Heteroscedasticity in Survey Data and Model Selection based on Weighted Schwarz-Bayesian Information Criterion

Abstract

Abstract This paper proposed Weighted Schwarz Bayesian Information criterion 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 criterion 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 criterion 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 is different from the traditional information criterion 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. Keywords: Schwarz Bayesian information criterion, Weighted Schwarz Bayesian information criterion, differential entropy, log-quantiles, variance to mean ratio