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.

翻译：Logistic回归模型是分析二元数据最强大的统计方法之一。该模型允许使用一组协变量来解释二元响应。混合Logistic回归模型通过无监督学习方法用于拟合异质性总体。多重共线性是逻辑回归及混合Logistic回归中最常见的问题之一，此时协变量高度相关。这一问题导致回归系数的最大似然估计不可靠。本研究开发了收缩方法来处理混合Logistic回归模型中的多重共线性。这些收缩方法包括岭估计量和Liu型估计量。通过广泛的数值研究，我们证明了所开发的方法在估计混合模型系数时能提供更可靠的结果。最后，我们应用这些收缩方法分析了50岁及以上女性的骨骼疾病状态。