Nested generalized linear mixed model with ordinal response: Simulation and application on poverty data in Java Island

Yekti Widyaningsih, Asep Saefuddin, Khairil A. Notodiputro, Aji H. Wigena

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The objective of this research is to build a nested generalized linear mixed model using an ordinal response variable with some covariates. There are three main jobs in this paper, i.e. parameters estimation procedure, simulation, and implementation of the model for the real data. At the part of parameters estimation procedure, concepts of threshold, nested random effect, and computational algorithm are described. The simulations data are built for 3 conditions to know the effect of different parameter values of random effect distributions. The last job is the implementation of the model for the data about poverty in 9 districts of Java Island. The districts are Kuningan, Karawang, and Majalengka chose randomly in West Java; Temanggung, Boyolali, and Cilacap from Central Java; and Blitar, Ngawi, and Jember from East Java. The covariates in this model are province, number of bad nutrition cases, number of farmer families, and number of health personnel. In this modeling, all covariates are grouped as ordinal scale. Unit observation in this research is sub-district (kecamatan) nested in district, and districts (kabupaten) are nested in province. For the result of simulation, ARB (Absolute Relative Bias) and RRMSE (Relative Root of mean square errors) scale is used. They show that prov parameters have the highest bias, but more stable RRMSE in all conditions. The simulation design needs to be improved by adding other condition, such as higher correlation between covariates. Furthermore, as the result of the model implementation for the data, only number of farmer family and number of medical personnel have significant contributions to the level of poverty in Central Java and East Java province, and only district 2 (Karawang) of province 1 (West Java) has different random effect from the others. The source of the data is PODES (Potensi Desa) 2008 from BPS (Badan Pusat Statistik).

Original languageEnglish
Title of host publication5th International Conference on Research and Education in Mathematics, ICREM5
Pages147-154
Number of pages8
DOIs
Publication statusPublished - 12 Jun 2012
Event5th International Conference on Research and Education in Mathematics, ICREM5 - Bandung, Indonesia
Duration: 22 Oct 201124 Oct 2011

Publication series

NameAIP Conference Proceedings
Volume1450
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference5th International Conference on Research and Education in Mathematics, ICREM5
Country/TerritoryIndonesia
CityBandung
Period22/10/1124/10/11

Keywords

  • Generalized linear mixed model
  • Nested
  • Ordinal response

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