Testing for Heteroscedasticity in Nonlinear Regression Models

Abstract

Homogeneity of variance is one of standard assumptions in regression analysis. However, this assumption is not necessarily appropriate. Cook and Weisberg (Cook, R. D., Weisberg, S. (1983). Diagnostics for heteroscedasticity in regression. Biometrika 70:1–10) provided a score test for heteroscedasticity in linear regression. Smith and Heitjan (Smith, P. J., Heitjan, D. F. (1993). Testing and adjusting for departures from nominal dispersion in generalized linear models. Applied Statistics 42:31–41) proposed a method based on the randomization of regression coefficients for detecting departures from nominal dispersion in generalized linear models. This paper is devoted to the tests for non-constant variance in the framework of nonlinear regression models (NLMs). We characterize three types of possible heterogeneity of variance in NLMs. One type is to introduce a variance function for the model, which is the extension of Cook and Weisberg (1983). The other two are based on the randomization of regression coefficients and variance parameters respectively, which are extensions of Smith and Heitjan (1993). For three types of heteroscedasticity, several score tests are developed and illustrated with European rabbit data (Ratkowsky, D. A. (1983). Nonlinear Regression Modelling. New York: Marcel Dekker, 108). The properties of test statistics are investigated through Monte Carlo simulations.

Keywords:

• Heteroscedasticity
• Nonlinear models
• Randomization
• Regression coefficients
• Score test
• Simulation study
• Variance function.

Acknowledgments

The authors gratefully acknowledge the Editor, Associate Editor and referees for their valuable comments and suggestions that substantially improved the paper. This work is supported in part by NNSFC (19631040) and NSSFC (02BTJ001).