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Non‐parametric generalized linear mixed models in small area estimation
Author(s) -
Torabi Mahmoud,
Shokoohi Farhad
Publication year - 2015
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11236
Subject(s) - small area estimation , covariate , statistics , generalized linear mixed model , estimation , mixed model , spline (mechanical) , linear model , mathematics , linear regression , parametric statistics , econometrics , regression analysis , computer science , engineering , estimator , systems engineering , structural engineering
Mixed models are commonly used for the analysis of small area estimation. In particular, small area estimation has been extensively studied under linear mixed models. Recently, small area estimation under the linear mixed model with penalized spline (P‐spline) regression model, for fixed part of the model, has been proposed. However, in practice there are many situations that we have counts or proportions in small areas; for example a dataset on the number of asthma physician visits in small areas in Manitoba. In particular, the covariates age, genetic, environmental factors, among other covariates seem to predict asthma physician visits, however, these relationships may not be linear (see Section 5). In this paper, small area estimation under generalized linear mixed models using P‐spline regression models is proposed to cover Normal and non‐Normal responses. In particular, the empirical best predictor of small area parameters with corresponding prediction intervals are studied. The performance of the proposed approach is evaluated through simulation studies and also by a real dataset. The Canadian Journal of Statistics 43: 82–96; 2015 © 2015 Statistical Society of Canada