-, Suyitno (2017) Model Geographically Weighted Multivariate Weibull Regression Studi Kasus : Pemodelan Indikator Pencemaran Air (COD, DO, PO4) Pada Air Sungai di Surabaya Tahun 2013. Doctoral thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Penelitian ini membahas model regresi Weibull multivariat (RWM) dan model geographically weighted multivariate Weibull regression (GWMWR). RWM adalah model regresi yang dikembangkan dari distribusi Weibull multivariat, yakni fungsi kepadatan peluang bersama distribusi Weibull multivariat, dengan parameter-parameter skala dinyatakan dalam parameter regresi. Model RWM dikonstruksi dari fungsi survival bersama distribusi Weibull multivariat. Model GWMWR adalah model RWM dengan semua parameter bergantung pada lokasi geografis, dan penaksiran parameter dilakukan secara lokal pada setiap lokasi pengamatan menggunakan pembobot spasial.
Tujuan penelitian ini adalah mendapatkan penaksir parameter model RWM dan GWMWR menggunakan metode maximum likelihood estimation (MLE); mendapatkan statistik uji, distribusi statistik uji dan daerah kritis pengujian hipotesis parameter regresi model RWM; mendapatkan algoritma penaksiran parameter model RWM dan GWMWR; mendapatkan algoritma pengujian hipotesis parameter model RWM; mendapatkan model GWMWR data indikator pencemaran air COD, DO dan PO4 dan mendapatkan faktor-faktor yang berpengaruh terhadap model GWMWR indikator pencemaran air sungai di Surabaya.
Berdasarkan hasil penaksiran parameter disimpulkan bahwa, bentuk eksplisit (closed form) penaksir maximum likelihood model RWM dan GWMWR tidak dapat ditemukan secara analitikal, dan hampiran penaksir parameter kedua model tersebut diperoleh secara numerik dengan metode iteratif Newton-Raphson. Statistik uji pengujian parameter regresi model RWM secara serentak adalah statistik Wilk’s likelihood ratio. Statistik Wilk berdistribusi Khi-kuadrat, dan diturunkan berdasarkan metode likelihood ratio test (LRT). Hasil penghitungan penaksir parameter secara iteratif berdasarkan algoritma Newton-Raphson didapat penaksir parameter model RWM dan GWMWR yang konvergen.
Berdasarkan nilai BIC dan AIC, model GWMWR lebih baik dari pada model RWM dalam pemodelan indikator pencemaran air COD, DO dan PO4. Model GWMWR indikator pencemaran air terbaik diperoleh dari hasil penaksiran parameter menggunakan fungsi pembobot Gauss adaptif. Model GWMWR terbaik dipilih dari hasil-hasil penaksiran parameter dengan pembobot spasial fungsi Gauss adaptif, bi-square adaptif dan tricube adaptif, yang memberikan nilai BIC minimum. Berdasarkan hasil pengujian hipotesis terhadap seluruh parameter regresi disimpulkan bahwa, debit air, konsentrasi deterjen dan TSS berpengaruh signifikan terhadap model GWMWR pada Kali Mas di Jembatan Kebon Rojo; kecepatan aliran air, debit air dan TSS berpengaruh signifikan terhadap model GWMWR pada Kali Makmur di Lidah Kulon dan faktor-faktor yang berpengaruh terhadap model GWMWR pada Kali Surabaya di Kedurus, Kali Surabaya di Jembatan Wonokromo, Kali Mas di Jembatan Ngagel, Kali Mas di Jembatan Keputran Selatan, Saluran Darmo di Pompa air Darmo Kali dan Bozem Kedurus adalah kecepatan aliran air, debit air, konsentrasi deterjen dan TSS.
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This study discusses a multivariate Weibull regression (MWR) and
geographically weighted multivariate Weibull regression (GWMWR) models.
MWR is a regression model developed from a multivariate Weibull distribution,
namely the joint probability density function of the multivariate Weibull
distribution in which the scale parameters are stated in the term of the regression
parameters. The MWR model is constructed from a joint survival function of the
multivariate Weibull distribution. The GWMWR is a MWR model which all of
the parameters depend on the geographical location, and parameter estimation is
done locally at each location in the study area using the spatial weighting.
The aims of this study are to obtain the estimated parameters of the MWR
and GWMWR models using maximum likelihood estimation (MLE) method; to
test the regression parameters of the MWR model; to obtain an algorithm on the
parameter estimation and testing the regression parameter; to obtain the best
model of GWMWR applied to the river water pollution indicators data and to
obtain the factors which influence the GWMWR model applying to the data of the
river water pollution indicators COD, DO and PO4 in the Kali Surabaya.
The result shows that the maximum likelihood estimator for both MWR
and GWMWR models are not closed form, and they can be optimized by using
the Newton-Raphson iterative method. The test statistic for simultaneous test of
the MWR model is Wilk’s likelihood ratio. Wilk statistic follows Chi-square
distribution and it can be derived from the likelihood ratio test (LRT) method. The
result of calculating of the parameter estimation iteratively using the Newton-
Raphson algorithm yields the convergent parameter estimator of the MWR and
GWMWR models.
Based on the BIC and AIC values, the GWMWR model outperforms
RWM model applied to the data of the river water pollution indicators COD, DO
and PO4. The best of GWMWR model is selected from the results of parameter
estimation using the Gaussian weighting function, bi-square and tri-cube adaptive
resulting the minimum BIC. Considering the result of testing regression
parameter, it can be concluded that the river water discharge, detergent and TSS
influence the GWMWR model on the Kali Mas in Kebon Rojo bridge; the speed
of water stream, the river water discharge and TSS influence the GWMWR model
on the Kali Makmur in Lidah Kulon and the factors affecting the GWMWR model
on the Kali Surabaya in Kedurus, Kali Surabaya in Wonokromo bridge, Kali Mas
in Ngagel bridge, Kali Mas in Keputran Selatan bridge, Darmo channel
vi
in Darmo Kali water pump and Bozem Kedurus are the speed of water stream, the
river water discharge, detergent and TSS.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Additional Information: | RDSt 519.536 Suy m-1 |
| Uncontrolled Keywords: | Model RWM, GWMWR, MLE, statistik Wilk, LRT, statistik Wald. |
| Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression |
| Divisions: | Faculty of Mathematics and Science > Statistics > 49001-(S3) PhD Thesis |
| Depositing User: | suyitno - |
| Date Deposited: | 30 Oct 2017 07:19 |
| Last Modified: | 05 Mar 2019 02:59 |
| URI: | http://repository.its.ac.id/id/eprint/42212 |
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