Profiling heteroscedasticity in linear regression models

Abstract

AbstractDiagnostics for heteroscedasticity in linear regression models have been intensively investigated in the literature. However, limited attention has been paid on how to identify covariates associated with heteroscedastic error variances. This problem is critical in correctly modelling the variance structure in weighted least squares estimation, which leads to improved estimation efficiency. We propose covariate‐specific statistics based on information ratios formed as comparisons between the model‐based and sandwich variance estimators. A two‐step diagnostic procedure is established, first to detect heteroscedasticity in error variances, and then to identify covariates the error variance structure might depend on. This proposed method is generalized to accommodate practical complications, such as when covariates associated with the heteroscedastic variances might not be associated with the mean structure of the response variable, or when strong correlation is present amongst covariates. The performance of the proposed method is assessed via a simulation study and is illustrated through a data analysis in which we show the importance of correct identification of covariates associated with the variance structure in estimation and inference.The Canadian Journal of Statistics43: 358–377; 2015 © 2015 Statistical Society of Canada