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ESTIMATION AND STATISTICAL TEST IN BIVARIATE BINARY PROBIT MODEL Ratnasari, Vita; Purhadi, Purhadi; Ismaini, Ismaini; Suhartono, Suhartono
Jurnal ILMU DASAR Vol 12 No 1 (2011)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

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Abstract

One of the models that can be used to analyze two binary response variables data is bivariate binary probit model. This paper tried to estimate the parameters of bivariate binary probit model using Maximum Likelihood Estimationmethod, whereastoget the statistical test using Maximum Likelihood Ratio Test method.
OUTLIER DETECTION IN OBSERVATION AT MULTIVARIATE LINEAR MODELS WITH LIKELIHOOD DISPLACEMENT STATISTIC-LAGRANGE METHOD Makkulau, Makkulau; Linuwih, Susanti; Purhadi, Purhadi; Mashuri, Muhammad
Jurnal ILMU DASAR Vol 12 No 1 (2011)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

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Abstract

There are two different outliers, i.e outlier in observations and outlier in models. The existing outlier detection method in models is using common Likelihood method. The limitation of this method is the optimal value produced might be not the real optimal values. This research yields a method for outlier detection in multivariate linear models with Likelihood Displacement Statistic-Lagrange method (LDL method). This method uses multiplier Lagrange with constraint the confidence interval of parameter?s vector. This parameter?s vector is obtained from the data set which is outlier free. This parameter estimation process uses numerical method with Karush-Kuhn Tucker condition in nonlinear programming. This method compares between LDL value and the table F value that follows the distribution of F value to indentify the outlier in models.
ESTIMASI PARAMETER DAN PENGUJIAN HIPOTESISMODEL REGRESI BURRTIGA PARAMETER TIPE XII Arisandi, Rizwan; Purhadi, Purhadi
Prosiding Seminar Matematika dan Pendidikan Matematik Vol 1, No 1 (2014): Prosiding Seminar Nasional Matematika 2014
Publisher : Prosiding Seminar Matematika dan Pendidikan Matematik

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Abstract

Analisis regresi adalah metode statistik yang berguna untuk memeriksa dan memodelkan hubungan diantara variabel-variabel respon dan prediktor. Model regresi pada umumnya dibangun berdasarkan asumsi bahwa data mengikuti distribusi Normal, namun terbatasnya jumlah data dalam analisis dan pemodelan data statistika membuat asumsi kenormalan tidak tepat digunakan karena mungkin saja distribusi data bersifat menceng (asimetri) dan bahkan bisa juga berekor lebih tebal atau berekor lebih tipis dari distribusi normal (neo normal). Ada beberapa distribusi data yang relaksasinya mampu menangkap pola kemencengan dan ketebalan pada ekor datanya salah satunya adalah distribusi Burr.Ketika pola data menceng atau berekor tebal, pemodelan dan pengolahan data harus dilakukan secara hati-hati. Analisis klasik terutama dengan inferensi statistiknya terhadap parameter model tidak akan memberikan hasil yang lebih baik, oleh sebab itu distribusi Burr dirancang utuk mengatasi pola data yang sedikit miring atau tidak simetri karena distribusi ini didesain sebagai distribusi yang fleksibel dan adaptif. Untuk estimasi parameter regresi Burr menggunakan metode maximum likelihood estimation (MLE), namun hasil yang diperoleh tidak close form sehingga secara numerik digunakan metode iterasi Newton-Raphson. Dalam pengujian hipotesis menggunakan maksimum likelihood Ratio test (MLRT). Uji yang digunakan adalah uji serentak dan parsial yang dilakukan dengan statistik uji yang berdistribusi chi-square. Penelitian ini mengkaji estimasi parameter dan uji hipotesis model regresi Burr tiga parameter tipe XII. Hasil penelitian pada estimasi parameter dibawah populasi yaitu θ =[θ0 , θ1 , θ2 , ..., θJ], l, b dan parameter  di  bawah  H0 yaitu l, b serta perbandingkan nilai lnlikelihood di bawah  H0 dengan  lnlikelihood di  bawah populasi atau dengan perumusan  , pada pengujian hipotesis.
PEMODELAN REGRESI ZERO INFLATED POISSON (APLIKASI PADA DATA PEKERJA SEKS KOMERSIAL DI KLINIK REPRODUKSI PUTAT JAYA SURABAYA) Lestari, Alia; Purhadi, Purhadi; Ratna, Madu
Pythagoras: Jurnal Pendidikan Matematika Vol 5, No 2: Desember 2009
Publisher : Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (333.28 KB) | DOI: 10.21831/pg.v5i2.546

Abstract

Dalam menganalisis hubungan antara beberapa variabel, terdapat sejumlah fenomena dimana variabel responsnya berbentuk biner ataupun berbentuk diskrit. Fenomena dimana variabel responsnya berbentuk diskrit tapi tidak biner, biasanya dianalisis dengan Regresi Poisson. Namun demikian dalam kasus tertentu sering dihadapi suatu peristiwa yang sangat jarang terjadi atau responsnya mempunyai data nol yang sangat banyak, sehingga analisis dengan pendekatan distribusi Poisson seringkali tidak lagi memberikan kesimpulan yang tepat. Pada penelitian ini akan dikaji suatu metode untuk mengatasi banyaknya respons bernilai nol yang telah dikembangkan oleh Lambert (1992) yaitu Regresi Zero-Inflated Poisson (ZIP). Estimasi parameter model ini menggunakan Algoritma EM dan pengujian hipotesisnya menggunakan Likelihood Ratio Test. Aplikasi pada data Pekerja Seks Komersial di Klinik Reproduksi Putat Jaya Surabaya menunjukkan bahwa variabel yang mempengaruhi zero state atau peluang yi bernilai nol sama dengan variabel yang mempengaruhi poisson state atau peluang yi berdistribusi Poisson, yaitu lamanya seorang PSK menjalani profesinya dan proporsi pemakaian kondom. Statistik Vuong yang dihasilkan menunjukkan bahwa Pemodelan Regresi ZIP menghasilkan model yang lebih baik daripada Regresi Poisson.Kata kunci :    Algoritma EM, Pekerja Seks Komersial (PSK), Penyakit Menular Seksual (PMS), Regresi Poisson, Zero Inflated Poisson (ZIP).
PENDETEKSIAN OUTLIER DAN PENENTUAN FAKTOR-FAKTOR YANG MEMPENGARUHI PRODUKSI GULA DAN TETES TEBU DENGAN METODE LIKELIHOOD DISPLACEMENT STATISTIC-LAGRANGE Makkulau, Makkulau; Linuwih, Susanti; Purhadi, Purhadi; Mashuri, Muhammad
Jurnal Teknik Industri Vol 12, No 2 (2010): DECEMBER 2010
Publisher : Institute of Research and Community Outreach - Petra Christian University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (185.131 KB) | DOI: 10.9744/jti.12.2.pp. 95-100

Abstract

There are several problems in industrial process for example problems associated with product quality. In statistics, observation which is significantly different to the average is called outlier. The outlier can give significant influence to the result of modeling, which can affect the decision making. This research develops the outlier detection method using the Likelihood Displacement Statistic method, called Likelihood Displacement Statistic-Lagrange (LDL) method. The LDL method is applied to sugar and molasses production data of Djombang Baru Sugar Factory, Jombang, East Java. The result of this research shows that factors influenced the sugar and molasses production are sugar cane with the dirt less than 5%, sugar cane with the dirt between 5% to 7%, sugar cane with the dirt higher than 7%, and imbibition water
ESTIMASI PARAMETER DAN UJI HIPOTESIS PADA MODEL LINEAR MULTIVARIAT DENGAN METODE LDL Makkulau, Makkulau; Linuwih, Susanti; Purhadi, Purhadi; Mashuri, Muhammad; Pane, Rahmawati
Jurnal Matematika Sains dan Teknologi Vol 11 No 1 (2010)
Publisher : LPPM Universitas Terbuka

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Abstract

Outliers are observations (data) that lies in an abnormal distance from other observations. Outliers can be distinguished into outliers of univariate or multivariate observation and outliers of univariate or multivariate linear models. Multivariate linear model is a linear model with more than one dependent (response) variables. This research studied parameter estimation and hypothesis test for multivariate linear model using Likelihood Displacement Statistic-Lagrange Method called as LDL method for detecting outlier observations in multivariate linear models with the LDLAm statistical test.
OPTIMUM SIMPLEX LATTICE DESIGNS OF LOW ORDER MULTIRESPONSE SURFACE MODEL BY D-OPTIMUM CRITERION Ruslan, Ruslan; Linuwih, Susanti; Purhadi, Purhadi; S, Sony
Jurnal ILMU DASAR Vol 11 No 2 (2010)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

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Abstract

Simplex lattice design is a part of mixture designs has patterns simplex {q, m} where q is number of factors andm is degree of polynomial. If entangling a number of the response variables which measured from a number offactors called the multiresponse surface model, hence to obtain get the matrix designs of optimum mixture atmultiresponse surface model will be used by the optimum-D criterion. In this research, we studied abouttheoretical approach to get optimum simplex lattice design of low order multiresponse surface model byoptimum-D criterion. We assumed that design points have similar weighted values.
Pendeteksian Outlier dan Penentuan Faktor-Faktor yang Mempengaruhi Produksi Gula dan Tetes Tebu dengan Metode Likelihood Displacement Statistic-Lagrange Makkulau, Makkulau; Linuwih, Susanti; Purhadi, Purhadi; Mashuri, Muhammad
Jurnal Teknik Industri Vol 12, No 2 (2010): DECEMBER 2010
Publisher : Institute of Research and Community Outreach - Petra Christian University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (185.131 KB) | DOI: 10.9744/jti.12.2.pp. 95-100

Abstract

There are several problems in industrial process for example problems associated with product quality. In statistics, observation which is significantly different to the average is called outlier. The outlier can give significant influence to the result of modeling, which can affect the decision making. This research develops the outlier detection method using the Likelihood Displacement Statistic method, called Likelihood Displacement Statistic-Lagrange (LDL) method. The LDL method is applied to sugar and molasses production data of Djombang Baru Sugar Factory, Jombang, East Java. The result of this research shows that factors influenced the sugar and molasses production are sugar cane with the dirt less than 5%, sugar cane with the dirt between 5% to 7%, sugar cane with the dirt higher than 7%, and imbibition water
Model Probit Spasial pada Faktor-Faktor yang Mempengaruhi Klasifikasi IPM di Pulau Jawa Puspita, Feni Ira; Ratnasari, Vita; Purhadi, Purhadi
CAUCHY Vol 2, No 4 (2013): CAUCHY
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (973.126 KB) | DOI: 10.18860/ca.v2i4.3116

Abstract

Human pembagunan Index (HDI) is a composite index that includes three basic dimensions of human development is considered to reflect the status of the populations basic abilities of health, educational attainment, and purchasing power. Data IPM classified into four, namely low, lower middle, upper middle, and high. Therefore, determining the HDI can be done with the data probit regression approach. In the data found that there were similarities between the HDI value of geographically adjacent regions which resulted in the classification of the adjacent HDI same region. This is presumably due to the inter-regional dependency. This phenomenon is suspected because of the spatial dependencies can be described through spatial methods. From the explanation above, the HDI of data in this study are based on the spatial probit regression method are compared with the probit method. This study aims to assess the predictors for estimating parameters and testing parameters were applied to the data classification IPM in Java. MCMC is used as a method of estimating the parameters in the assessment. While the assessment test parameters used are 25% to 75% of the estimated parameters
RANCANGAN 2K , 2K-L FAKTORIAL YANG OPTIMALPADA MODEL PERMUKAAN MULTIRESPON ORDE SATU Purhadi, Purhadi; Guritno, Suryo; Linuwih, Susanti
STATISTIKA: Forum Teori dan Aplikasi Statistika Vol 4, No 2 (2004)
Publisher : Program Studi Statistika Unisba

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29313/jstat.v4i2.895

Abstract

parameter pada model permukaan multirespon yang bersifat tidak bias, konsisten dan efisien. Kriteria lain agar matrikrancangan percobaan optimal adalah variansi dari penaksir respon-responnya bernilai minimum. Beberapa rancanganpercobaan model orde satu yaitu rancangan Faktorial, Fraksional faktorial, Simplek dan Placket Burman. Denganmenggunakan pembobotan pada titik-titik percobaan sehingga memenuhi kriteria optimum-D, A, E maka didapatkanmatrik rancangan percobaan yang optimal untuk model permukaan multirespon orde satu. Dengan mengunakan ketigakriteria tersebut didapat hasil nilai determinan matrik informasi yang hampir sama. Eff-D digunakan untukmembandingkan beberapa rancangan percobaan.Apabila penambahan titik-titik percobaan dilakukan hal ini dapat secara proposional sesuai dengan nilai pembobotannyasehingga rancangan percobaan masih optimal. Hal diatas bisa juga dilakukan dengan cara menerapkan Algoritma Fedorovatau Algoritma Fedorov yang dimodifikasi jika matrik variansi kovariansi dari error tidak diketahui.