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In practice many applications of small area models use a `Normal-Normal-Linear' assumption, i.e., a normality assumption for the design-based survey estimates and for the area-level random effects and a linear regression function relating the true parameters to available co-variates. We compare the performance of rate models by slightly changing the assumptions and using internal and external checks, when area sample sizes are in the hundreds, empirical analyses using a 'Normal-t-Linear' to protect against outliers, or a seemingly reasonable `Beta-logistic' assumption for rates, show no gain over the `Normal-Normal-Linear' type model. However, the same type of analyses show additional benefit from including historical data through a cross-sectional and time series model. We use Monte Carlo Markov Chain (MCMC) to implement the proposed models, posterior predictive checks, as well as external checks for model comparisons.
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