Generalized linear models for small-area estimation

Malay Ghosh, Kannan Natarajan, T. W.F. Stroud, Bradley P. Carlin

Research output: Contribution to journalArticlepeer-review

120 Scopus citations

Abstract

Bayesian methods have been used quite extensively in recent years for solving small-area estimation problems. Particularly effective in this regard has been the hierarchical or empirical Bayes approach, which is especially suitable for a systematic connection of local areas through models. However, the development to date has mainly concentrated on continuous-valued variates. Often the survey data are discrete or categorical, so that hierarchical or empirical Bayes techniques designed for continuous variates are inappropriate. This article considers hierarchical Bayes generalized linear models for a unified analysis of both discrete and continuous data. A general theorem is provided that ensures the propriety of posteriors under diffuse priors. This result is then extended to the case of spatial generalized linear models. The hierarchical Bayes procedure is implemented via Markov chain Monte Carlo integration techniques. Two examples (one featuring spatial correlation structure) are given to illustrate the general method.

Original languageEnglish (US)
Pages (from-to)273-282
Number of pages10
JournalJournal of the American Statistical Association
Volume93
Issue number441
DOIs
StatePublished - Mar 1 1998

Keywords

  • Hierarchical model
  • Markov chain Monte Carlo
  • Posterior propriety
  • Spatial statistics

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