# Are the interaction terms in these two models equivalent?

I am trying to understand if the outcome of one model is equivalent to another.

So for instance, I have three variables: wealth (continuous in dollars), productive (dichotomous: yes or no) and age_group (categorical: young,mid,old).

First model: wealth~productive*age_group
Second model: productive~wealth*age_group

So the interaction term in my first model represents whether the relationship between productive and wealth is age_group dependent and the interaction of second model represents whether the relationship between wealth and productive is age_group dependent.

Are these two interaction terms explaining the same thing?

Update: I am doing this in R:

• First model: lmmodel <- lm(wealth~productive*age_group)
• Second model: glmmodel <- glm(productive~wealth*age_group,family=binomial(link='logit'‌​),na.action=na.omit)
• Can you say a little more about the modeling approach you are using? – Willie Wheeler Oct 14 '16 at 17:37
• @WillieWheeler I am doing this in R: First model: lmmodel <- lm(wealth~productive*age_group) Second model: glmmodel <- glm(productive~wealth*age_group,family=binomial(link='logit'),na.action=na.omit) – mmm Oct 14 '16 at 18:52
• These are totally different models because the response variables switch roles with the regressor variables. They "explain" completely different things! What, then, do you mean by an "outcome" of a model and what form of "equivalent" do you have in mind? – whuber Oct 14 '16 at 21:21
• What I mean by outcome is, if I run the first model and determine that the effect of productive on wealth is age group contextual (I.e a significant interaction term), can I then conclude that the effect of wealth on productive is age group contextual? – mmm Oct 17 '16 at 1:26