Diagnostics for heteroscedasticity in regression

SUMMARY For the usual regression model without replication, we provide a diagnostic test for heteroscedasticity based on the score statistic. A graphical procedure to complement the score test is also presented. Some key u'ords: Influence; Linear model; Residual; Score test. Diagnostic methods in linear regression are used to examine the appropriateness of assumptions underlying the modelling process and to locate unusual characteristics of the data that may influence conclusions. The recent literature on diagnostics is dominated by studies of methods for the detection of influential observations. Cook & Weisberg (1982) provide a review. Diagnostics for the relevance of specific assumptions, however, have not received the same degree of attention, even though these may be of equal importance. Our purpose here is to provide appropriate diagnostic techniques to aid in an assessment of the validity of the usual assumption of homoscedasticity when little or no replication is present. Available methods for studying this assumption include both graphical and nongraphical procedures. The usual graphical procedure consists of plotting the ordinary least squares residuals against fitted values or an explanatory variable. A megaphone shaped pattern is taken as evidence that the variance depends on the quantity plotted on tlle abscissa (Weisberg, 1980, Chapter 6). In ? 3 we suggest several ways in which this

[1]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[2]  Anthony C. Atkinson,et al.  Regression Diagnostics, Transformations and Constructed Variables , 1982 .

[3]  D. Pregibon.  Logistic Regression Diagnostics , 1981 .

[4]  T. Hassard,et al.  Applied Linear Regression , 2005 .

[5]  A. C. Atkinson,et al.  Two graphical displays for outlying and influential observations in regression , 1981 .

[6]  T. Hammerstrom.  Asymptotically Optimal Tests for Heteroscedasticity in the General Linear Model , 1981 .

[7]  David Ruppert,et al.  On Robust Tests for Heteroscedasticity , 1981 .

[8]  Heteroscedasticity of residuals: a non-parametric alternative to the goldfeld-quandt peak test , 1981 .

[9]  S. Weisberg,et al.  Characterizations of an Empirical Influence Function for Detecting Influential Cases in Regression , 1980 .

[10]  Wayne A. Fuller,et al.  Least Squares Estimation When the Covariance Matrix and Parameter Vector are Functionally Related , 1980 .

[11]  M. J. Harrison,et al.  A Test for Heteroscedasticity Based on Ordinary Least Squares Residuals , 1979 .

[12]  T. A. Ryan,et al.  Minitab Student Handbook , 1979 .

[13]  P. Bickel,et al.  Using Residuals Robustly I: Tests for Heteroscedasticity, Nonlinearity , 1975 .

[14]  George E. P. Box,et al.  Correcting Inhomogeneity of Variance with Power Transformation Weighting , 1974 .

[15]  Anthony C. Atkinson,et al.  Testing Transformations to Normality , 1973 .

[16]  T. A. Bray,et al.  A Convenient Method for Generating Normal Variables , 1964 .

[17]  F. J. Anscombe,et al.  Examination of Residuals , 1961 .

[18]  J. Durbin,et al.  Testing for serial correlation in least squares regression. II. , 1950, Biometrika.