Comparing logistic regression models with the same IVs

Question

I have multiple logistic regression models with all of the same IVs/controls and a variety of DVs (all health outcomes from the same sample). The primary IV is the sum of types of childhood abuse (emotional, physical or sexual). I made dummy variables that represent any one type of experience, any two types of experiences, or all three types of experiences (so each is mutually exclusive). This is the same type of model the CDC uses for their ACEs study which is where I borrowed the method from.

Question 1: Can I compare the one experience dummy to the two experience dummy within the same model? That is, talk about the odds ratios in comparison to one another without standardizing the coefficients? My sense is yes and I've seen it done all over the place but I recently was given a dissenting opinion saying that since I am only comparing each IV to the dummy referent of 0 experiences, I can't compare them to one another without standardizing first.

Question 2: What's the best method to make comparisons across models (with all the same IVs)? I'm testing the dummy IVs against a variety of physical and mental health outcomes and I'd like to compare the odds ratios for each DV based on any one type of experience, two experiences or three experiences. It would be nice to say, one experience increases the odds of this outcome by 3.2 times, this outcome by 2.1 times, etc. Therefore, I can say that one type of abuse increases the risk of depression more than anxiety disorder or two types of abuse increases the risk of PTSD over depression etc (assuming no overlap in confidence intervals).

I've read Menard's 2011 piece on standardized LR coefficients and that makes sense as to what mechanism to use within a single model (as I would apply in question 1 if necessary), but I can't tell if this can be applied across DV models if I'm using all the same IVs/controls from the same sample. If I standardize each IV coefficient, then are they comparable across models? It's a random sample and each model has the same number of valid cases (1073) with no missing data.

Answer 1

Q1: For all but the most rigorous audiences/contexts you should be able to compare these predictors' odds ratios. In a sense the variables are already standardized since they are on the same 0/1 "scale". The fact that they might have different standard deviations might bother some more technically-minded people but to me that seems almost like a splitting of hairs.

Q2: Why not convert these dummy variables to a single predictor taking on values of 1, 2, or 3. That seems to match what you are trying to do conceptually: compare results for people who have had 1, 2, or 3 types of these experiences. You seem to want to quantify this continuum of "types of experiences," so it would make sense to bring these three dummies together into a single, quantitative predictor. It would make interpretation more concise and would reduce the degrees of freedom to boot. The only reason not to do so that I can think of would be any suspicion of a distinct nonlinear effect whereby the logit would be a nonlinear function of this predictor. This would occur if, for example, people with values of 2 had much better outcomes than either those with 1 or those with 3.

On the other hand, comparing effects for this variable to effects for others such as anxiety or depression will be more complicated if there are substantial correlations among these "earlier" and "later" predictors, and, even more to the point, if there are causal connections. Suppose level of anxiety were caused by extent of past abuse (which is, indirectly, what a 1/2/3 'types of abuse' predictor would be measuring). In that case you'd need to think through different approaches to capturing these different effects, e.g., sequential regression or some equivalent to path analysis or structural equation modeling that applies when you have a binary outcome.