A Bayesian Nominal Regression Model with Random Effects for Analysing Tehran Labor Force Survey Data

Large survey data are often accompanied by sampling weights that reflect the inequality probabilities for selecting samples in complex sampling. Sampling weights act as an expansion factor that, by scaling the subjects, turns the sample into a representative of the community. The quasi-maximum likelihood method is one of the approaches for considering sampling weights in the frequentist framework. To obtain it the ordinary log-likelihood is replaced by the weighted log-likelihood. There is a Bayesian framework as a counterpart to quasi-maximum likelihood method is called Bayesian pseudo posterior estimator. This method is the usual Bayesian approach by replacing likelihood with quasi-likelihood function. Another approach for considering sampling weights called the Bayesian weighted estimator. This method is in fact a data augmentation method in which a quasi-representative sample is generated by sampling instead of the observed data using normalized sampling weights. In this paper, these two approaches are used for parameter estimation of a nominal regression model with random effects. The proposed method is applied to small area estimates for the Tehran labor force survey in 2018.