# Interaction/moderation in probit/logit

#### Ute

##### New Member
Dear all,

in my studies some (maybe trivial...?) questions on interaction/moderation in probit/logit regression came up. Imagine the following setting (to be analysed with probit/logit):

dependent variable D (discrete)
independent variable IN
variable V
hypothesis I: IN has a negative effect on D.
hypothesis II: if V is high, IN's effect on D is not so strong.

First of all, I get confused on what is the difference between interaction and moderation? As I see it, in technical terms, these are all about "interaction"?

Now, when I analyse hypII, what do I include in the model? I would include IN and IN*V to explain D. Do I need to include V as a separate variable? If so, why?
Without V as a separate variable, regression shows significant results. When I include V as a separate variable, the independent variables are not significant anymore. What does the imply?

When I apply this logic to a different dependent variable, is there a difference between probit/logit and OLS?

Thank you very much in advance.

Kind regards
Ute

#### noetsi

##### Fortran must die
I have never seen a formal definition of moderation and I am anything but an expert in it. That said it appears to me from the few times I have run into moderation, that interaction effects both variables similarly and moderation does not. So with two variables A and B when they interact A has some effect at specific levels of B and B has some effect at specific levels of A. With moderation A influences the slope of B but I don't think B varies at levels of A and B has no impact on A's slope at all (or none that anyone cares about). A is simply there, in which case it effects B, or its not. The level of A does not matter as long as its significant.

If you are testing a hypothesis that IN's effect varies at levels of V (as seems the case) then you specify an interaction variable. If its not significant IN's effect on D should not be influenced by V.

As far as I know interaction works the same way in logistic regression as it does in linear regression (you will be punished on this board if thou refers to linear regression as OLS).

#### hlsmith

##### Omega Contributor
In the literature you will find interaction and effect modification used interchangeably, with the latter typically used as the general topic.

The format/groupings for IN and V are not clear in your description. I will assume they are both binary.

If you are testing an interaction, you keep all main effect terms within the interaction in the model. So, y = Bo + B1(IN) + B2(V) + B3(IN*V). They are included because if you were trying to fully explain everything, even when conditional, you would want to account for all of the contributing components.

If the interaction term is significant, then there is a difference when stratifying by a covariate of interest. If all variables are binary, I would calculate (using the model), the odds ratio of outcome for IN stratifying by V. Also provide the 95% confidence intervals. Typically you stratify by the variable in the interaction term that is modifiable. So if you had education and sex, you would stratify by education since you can't change a persons biological sex. Your scenario would also benefit by graphing IN and V = 0 connected to IN = 0 and V = 1 as well as IN = 1 and V = 0 connected to IN = 1 and V = 1. You can graph the predicted probabilities in this graph and see non-parallel lines.

Lastly, you should look at the effect size of the interaction term and contemplate if is significant given the content, but not statistically significant given the power of the sample size.