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.

中文翻译：

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一般单形回归的残差和影响分析

在本文中，我们提出了一般类单纯形回归模型中用于诊断的残差和局部影响分析。在这里，我们介绍此类，其中预测变量在参数中涉及协变量和非线性函数。我们提供分数函数，信息矩阵的封闭式表达式，以及用于选择费舍尔迭代方案中用于通过最大似然估计的初始猜测的过程。还针对线性单纯形模型调整了所有诊断技术。我们目前进行蒙特卡洛模拟，以研究建议残差的经验分布和起点方案的性能。我们还对真实数据执行了三个应用程序；其中之一探讨了非线性回归的特征。通过执行诊断分析，我们将beta和单纯形拟合与两个数据集进行比较。应用结果有利于单纯形回归，以使数据适合单位间隔的边界附近。确实，单纯形回归可以通过最大似然程序来提供比β回归对影响案例更可靠的估计。