论文标题
LIU型逻辑回归混合物的收缩估计量：骨质疏松研究
Liu-type Shrinkage Estimators for Mixture of Logistic Regressions: An Osteoporosis Study
论文作者
论文摘要
逻辑回归模型是用于分析二进制数据的最强大的统计方法之一。逻辑回归允许使用一组协变量来解释二进制响应。逻辑回归模型的混合物用于通过无监督的学习方法来适合异质种群。多重共线性问题是物流中最常见的问题之一，也是相协变量高度相关的物流回归的混合物。此问题导致回归系数的最大似然估计。这项研究开发了收缩方法来处理逻辑回归模型的混合物中的多重共线性。这些收缩方法包括脊和刘型估计器。通过广泛的数值研究，我们表明，开发的方法在估计混合物系数方面提供了更可靠的结果。最后，我们应用了收缩方法来分析50岁及50岁妇女的骨骼疾病状况。
The logistic regression model is one of the most powerful statistical methods for the analysis of binary data. The logistic regression allows to use a set of covariates to explain the binary responses. The mixture of logistic regression models is used to fit heterogeneous populations through an unsupervised learning approach. The multicollinearity problem is one of the most common problems in logistics and a mixture of logistic regressions where the covariates are highly correlated. This problem results in unreliable maximum likelihood estimates for the regression coefficients. This research developed shrinkage methods to deal with the multicollinearity in a mixture of logistic regression models. These shrinkage methods include ridge and Liu-type estimators. Through extensive numerical studies, we show that the developed methods provide more reliable results in estimating the coefficients of the mixture. Finally, we applied the shrinkage methods to analyze the bone disorder status of women aged 50 and older.
