On nonlinear beta regression residuals

Abstract

We proposed a new residual to be used in linear and nonlinear beta regressions. Unlike the residuals that had already been proposed, the derivation of the new residual takes into account not only information relative to the estimation of the mean submodel but also takes into account information obtained from the precision submodel. This is an advantage of the residual we introduced. Additionally, the new residual is computationally less intensive than the weighted residual. Recall that the computation of the latter involves an n×n matrix, where n is the sample size. Obviously, that can be a problem when the sample size is very large. In contrast, our residual does not suffer from that. It can be easily computed even in large samples. Finally, our residual proved to be able to identify atypical observations as well as the weighted residual. We also propose new thresholds for residual plots and a scheme for the choice of starting values to be used in maximum likelihood point estimation in the class of nonlinear beta regression models. We report Monte Carlo simulation results on the behavior of different residuals. We also present and discuss two empirical applications; one uses the proportion of killed grasshoppers in an assay on the grasshopper Melanopus sanguinipes with the insecticide carbofuran and the synergist piperonyl butoxide, which enhances the toxicity of the insecticide, and the other uses simulated data. The results favor the new methodology we introduce.