Nested Error Regression Models with Missing Values and Non-ignorable Non-response.


Bayesian methods (2)

Hiromasa Tamae (Graduate School of Economics, University of Tokyo) (Speaker)
Shonosuke Sugasawa (Risk Analysis Research Center, The Institute of Statistical Mathematics)
Tatsuya Kubokawa (Faculty of Economics, University of Tokyo)

In most small area estimation problems there is a small sample size in each small area or segment. When the data have a two-level hierarchical structure, the nested error regression model proposed by Battese et al (1998) is a powerful tool for building a stable predictor. This model assumes that the sample is drawn at random with reference to a specified sampling scheme. However if non-response is an issue (which it often is in real-world surveys) and non-response is not completely at random then the model may not work well for accurate inference, i.e., when there is selection bias, small area estimation can be complicated by missing data. To deal with this problem, we introduce a missing mechanism used in Faes and et al (2011) which considers missing explanatory variables, and apply it to the nested error regression model. We propose a nested error regression model, in conjunction with non-ignorable missing response mechanism which is explicitly expressed as probit regression that relates binary observation variables to a continuous response variable.
For estimation of the model parameters, a Bayesian technique with non-informative prior distributions for model parameters is used. For Markov Chain Monte Carlo, we construct the Gibbs sampler for all the full conditional distributions. Under mild condition, it is shown that posterior distribution of the model parameters is proper. The proposed model is compared with the standard nested error regression model through numerical simulations and real data analysis.

Battese, G. E., Harter, R. M., & Fuller, W. A. (1988). An error-components model for prediction of county crop areas using survey and satellite data. Journal of the American Statistical Association, 83(401), 28-36. Faes, C., Ormerod, J. T., & Wand, M. P. (2011). Variational Bayesian inference for parametric and nonparametric regression with missing data. Journal of the American Statistical Association, 106(495), 959-971.
Keywords: Bayesian inference, Gibbs sampling, hierarchical Bayes, Nested error regression model, Missing at random, Probit regression, Variational Bayes.

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