I have inherited some logistic regression analysis, and am trying to understand the approach that was taken.
In the generalized linear model, the response is binary (positive or negative) and so are all six potential predictors.
The previous analyst was interested in seeing the probabilities of a positive response for each predictor and combination of predictors. The approach they took was to build all possible models with the six predictors (so 63 in total), then for each model convert any coefficients (including for the intercept) to probabilities using the formula EXP(coefficient))/(1+EXP(coefficent)). They then sum these probabilities for each model to give a total probability of getting a positive response for that combination of predictor(s). They then present this as a list, showing which combinations have the highest and lowest total probabilities.
I've not come across this approach before, and am confused as to whether it is appropriate. I can see that two of the models (one with six predictors and one with five) have much lower AIC scores than the others, so I thought it would be best to use these models rather than all 63. If I was starting from scratch and aiming to get similar outputs I would produce predictions for each combination of predictors, probably using model averaging across the two best models. I would also specify
se.fit=TRUE in my predictions, so I could add confidence intervals around the probabilities.
Which approach sounds most appropriate? The previous analysis has been in use for some time, so if I'm to change things I would need to be able to explain properly what is better about my new approach.