The most complicated part about interaction analysis is the interpretation. It is important that you keep track how your variables are coded, if you want to say something about what the interaction means. The example below is based on Approach A.

Example We want to examine the association between social support (x) and happiness (y). We think that the association may be moderated by gender (z). The following hypotheses are formulated: 1) Those with higher levels of social support are more likely to be happy, 2) Women are more likely to be happy, and 3) Social support is more strongly associated with happiness among women than among men.   Since the outcome is binary (0=Not happy and 1=Happy), we choose logistic regression analysis. Social support ranges between 0 and 10, where higher values reflect higher levels of social support. Gender has the values 0=Man and 1=Women.   To begin with, we examine the association between x and y: the odds ratio for social support is 1.20, which confirmed our first hypothesis. Next, we examine the association between z and y: the odds ratio for gender is 1.17, which confirms the second hypothesis. Finally, we include x and z as well as the interaction in the model. The interaction term is statistically significant (p<0.05) and the odds ratio is 1.45, which means that the combination of having higher levels of social support and being a woman is associated with increasing chances of being happy.

If the interpretation of the interaction analysis is difficult, you may improve your understanding by doing a separate regression analysis for each category of the z-variable (this is of course only possible if you have a rather large dataset – and thus enough power – and not too many categories in your z-variable). This is sometimes referred to as stratified analyses. However, stratification can also mean many other things in statistics. To make things clear, we will refer to it these kind of separate regression analyses as “specific” – e.g. sex-specific regression analysis.

We can go back to the example to illustrate what specific regression analyses can look like:

Example We want to examine the association between social support (x) and happiness (y). We think that the association may be moderated by gender (z). The following hypotheses are formulated: 1) Those with higher levels of social support are more likely to be happy, 2) Women are more likely to be happy, and 3) Social support is more strongly associated with happiness among women than among men.   Since the outcome is binary (0=Not happy and 1=Happy), we choose logistic regression analysis. Social support ranges between 0 and 10, where higher values reflect higher levels of social support. Gender has the values 0=Man and 1=Women.   To begin with, we examine the association between x and y among men only: the odds ratio for social support is 1.04. Next, we examine the association between x and y among women only: the odds ratio for social support is 1.76. Thus, we now see that we have a stronger effect of social support on happiness among women than among men (just like the interaction analysis said).

Remember, however: these kinds of specific or separate analyses are perhaps easier to understand, but if you want to say that any differences between groups (i.e. categories of the z-variable) are statistically significant, you should do a proper interaction analysis.