PENERAPAN MODEL SPATIAL LOGIT-NORMAL PADA SMALL AREA ESTIMATION DENGAN METODE HIERARCHICAL BAYES

Penelitian ini menerapkan model Spatial Logit-normal pada Small Area Estimation (SAE) untuk estimasi proporsi penduduk dengan asupan kalori minimum di bawah 1.400 kkal/kapita/hari pada level kecamatan di Provinsi Bali Tahun 2014 yang merupakan indikator 2.1.2(A) pada tujuan ke-2 SDGs dalam rangka mengukur capaian dan mendukung tercapainya target SDGs pada level lebih tinggi. Terdapat tiga model SAE yang digunakan dengan spesifikasi random effect yang berbeda, yaitu model dengan random effect yang bersifat saling bebas (independen), spatial random effect (iCAR) serta model dengan kedua jenis random effect sekaligus (BYM). Penggunaan unsur spatial random effect diharapkan dapat meningkatkan efisiensi hasil estimasi. Metode estimasi menggunakan pendekatan Hierarchical Bayes (HB) dengan metode Markov Chain Monte Carlo (MCMC) algoritma Gibbs Sampling. Estimasi parameter pada ketiga model menunjukkan hasil yang relatif tidak berbeda dimana hanya ada satu variabel prediktor yang memiliki pengaruh signifikan, yaitu proporsi keluarga pertanian, pada model dengan random effect independen dan model BYM. Sedangkan pada model iCAR tidak ada satu pun variabel prediktor yang berpengaruh signifikan. Berdasarkan nilai Deviance Information Criterion (DIC), model terbaik adalah model BYM. Akan tetapi penambahan unsur spatial random effect bersamaan dengan random effect independen tidak secara signifikan dapat meningkatkan efisiensi hasil estimasi akibat dari minimnya nilai dependensi spasial Moran’s I. Secara visual, pemetaan hasil estimasi dengan model terbaik tidak menunjukkan adanya pola persebaran atau pengelompokan tertentu pada level kecamatan.

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PENDUGAAN ANGKA KEMISKINAN DI KABUPATEN PADANG PARIAMAN MENGGUNAKAN SMALL AREA ESTIMATION DENGAN PENDEKATAN HIERARCHICAL BAYESIAN (HB) LOGLOGISTIK

Jurnal Matematika UNAND ◽

10.25077/jmu.8.2.76-83.2019 ◽

2019 ◽

Vol 8 (2) ◽

pp. 76

Author(s):

Jusri Repi Basri Yuliani ◽

Maiyastri Maiyastri ◽

Rita Diana

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Gibbs Sampling ◽

Standard Error ◽

Small Area ◽

Small Area Estimation ◽

Hierarchical Bayesian ◽

Area Estimation ◽

Level Model

Penelitian ini mengkaji tentang pendekatan Hierarchical Bayesian (HB) Loglogistik yang diaplikasikan pada Small Area Estimation (SAE) dengan tujuan mengestimasi tingkat kemiskinan di Kabupaten Padang Pariaman. Metode pendugaan area kecil yang digunakan pada penelitian ini adalah model level area dasar (basic area level model ) dengan bantuan variabel penyerta yang tersedia pada level kecamatan. Variabel penyerta yang digunakan pada penelitian ini yaitu rasio SLTA/Sederajat (X1), persentase keluarga pertanian (X2), rasio industri mikro kecil (X3), persentase buruh tani dalam setiap anggota keluarga (X4), kepadatan penduduk (X5), dan persentase penduduk pelanggan listrik PLN (X6). Bentuk integrasi yang kompleks dari sebaran peluang bersyarat pada model diselesaikan menggunakan Markov Chain Monte Carlo (MCMC) dengan menerapkan algortima Gibbs Sampling dan bantuan software WinBugs 1.4.3. Hasil estimasi menggunkan model HB yang diperoleh dibandingkan dengan hasil estimasi pendugaan langsung dengan memperhatikan nilai standard error sebagai tolok ukurnya. Hasil pendugaan tingkat kemiskinan untuk level kecamatan di Kabupaten Padang Pariaman dengan model HB menunjukkan nilai standard error yang kecil.Kata Kunci: Tingkat kemiskinan, Small Area Estimation, Hierarchical Bayesian

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Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation

Mathematics ◽

10.3390/math9030248 ◽

2021 ◽

Vol 9 (3) ◽

pp. 248

Author(s):

Reem Aljarallah ◽

Samer A Kharroubi

Keyword(s):

Monte Carlo ◽

Down Syndrome ◽

Mental Retardation ◽

Markov Chain ◽

Markov Chain Monte Carlo ◽

Univariate Analysis ◽

Deviance Information Criterion ◽

Predictive Ability ◽

Information Criterion ◽

Medical Genetic

Logit, probit and complementary log-log models are the most widely used models when binary dependent variables are available. Conventionally, these models have been frequentists. This paper aims to demonstrate how such models can be implemented relatively quickly and easily from a Bayesian framework using Gibbs sampling Markov chain Monte Carlo simulation methods in WinBUGS. We focus on the modeling and prediction of Down syndrome (DS) and Mental retardation (MR) data from an observational study at Kuwait Medical Genetic Center over a 30-year time period between 1979 and 2009. Modeling algorithms were used in two distinct ways; firstly, using three different methods at the disease level, including logistic, probit and cloglog models, and, secondly, using bivariate logistic regression to study the association between the two diseases in question. The models are compared in terms of their predictive ability via R2, adjusted R2, root mean square error (RMSE) and Bayesian Deviance Information Criterion (DIC). In the univariate analysis, the logistic model performed best, with R2 (0.1145), adjusted R2 (0.114), RMSE (0.3074) and DIC (7435.98) for DS, and R2 (0.0626), adjusted R2 (0.0621), RMSE (0.4676) and DIC (23120) for MR. In the bivariate case, results revealed that 7 and 8 out of the 10 selected covariates were significantly associated with DS and MR respectively, whilst none were associated with the interaction between the two outcomes. Bayesian methods are more flexible in handling complex non-standard models as well as they allow model fit and complexity to be assessed straightforwardly for non-nested hierarchical models.

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Small area estimation of general parameters with application to poverty indicators: A hierarchical Bayes approach

The Annals of Applied Statistics ◽

10.1214/13-aoas702 ◽

2014 ◽

Vol 8 (2) ◽

pp. 852-885 ◽

Cited By ~ 37

Author(s):

Isabel Molina ◽

Balgobin Nandram ◽

J. N. K. Rao

Keyword(s):

Small Area ◽

Small Area Estimation ◽

Hierarchical Bayes ◽

Area Estimation ◽

Poverty Indicators ◽

Bayes Approach

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Expenditure Per Capita Model with Spatial Small Area Estimation

Parameter: Journal of Statistics ◽

10.22487/27765660.2021.v1.i2.15502 ◽

2021 ◽

Vol 1 (2) ◽

pp. 38-47

Author(s):

Ahmad Risal

Keyword(s):

Small Area ◽

Spatial Information ◽

Small Area Estimation ◽

Random Effect ◽

Development Program ◽

Data Availability ◽

Estimation Model ◽

Policy Makers ◽

Area Estimation ◽

Direct Estimation

Indonesia is one of many countries around the world that attempt to suffer from high poverty rates. Since, poverty information in a certain area is a point of interest to researchers and policy makers. One problem faced is for the development program to be carried out more effectively and efficiently, it is necessary to have data availability up to the micro-scale. The technique used to reach the goal is Small Area Estimation (SAE). Fay-herriot (FH) model is one method on Small Area Estimation. Since, the SAE techniques require “borrow strength” across neighbor areas so thus Fay-Herriot model approach was developed by integrating spatial information into the model. This method known as Spatial Fay-Herriot Model (SFH) or Spatial Empirical Best Linear Unbiased Prediction (SEBLUP). This study aims to compare MSE of direct estimation, FH, and SFH Model to see which method gives the best result in estimating expenditure. The MSE value of the estimated SFH is smaller than direct estimation and FH, but it does not significant. It means adding spatial information in the small area estimation model does not give a better prediction than the simple small area estimation which is takes account the area as a specific random effect.

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