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Title: Nested error regression model with non ignorable missing values Authors:  Hiromasa Tamae - University of Tokyo (Japan) [presenting]
Shonosuke Sugasawa - University of Tokyo (Japan)
Tatsuya Kubokawa - Faculty of Economics University of Tokyo (Japan)
Abstract: In the context of small area problem, small sample size in each segment, nested error regression model is a powerful tool to build a stable predictor. This, however, assumes that the samples are drawn randomly; seldom achieved in real data survey. Caring selection bias, small area problem can be seen by another aspect: severe missing problem in each area. Unless the missing mechanism is completely random, conventional model does not work well for an accurate inference. We propose a nested error regression model cooperating with non ignorable missing value in which the missing mechanism explicitly expressed as probit regression relating binary observation variables with continuous response variable. For estimation of the model parameters, a Bayesian inference is suggested by setting non-informative prior distributions on the model parameters. To conduct Markov Chain Monte Carlo methods, we construct the Gibbs sampling method for all the full conditional distributions. The proposed model is compared with the standard nested error regression model through numerical simulations.