# Interaction terms

#### DrFurbs

##### New Member
rogojel thank you..may I ask, if you are doing this by hand, why are your calculations not the same as the Mplus output? Is Mplus wrong?

#### rogojel

##### TS Contributor
hi,
no, but it is only giving the ORs for the simple cases like the OR between no symptoms and anxiety. The combined case w =1 and x6 = 1 is not given, wich is imho ok. I suspect that the value in the OR column at the interaction term is simply the exponential of the corresponding coefficient , which for the simple terms is really the OR but I guess it has no straight interpretation for the interaction term.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
rogojel,

tomorrow morning I am going to run it my traditional way and will get back to you!!!!

#### DrFurbs

##### New Member
I wish you guys would fly some of that genius my way!

i have the SPSS file here, feel free to ask for it lol

#### rogojel

##### TS Contributor
Hi,
do you have the data set in excel? Could be fun to run the regression in Minitab, say.

regards

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Yes i wouldnt mind playing around with it as well.

#### Mean Joe

##### TS Contributor
Are the binary variables coded 0/1, or some other way? Would be best to have them coded 0/1. I'll assume that you do.

However the interaction is less than 1 (0.52) (meaning if you have psychotic symptoms and anx /dep you are less likely to seek help).
Ok I think you mentioned the OR for psychotic symptoms was 5, and the OR for anx/dep was 6? So you might think that a person with both would have an OR of 30, but there is an interaction effect of psychotic symptoms with anx/dep so the OR for a person with both is actually 0.52 * 30 = 15.6.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Yes meanjoe that would be the interpretation or 15.6/30 = 0.52. This would mean negative multiplicative interaction. I was hoping to play around with the numbers tomorrow.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Alright this thread got out control.

I agree with Rogojel's post #19 and meanjoe's generalization in # 26.

I did the math and their approaches give the same result as my proposed method of stratifying on one of the variables and looking at the ratio of the two ORs.

Their appoach, calculate the expected OR via the product of the OR of W and OR of X6 = 18.86, then multiply that by 0.539, which equals actual OR in the model for outcome given both condtions present (i.e., odds of both present over odds of neither present). This value is 10.16. Which we can see is a negative multiplicative interaction.

The method I was proposing was to calculate the OR of W present versus not present in patients with X6 present, divided by, the OR of W present versus not present in patient with out x6 present.

Thus the OR of W*X6 = observed/expected, and since it is < 1, the observed was lower than expected if the two covariates were truly independent. And given my approach it means the percent lower the OR was when the second variable was present versus not present. Big picture the cross product term in the model represents the deviation of the two lines from being parallel (lines are the plotted log odds based on stratifying on one of the two covariates of interest).

Thanks everybody for bearing with me while I also tried to wrap my head around this!!

#### hlsmith

##### Less is more. Stay pure. Stay poor.
rogojel,

There was no intercept, so you assumed the odds of (Y=1|W=0,X6=0) = 1 (I agree with this). Given this, would you still use the covariates in your calculations or are they already controlled for in the calculation of the beta coefficients. I originally wanted to incorporate the intercept and covariates in all of the conversions of betas to odds. I wanted to go:

b0 = 0;
b1 =
1.314;
b2 =
1.623;
b3 = -
0.612;
b4 =
1.913; Sum of all of the covariates controlled for in the model.

So, for W=1 and X6 = 0.
p10 = 1/(1+exp(-(b0 + b1*1 + B4*1))); Probability
p10_odds = p10/(
1-p10); Odds

You can see I incorporated the other covariates in the calculation. Is that correct or not, since the beta coefficient was 0?

#### DrFurbs

##### New Member
wow im offically lost and in awe lol.

hlsmith
So from your analysis, what are exactly are you saying? (in laymans terms) that I have misinterpreted the interaction? have pmed you the dataset if you would like a play.

#### DrFurbs

##### New Member
Are the binary variables coded 0/1, or some other way? Would be best to have them coded 0/1. I'll assume that you do.

Ok I think you mentioned the OR for psychotic symptoms was 5, and the OR for anx/dep was 6? So you might think that a person with both would have an OR of 30, but there is an interaction effect of psychotic symptoms with anx/dep so the OR for a person with both is actually 0.52 * 30 = 15.6.

Hi Joe, yes i have coded them as 0,1 (no,yes). The coefficient is significant and negative - for some reason I thought that the effect of anx/dep on psychosis was reduced not multiplied. I have a lot to learn on this subject obviously.