Multivariate analysis. Correspondence analysis (Statistics) |
| Divisions: | Faculty of Mathematics, Computation, and Data Science > Statistics > 49001-(S3) PhD Thesis |
| Depositing User: | Sugiarti Harmi |
| Date Deposited: | 26 Apr 2018 02:59 |
| Last Modified: | 30 Jun 2020 07:12 |
| URI: | http://repository.its.ac.id/id/eprint/51118 |
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