Heteroscedasticity in survey data and model selection based on weighted Schwarz bayesian information criteria

Abstract

This paper proposed Weighted Schwarz Bayesian Information criteria for the purpose of selecting a best model from various competing models, when heteroscedasticity is present in the survey data. The authors found that the information loss between the true model and fitted models are equally weighted, instead of giving unequal weights. The computation of weights purely depends on the differential entropy of each sample observation and traditional Schwarz Bayesian information criteria was penalized by the weight function which comprised of the Inverse variance to mean ratio (VMR) of the fitted log quantiles. The weighted Schwarz Bayesian information criteria was proposed in two versions based on the nature of the estimated error variances of the model namely Homogeneous and Heterogeneous WSBIC respectively. The proposed WSBIC outperforms the traditional information criteria of model selection and it leads to conduct a logical statistical treatment for selecting a best model. Finally this procedure was numerically illustrated by fitting 12 different types of stepwise regression models based on 44 independent variables in a BSQ (Bank service Quality) study.