Logistic regression with only dichotomous (0,1) predictors and response

Question

I'm doing some glm in R, where I have response of not being depressed (0) and being depressed (1). I have three predictors, first one being relationship situation (in a relationship = 0, single = 1). The second one is age (under 35 = 0, over 35 = 1) and the last one is education (college level = 1, under college level = 0).

So my model looks like this (in R)

glm(depression ~ relationship + age + education, family = binomial("logit")).

The point of age and education are just to get adjusted odds ratios of being depressed when comparing people who are in a relationship and single. So is it valid to say, for example if I get OR of 2.5, that "people that are single have 2.5 times the odds of being depressed compared to people who are in a relationship, adjusting for age and education". So, is my model statistically correct?

The thing I'm wondering in this model is, when I change places of depression and relationship status, such that relationship is response and depression is predictor, I get almost identical odds ratio and confidence intervals. Why is this? Does it change the interpretation of results, in my understanding it should be in this case "depressed people have 2.5 times OR of being single compared to non-depressed people, adjusting for age and education".

This same thing applies to many more variables and responses in my data, so I think it has something to do with the dichotomous nature of the variables, or am I doing something wrong here? I also get (almost) only significant results, which is whole another thing to worry about ...

Answer 1

First, yes, your interpretation sounds right to me.

Second, binning age this way is almost certainly a mistake. Frank Harrell gives a lengthy list of what goes wrong in his book Regression Modeling Strategies. I give a graphical explanation here.

Third, about what you are wondering. Let's make it a little simpler and have just one IV (so, no age or relationship status). Then you have a 2x2 table with depression (yes/no) and relationship (single/involved) and you have four numbers: YS, YR, NS and NR.

The OR is given by $\frac{YS*NR}{NS*YR}$ and these will be identical in either direction. Adding covariates can change this; in your case, it apparently didn't change it much.

This is a good example of the computer not knowing what the dependent variable is. In an observational study, you have to figure that out based on substantive knowledge. In your case, "causation" and "direction" seem likely to go both ways. That is - you're depressed because you're not in a relationship so you don't get into a new relationship because you're depressed.