Bayesian Predictive Inference Under Nine Methods for Incorporating Survey Weights

Sample surveys play a significant role in obtaining reliable estimators of finite population quantities, and survey weights are used to deal with selection bias and non-response bias. The main idea of this research is to compare the performance of nine methods with differently constructed survey weights, and we can use these methods for non-probability sampling after weights are estimated (e.g. quasi-randomization). The original survey weights are calibrated to the population size. In particular, the base model does not include survey weights or design weights. We use original survey weights, adjusted survey weights, trimmed survey weights, and adjusted trimmed survey weights into pseudo-likelihood function to build unnormalized or normalized posterior distributions. In this research, we focus on binary data, which occur in many different situations. A simulation study is performed and we analyze the simulated data using average posterior mean, average posterior standard deviation, average relative bias, average posterior root mean squared error, and the coverage rate of 95% credible intervals. We also performed an application on body mass index to further understand these nine methods. The results show that methods with trimmed weights are preferred than methods with untrimmed weights, and methods with adjusted weights have higher variability than methods with unadjusted weights.