I have three groups, where I have conducted cross validated binary logistic regression models test the classification accuracy of a model (three predictors/covariates) for predicting participants within group A relative to group B, A relative to C, and B relative to C. A reviewer suggested multinomial regression (rather than 3 binary logistic regression models). However, from what I understand, multinomial regression conducts M-1 binary logistic models, such that it compares two groups to the one reference category. e.g. A versus C, and B versus C. It would not test a model for A versus B. My intuition is that the binary log models directly test my questions, allows for straight forward calculation of sensitivity and specificity for predicting members within those groups. But, it does not account for any shared variance among the three models. Does anyone have any suggestions as to other regression or classification tools, that would allow me to examine whether my model (with three predictors) can significantly differentiate between three different groups? Thanks!
You’re absolutely right. Logistic Regression is a natively binary “classification” method with shoehorned methods to make it into a multivariate “classification” method (eg. all vs. 1, softmax). The softmax method may be a little closer to what you’re looking for, but if not, neighbourhood / tree methods natively handle multivariate data.