In my analysis, I am studying the association between a continuous predictor cont1 and a binary outcome bin_outc, and I am particularly interested in how this relationship changes across levels of another continuous variable cont2.
In a previous attempt, I divided the population into quantiles of cont2, ran separate logistic regressions within each subgroup, and extracted the odds ratios (ORs) for cont1. I then plotted these ORs against the median value of cont2 in each subgroup and fitted a line through them to visualize how the effect of cont1 varied with cont2. While this approach was intuitive, I realize that binning continuous variables is not statistically ideal.
What I would like to do is avoid binning and instead treat cont2 continuously, while still being able to visualize how the OR for cont1 changes across values of cont2. What would be the best practice to show how the effect of one continuous variable depends on the level of another continuous variable, without resorting to binning?
Any methodological guidance or visualization strategies would be greatly appreciated.