To understand interactions in logistic regression, I found [this posting](http://stats.stackexchange.com/questions/81022/how-to-interpret-interaction-continuos-variables-in-logistic-regression) helpful.

I personally find visual inspection helpful, especially when you have interaction terms in logistic regression. In my [sjPlot-package](http://cran.r-project.org/web/packages/sjPlot/index.html) there's a function to plot interaction terms of (generalized) linear (mixed effects) models. You can find some examples [in this online-manual](http://www.strengejacke.de/sjPlot/sjp.int/). The formula to calculate the interaction is based on what Karen Grace described [here](http://www.theanalysisfactor.com/interpreting-interactions-in-regression/) and [here](http://www.theanalysisfactor.com/clarifications-on-interpreting-interactions-in-regression/).

For logistic regressions, the odds ratios are translated into probabilities.

Here's an example from the sample data set with a simple `glm`:

    # load sample data
    data(efc)
    # create binary response
    care.burden <- ifelse(efc$neg_c_7 < median(na.omit(efc$neg_c_7)), 0, 1)
    # create data frame for fitted model
    mydf <- data.frame(care.burden = as.factor(care.burden),
                       sex = as.factor(efc$c161sex),
                       barthel = as.numeric(efc$barthtot))
    # fit model
    fit <- glm(care.burden ~ sex * barthel,
               data = mydf,
               family = binomial(link = "logit"),
               x = TRUE)
    # plot interaction, increase p-level sensivity
    sjp.int(fit,
            legendLabels = sji.getValueLabels(efc$c161sex),
            plevel = 0.1)

![enter image description here][1]


  [1]: https://i.sstatic.net/UNM2X.png