Model misspecification in parametric dual modeling

Abstract

In typical normal theory regression, the assumption of homogeneity of variances is often not appropriate. Instead of treating the variances as a nuisance and transforming away the heterogeneity, the structure of the variances may be of interest and it is desirable to model the variances. Simultaneous modeling of the mean and variance of a response is known as dual modeling. When parametric models for the mean and variance are prescribed, estimation of the mean and variance parameters are interrelated. One commonly used dual model assumes a linear model for the mean and a log-linear variance model (Aitkin, 1987). This paper considers the impact of model misspecification (mean and variance) on the dual model estimation procedure. Asymptotic expressions for the mean and variance estimates, graphical illustrations of the impact of model misspecification, and simulation results are presented.

Keywords:

• Heteroscedasticity
• variance estimation
• regression
• generalized linear model

^*Coressponding author

^*Coressponding author

Notes

^*Coressponding author