Diagnostics for Nonlinearity and Heteroscedasticity in Errors-in-Variables Regression

Abstract

We suggest new plotting methods for residual analysis in errors-in-variables regression. The standard residuals analyses are based on the methods of Miller and Fuller and are appropriate when the errors in the regression and the measurement error are symmetrically distributed. By “appropriate,” we mean that in large samples the plots will not falsely identify a nonexistent pattern of heteroscedasticity or nonlinearity. The standard methods are not appropriate in this sense for skewed error distributions. Our methods require replication of the error-prone predictors, but they are appropriate for both symmetric and skewed error distributions. Besides residual plots, we also construct hypothesis tests for heteroscedasticity. In terms of power for detecting heteroscedasticity, we show that the standard plot is more efficient when the residuals are normally distributed, although it does not achieve its nominal level for skewed error distributions. Simulations are used to illustrate the results. We also conside...