Someone help me make sense of this regression analysis

#1
Hello,

I was reading a paper "Sociable and Prosocial Dimensions of Social Competence
in Chinese Children: Common and Unique Contributions to Social, Academic, and Psychological Adjustment" by Chen et al 2000 (developmental psychology 36(3)), and was a little unsure how to interpret one of thei analyses.

They have depression measured at two time points, and seem to regress time 2 depression onto time 1 depression and other predictor variables, including a prosociality variable. So i'd normally intrepret the effect of prosociality in this model as predicting the change in depression over time.

They then include an interaction term between time 1 depression and prosociality, which is significant. Looking at simple slopes, prosociality is more related to time 2 depression for those kids who are more depressed at time 1.

Its this interaction effect i'm struggling with. Is it still the change in depression from time 1 to time 2 that is being predicted by this interaction effect (as is the case if we're just looking at the prosociality predictor), or can I no longer interpret this effect as being prospective (i.e., telling me something about the direction of the relationship), since the time 1 depression variable whose variance is being removed from time 2 depression also forms part of the interaction effect.

I've never seen this done before in a multiple regression. Any assistance in what to make of this effect would be greatly appreciated. Thanks
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
Forward confession, I have not looked at the article. Per your description, they could still be predicting the same dependent variable, however a third variable is an effect modifier. Meaning if you plot the previous dependent and independent variables and incorporate this interaction term, now the slopes change and are no longer congruent. So if the interaction term was categorical, now they stratified the data into two groups and have two slope lines that cross or will cross each other, meaning they do not have the same slope. If the interaction term is continous, now I believe you are using 3-dimensional space and the slopes are also not congruent in this figure.