Modelling Variance Heterogeneity: Residual Maximum Likelihood and Diagnostics

• Published in: Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1993-01, Vol.55 (2), p.493-508
• Main Author: Verbyla, A. P.
• Format: Article
• Language: English
• Subjects: Approximation; diagnostics; Estimators for the mean; Exact sciences and technology; Graph theory; Linear inference, regression; Linear models; log‐linear model; Mathematics; maximum likelihood; Maximum likelihood estimation; Parametric models; Probability and statistics; regression; Regression analysis; residual maximum likelihood; Sciences and techniques of general use; score test; Statistical discrepancies; Statistical variance; Statistics; Variance; variance heterogeneity; variance model
• ISSN: 0035-9246; 1369-7412; 2517-6161; 1467-9868
• DOI: 10.1111/j.2517-6161.1993.tb01918.x

The assumption of equal variance in the normal regression model is not always appropriate. To attempt to eliminate unequal variance a transformation is often used but if the transformation is not successful, or the variances are of intrinsic interest, it may be necessary to model the variances in some way. We consider the normal regression model when log-linear dependence of the variances on explanatory variables is suspected. Detection of the dependence, estimation and tests of homogeneity based on full and residual maximum likelihood are discussed as are regression diagnostic methods based on case deletion and log-likelihood displacement. Whereas the behaviour of full and residual maximum likelihood is similar under case deletion, changes in residual maximum likelihood estimates and log-likelihood displacements tend to be smaller than maximum likelihood.