Testing inference in variable dispersion beta regressions
Testing inference in variable dispersion beta regressions
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DOI：
10.1080/00949655.2011.599033
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发表时间：
2012-11
影响因子：
1.2
通讯作者：
Francisco Cribari‐Neto;Tatiene C. Souza
中科院分区：
文献类型：
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作者：
Francisco Cribari‐Neto;Tatiene C. Souza
Ferrari和Cribari-Neto提出的一类beta回归模型[用于比率和比例建模的beta回归，Journal of Applied Statistics 31(2004)，第799-815页]对于在标准单位区间（0,1）中假设值的数据建模是有用的。因变量通过链接函数与线性预测器相关，线性预测器包括回归量和未知参数。该模型还通过精度参数进行索引，该参数通常对所有观测值都是恒定的。然而，一些作者使用了可变分散beta回归模型，即包括精度参数的回归子模型的模型。在本文中，我们展示了如何在不需要对数据精度建模的情况下对索引均值子模型的参数进行测试推理。这种策略很有用，因为通常比平均效应更难建模离散效应。所提出的推理程序即使在变色散情况下也是准确的。我们提出了广泛的蒙特卡罗模拟的结果，其中我们的测试策略与从业者对潜在分散进行建模然后执行测试推理的测试策略形成对比。还介绍和讨论了一个使用真实（非模拟）数据的经验应用。
The class of beta regression models proposed by Ferrari and Cribari-Neto [Beta regression for modelling rates and proportions, Journal of Applied Statistics 31 (2004), pp. 799–815] is useful for modelling data that assume values in the standard unit interval (0, 1). The dependent variable relates to a linear predictor that includes regressors and unknown parameters through a link function. The model is also indexed by a precision parameter, which is typically taken to be constant for all observations. Some authors have used, however, variable dispersion beta regression models, i.e., models that include a regression submodel for the precision parameter. In this paper, we show how to perform testing inference on the parameters that index the mean submodel without having to model the data precision. This strategy is useful as it is typically harder to model dispersion effects than mean effects. The proposed inference procedure is accurate even under variable dispersion. We present the results of extensive Monte Carlo simulations where our testing strategy is contrasted to that in which the practitioner models the underlying dispersion and then performs testing inference. An empirical application that uses real (not simulated) data is also presented and discussed.