In many applications (e.g., medical studies), the population of interest (e.g., disease status) comprises heterogeneous subpopulations. The mixture of probabilistic regression models is one of the most common techniques to incorporate the information of covariates into learning of the population heterogeneity. Despite its flexibility, the model may lead to unreliable estimates in the presence of multicollinearity problem. In this paper, we develop Liu-type shrinkage methods through an unsupervised learning approach to estimate the model coefficients in multicollinearity. The performance of the developed methods is evaluated via classification and stochastic versions of EM algorithms. The numerical studies show that the proposed methods outperform their Ridge and maximum likelihood counterparts. Finally, the developed methods are applied to analyze the bone mineral data of women aged 50 and older.
翻译:在许多应用(如医学研究)中,受关注人群(如疾病状况)包括多种亚群,概率回归模型的混合是将共变信息纳入人口异质性学习的最常用技术之一,尽管该模型具有灵活性,但可能会在多线性问题面前导致不可靠的估计;在本文件中,我们通过一种不受监督的学习方法,开发了刘型缩缩缩方法,以估算多线性模型系数;通过对EM算法进行分类和随机化版本来评估所开发方法的性能;数字研究表明,拟议方法优于其脊和最大可能性;最后,开发的方法被用于分析50岁及50岁以上的妇女的骨矿数据。