Logistic regression Interactional effect problem


For my MSc we have to analyse some data and create a logistic regression nested model with an interaction effect. I have done this. However, I am stuck on the interpretation.

On the graph, STRATA produces it shows me data on the interactional effect between free school meals (FSM) and unhappiness has on the likelihood of smoking in adolescents. It shows that if you are happy and are on free school meals you are more likely to smoke than someone that is happy and not on free school meals. However, if students are unhappy, it doesn't matter if they receive free school meals as both groups have a similar/ same likelihood of smoking. I have left out the subgroup "sometimes happy" because the p-value is above 0.05. This is great, the data is giving me information.

However, I am having difficulty interpreting the numbers of the interactional effect. We have been told to use odds ratio. To change the odds ratio into a probability we have been told to take 1. So I have done this:

always unhappy#free school meals - 0.6132822 - 1 = -0.387

I am confused as I thought the probability will be positive as its more likely to smoke than someone that is happy. Can anyone help explain this?

I am new to statistics so maybe its an easy explanation that I have missed.



Less is more. Stay pure. Stay poor.
It is hard to tell what you are doing without full code and output, but yes probabilities are always between 0-1.