Bradley R Lewis, Dipankar Bandyopadhyay, Stacia M DeSantis, Mike T John
Often in clinical dental research, clinical attachment level (CAL) is recorded at several sites throughout the mouth to assess the extent of periodontal disease (PD). One might be interested to quantify PD at the tooth-level via the proportion of diseased sites per tooth type (say, incisors, canines, pre-molars and molars) per subject. However, these studies might consist of relatively disease-free and highly diseased subjects leading to the proportion responses distributed in the interval [0, 1]. While beta regression (BR) is often the model of choice to assess covariate effects for proportion data, the presence (and/or abundance) of zeros and/or ones makes it inapplicable here because the beta support is defined in the interval (0, 1). Avoiding ad hoc data transformation, we explore the potential of the augmented BR framework which augments the beta density with non-zero masses at zero and one while accounting for the clustering induced. Our classical estimation framework using maximum likelihood utilizes the potential of the SAS® Proc NLMIXED procedure. We explore our methodology via simulation studies and application to a real cross-sectional dataset on PD, and we assess the gain in model fit and parameter estimation over other ad hoc alternatives. This reveals newer insights into risk quantification on clustered proportion responses. Our methods can be implemented using standard SAS software routines. The augmented BR model results in a better fit to clustered periodontal proportion data over the standard beta model. We recommend using it as a parametric alternative for fitting proportion data, and avoid ad hoc data transformation.
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Shimin Zheng, Uma Rao, Alfred A Bartolucci, Karan P Singh
Bartolucci et al.(2003) extended the distribution assumption from the normal (Lyles et al., 2000) to the elliptical contoured distribution (ECD) for random regression models used in analysis of longitudinal data accounting for both undetectable values and informative drop-outs. In this paper, the random regression models are constructed on the multivariate skew ECD. A real data set is used to illustrate that the skew ECDs can fit some unimodal continuous data better than the Gaussian distributions or more general continuous symmetric distributions when the symmetric distribution assumption is violated. Also, a simulation study is done for illustrating the model fitness from a variety of skew ECDs. The software we used is SAS/STAT, V. 9.13.
Bartolucci et al.(2003)将分布假设从正态(Lyles et al.， 2000)扩展到椭圆轮廓分布(ECD)，用于纵向数据分析的随机回归模型，考虑了不可检测值和信息缺失。本文建立了多元偏态ECD的随机回归模型。用一个真实的数据集说明，当对称分布假设被违反时，偏微分方程比高斯分布或更一般的连续对称分布能更好地拟合单峰连续数据。此外，本文还进行了仿真研究，以说明各种偏态ecd的模型适应度。我们使用的软件是SAS/STAT, V. 9.13。
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Pub Date : 2003-11-01DOI: 10.22237/JMASM/1067645340
S. Zheng, Uma Rao, A. Bartolucci, Karan P. Singh
Bartolucci et al.(2003) extended the distribution assumption from the normal (Lyles et al., 2000) to the elliptical contoured distribution (ECD) for random regression models used in analysis of longitudinal data accounting for both undetectable values and informative drop-outs. In this paper, the random regression models are constructed on the multivariate skew ECD. A real data set is used to illustrate that the skew ECDs can fit some unimodal continuous data better than the Gaussian distributions or more general continuous symmetric distributions when the symmetric distribution assumption is violated. Also, a simulation study is done for illustrating the model fitness from a variety of skew ECDs. The software we used is SAS/STAT, V. 9.13.
Bartolucci et al.(2003)将分布假设从正态(Lyles et al.， 2000)扩展到椭圆轮廓分布(ECD)，用于纵向数据分析的随机回归模型，考虑了不可检测值和信息缺失。本文建立了多元偏态ECD的随机回归模型。用一个真实的数据集说明，当对称分布假设被违反时，偏微分方程比高斯分布或更一般的连续对称分布能更好地拟合单峰连续数据。此外，本文还进行了仿真研究，以说明各种偏态ecd的模型适应度。我们使用的软件是SAS/STAT, V. 9.13。
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