## Non‐parametric generalized linear mixed models in small area estimation

Mahmoud Torabi, Farhad Shokoohi: Non‐parametric generalized linear mixed models in small area estimation. In: The Canadian Journal of Statistics, 43 , pp. 82–96, 2015.

## Abstract

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.

```@article{Shokoohi2015CJS,
title = {Non‐parametric generalized linear mixed models in small area estimation},
author = {Mahmoud Torabi and Farhad Shokoohi},
doi = {10.1002/cjs.11236},
year  = {2015},
date = {2015-01-14},
journal = {The Canadian Journal of Statistics},
volume = {43},
pages = {82–96},
abstract = {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.},
keywords = {Bayesian computation, Exponential family, Penalized spline, Prediction interval, Random effects, Small-area estimation},
pubstate = {published},
tppubtype = {article}
}
```