Petterle Ricardo R, Laureano Henrique A, da Silva Guilherme P, Bonat Wagner H
Department of Integrative Medicine, 28122Paraná Federal University, Curitiba, Brazil.
Laboratory of Statistics and Geoinformation, Department of Statistics, 28122Paraná Federal University, Curitiba, Brazil.
Stat Methods Med Res. 2021 Dec;30(12):2619-2633. doi: 10.1177/09622802211043276. Epub 2021 Nov 26.
We propose a multivariate regression model to handle multiple continuous bounded outcomes. We adopted the maximum likelihood approach for parameter estimation and inference. The model is specified by the product of univariate probability distributions and the correlation between the response variables is obtained through the correlation matrix of the random intercepts. For modeling continuous bounded variables on the interval we considered the beta and unit gamma distributions. The main advantage of the proposed model is that we can easily combine different marginal distributions for the response variable vector. The computational implementation is performed using Template Model Builder, which combines the Laplace approximation with automatic differentiation. Therefore, the proposed approach allows us to estimate the model parameters quickly and efficiently. We conducted a simulation study to evaluate the computational implementation and the properties of the maximum likelihood estimators under different scenarios. Moreover, we investigate the impact of distribution misspecification in the proposed model. Our model was motivated by a data set with multiple continuous bounded outcomes, which refer to the body fat percentage measured at five regions of the body. Simulation studies and data analysis showed that the proposed model provides a general and rich framework to deal with multiple continuous bounded outcomes.
我们提出了一个多元回归模型来处理多个连续有界结果。我们采用最大似然法进行参数估计和推断。该模型由单变量概率分布的乘积指定，响应变量之间的相关性通过随机截距的相关矩阵获得。为了对区间上的连续有界变量进行建模，我们考虑了贝塔分布和单位伽马分布。所提出模型的主要优点是我们可以轻松地为响应变量向量组合不同的边际分布。计算实现使用模板模型构建器进行，它将拉普拉斯近似与自动微分相结合。因此，所提出的方法使我们能够快速有效地估计模型参数。我们进行了一项模拟研究，以评估不同场景下的计算实现和最大似然估计量的性质。此外，我们研究了所提出模型中分布误设的影响。我们的模型是由一个具有多个连续有界结果的数据集驱动的，这些结果指的是在身体五个部位测量的体脂百分比。模拟研究和数据分析表明，所提出的模型为处理多个连续有界结果提供了一个通用且丰富的框架。
