Small area prediction based on unit level models when the covariate mean is measured with error

Agencies and policy makers are interested in constructing reliable estimates for areas with small sample sizes, where areas often refer to geographic areas and demographic groups. The estimation for such areas is known as small area estimation. Procedures based on models have been used to construct estimates for the small area means, by exploiting auxiliary information. Mixed models are suitable small area models because they combine different sources of information and contain different sources of error. The models studied in this dissertation are unit level generalized linear mixed models in situations where the mean of an auxiliary variable is subject to estimation error. Different cases of auxiliary information are considered. Prediction methods for the small area mean, estimation of the prediction mean squared error (MSE) and confidence intervals (CIs) for the small area means are presented for the case when the response variable is nonnormal. In the simulation studies, the response variable is binary. In the first study, two methods for constructing small area mean predictions are considered. The first method is based on the conditional distribution of the random area effects given the response variables. The second method, called the ’plug-in method’ is based on the direct substitution of the predicted random area effects into the small area mean expression. Using a simulation study, we show that the ’plug-in’ predictor for the small area mean can have sizeable bias. The estimation of prediction MSE for small area models is complicated, particularly in a nonlinear model setting. In the second study, the efficiency gains associated with the random specification for the auxiliary variable measured with error are demonstrated. The prediction MSE is smaller when additional auxiliary information is available and included in the estimation. The effect of including auxiliary information, if available, in the estimation is smaller for