We propose a multivariate regression model to deal with multiple continuous bounded data. The proposed model is based on second-moment assumptions, only. We adopted the quasi-score and Pearson estimating functions for estimation of the regression and dispersion parameters, respectively. Thus, the proposed approach does not require a multivariate probability distribution for the variable response vector. The multivariate quasi-beta regression model can easily handle multiple continuous bounded outcomes taking into account the correlation between the response variables. Furthermore, the model allows us to analyze continuous bounded data on the interval [0, 1], including zeros and/or ones. Simulation studies were conducted to investigate the behavior of the NORmal To Anything (NORTA) algorithm and to check the properties of the estimating function estimators to deal with multiple correlated response variables generated from marginal beta distributions. The model was motivated by a data set concerning the body fat percentage, which was measured at five regions of the body and represent the response variables. We analyze each response variable separately and compare it with the fit of the multivariate proposed model. The multivariate quasi-beta regression model provides better fit than its univariate counterparts, as well as allows us to measure the correlation between response variables. Finally, we adapted diagnostic tools to the proposed model. In the supplementary material, we provide the data set and R code.

中文翻译：

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连续有界数据的多元准β回归模型

我们提出了一种多元回归模型来处理多个连续有界数据。所提出的模型仅基于二阶矩假设。我们分别采用了 quasi-score 和 Pearson 估计函数来估计回归和离散参数。因此，所提出的方法不需要可变响应向量的多元概率分布。考虑到响应变量之间的相关性，多元准 beta 回归模型可以轻松处理多个连续有界结果。此外，该模型允许我们分析区间 [0, 1] 上的连续有界数据，包括零和/或一。进行了模拟研究以研究 NORmal To Anything (NORTA) 算法的行为，并检查估计函数估计器的属性，以处理从边际 Beta 分布生成的多个相关响应变量。该模型受有关体脂百分比的数据集的启发，该数据集在身体的五个区域测量并代表响应变量。我们分别分析每个响应变量，并将其与多变量建议模型的拟合进行比较。多元准 beta 回归模型比其单变量对应模型提供更好的拟合，并允许我们测量响应变量之间的相关性。最后，我们根据建议的模型调整了诊断工具。在补充材料中，我们提供了数据集和 R 代码。