  In this paper, we propose a simplex regression model in which both the mean
and the dispersion parameters are related to covariates by nonlinear
predictors. We provide closed-form expressions for the score function, for
Fisher's information matrix and its inverse. Some diagnostic measures are
introduced. We propose a residual, obtained using Fisher's scoring iterative
scheme for the estimation of the parameters that index the regression nonlinear
predictor to the mean response and numerically evaluate its behaviour. We also
derive the appropriate matrices for assessing local influence on the parameter
estimates under different perturbation schemes. We also proposed a scheme for
the choice of starting values for the Fisher's iterative scheme for nonlinear
simplex models. The diagnostic techniques were applied on actual data. The
local influence analyses reveal that the simplex models can be a modeling
alternative more robust to influential cases than the beta regression models,
both to linear and nonlinear models.
