  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.
