Silva Ana R S, Azevedo Caio L N, Bazán Jorge L, Nobre Juvêncio S
Department of Statistics, State University of Campinas, Campinas, Brazil.
Institute of Mathematical Science and Computing, University of São Paulo, São Paulo, Brazil.
J Appl Stat. 2020 Jun 30;48(11):1998-2021. doi: 10.1080/02664763.2020.1783518. eCollection 2021.
Studies of risk perceived using continuous scales of [0,100] were recently introduced in psychometrics, which can be transformed to the unit interval, but the presence of zeros or ones are commonly observed. Motivated by this, we introduce a full inferential set of tools that allows for augmented and limited data modeling. We considered parameter estimation, residual analysis, influence diagnostic and model selection for zero-and/or-one augmented beta rectangular (ZOABR) regression models and their particular nested models, which is based on a new parameterization of the beta rectangular distribution. Different from other alternatives, we performed maximum-likelihood estimation using a combination of the EM algorithm (for the continuous part) and Fisher scoring algorithm (for the discrete part). Also, we perform an additional step, by considering other link functions, besides the usual logistic link, for modeling the response mean. By considering randomized quantile residuals, (local) influence diagnostics and model selection tools, we identified that the ZOABR regression model is the best one. We also conducted extensive simulations studies, which indicate that all developed tools work properly. Finally, we discuss the use of this type of models to treat psychometric data. It is worthwhile to mention that applications of the developed methods go beyond to Psychometric data. Indeed, they can be useful when the response variable in bounded, including or not the respective limits.
最近在心理测量学中引入了使用[0,100]连续量表来感知风险的研究，该量表可转换为单位区间，但通常会观察到零或一的存在。受此启发，我们引入了一套完整的推理工具集，可用于增强型和有限数据建模。我们考虑了零和/或一增强贝塔矩形（ZOABR）回归模型及其特定嵌套模型的参数估计、残差分析、影响诊断和模型选择，该模型基于贝塔矩形分布的一种新参数化。与其他替代方法不同，我们使用期望最大化（EM）算法（用于连续部分）和费舍尔评分算法（用于离散部分）的组合进行最大似然估计。此外除了通常的逻辑链接外，我们还通过考虑其他链接函数对响应均值进行建模，从而执行额外的步骤。通过考虑随机分位数残差、（局部）影响诊断和模型选择工具，我们确定ZOABR回归模型是最佳模型。我们还进行了广泛的模拟研究，结果表明所有开发的工具都能正常工作。最后，我们讨论了使用这类模型来处理心理测量数据。值得一提的是，所开发方法的应用不限于心理测量数据。实际上，当响应变量有界时，无论是否包括各自的界限，它们都可能有用。
