Residual and influence analysis to a general class of simplex regression

Abstract

In this paper, we propose a residual and local influence analysis for diagnostics in a general class of simplex regression model. Here, we introduce this class in which the predictors involve covariates and nonlinear functions in the parameters. We provide closed-form expressions for the score functions, information matrices, as well a procedure for the choice of initial guesses to be used in the Fisher’s iterative scheme for the estimation by maximum likelihood. All diagnostic techniques were also adjusted for the linear simplex model. We present Monte Carlo simulations to investigate the empirical distribution of the proposed residual and the performance of the starting points scheme. We also performed three applications to real data; one of them explores the features of nonlinear regressions. By performing diagnostic analysis, we compare the beta and simplex fits to two datasets. The applications results favor the simplex regression to fit data close to the boundaries of the unit interval. Indeed, the simplex regression can present estimation by maximum likelihood procedure more robust to influential cases than the beta regression.