# Interaction terms

#### DrFurbs

##### New Member
Hi, nice forum

I have logistic regression model with an interaction and i need advice to understand if my interpretation is correct and did i do it correctly.

The model is in Mplus but I guess its still applicable in theory to any package. My hypothesis is, You are less likely to seek help if you experience psychotic symptoms and anxiety or depression.

The model is:
y1 on x6 w x6w ;

X6 (psychotic symptoms)
W (anxiety & depression)
Y1 (help seeking)

And the interaction term defined in mplus:

X1W (psychotic symps X anx/depression).

The results of the logistic regression appear good, all significant. All variables have high odds ratios as I would expect. 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).

Code:
Results
y1 on              EST          S.E        EST/S.E  P.Value
X6                 0.170      0.025      6.686      0.000
W                  0.346      0.018     19.406      0.000
X6W              -0.060      0.024     -2.508      0.012

X6                 3.721
W                  5.070
X6W               0.539
All variables are binary so no need to center. I'm wondering if my interpretation is correct including how I have operationalised the variables / model

Any advice would be appreciated, (such as if i did the analysis correct!)

#### rogojel

##### TS Contributor
hi,
I think this is not the right conclusion. Making some unfounded assumptions as I do not know Mplus I believe that the model looks like this

log(odds ofasking for help) = 0,17*x6+0,346*w-0,06*w*x6

whete x6=1 if someone has psychotic symptoms and 0 otherwise, same for w.

Now, based on this model someone with both symptoms still has the highest odds of seeking help, only the log odds are 0,06 less then the sum of 0,17 and 0,346 which would be the log odds if the two factors had no interaction.

I hope this helps
rogojel

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Not familiar with Mplus, but this seems straightforward enough. You keep the covariates in the model, but will not interpret them, only interpret the interaction term since it is significant. You also would not interpret the traditional odds ratios. What you need to do is stratify based on one of your independent variables, then calculate both odds ratios for the two datasets based on the remaining independent variable and the dependent variable. Examining these (with confidence interval) will help you understand your results.

I believe it may be standard to stratify on the variable you could not change (e.g., sex), however you have two dependent variables that are comparable in nature. Also, given my last sentence, I wonder if you tested the colinearity between your two binary independent variables?

#### DrFurbs

##### New Member
Hi guys , thank you both.

@hlsmith

Yes, apologies but for simplicity i didn't mention about the covariates etc. I have controlled for a bunch of stuff known to influence psychosis. I didnt think about collinearity - thanks, ill go check it now.

I guess what I'm really asking is, does the interaction make sense? Am i interpreting it correctly?

Would the ORs reduce in a model like this?

here are the overall results:

Code:
STANDARDIZED MODEL RESULTS

STDYX Standardization

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Y1         ON
B1                -0.029      0.023     -1.272      0.203
B2                 0.187      0.022      8.691      0.000
B3                -0.025      0.023     -1.088      0.277
B4                -0.099      0.025     -3.951      0.000
B5                 0.112      0.017      6.631      0.000
B6                 0.075      0.018      4.266      0.000
X6                 0.170      0.025      6.686      0.000
W                  0.346      0.018     19.406      0.000
X6W               -0.060      0.024     -2.508      0.012
and Odds ratios for the model (i have also requested 95%CI)

Code:
LOGISTIC REGRESSION ODDS RATIO RESULTS

Y1         ON
B1                 0.997
B2                 2.178
B3                 0.884
B4                 0.739
B5                 2.030
B6                 2.348
X6                 3.721
W                  5.070
[B]X6W                0.539[/B]

@rogojel

thanks so much for the reply. You think the interaction is wrong in this case or I have interpreted incorrectly?

#### rogojel

##### TS Contributor
hi,
i think the interpretation is not that one is less likely to seek help if one has both symptoms. Such a person is by far the most likely to seek help, only the odds are a bit less then what would follow from the assumption that both conditions contribute independently to the probability of seeking help.

#### DrFurbs

##### New Member
Hmm this is an odd one for me to get my head around. I mean the point of moderation is to change the strength or direction of variables and the interaction appears to do just this. the Odds ratio aren't just a bit less the indicate once the interaction takes place, the person is significantly less likely to seek help.

WOW ..ok thanks.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
hi,
I think this is not the right conclusion. Making some unfounded assumptions as I do not know Mplus I believe that the model looks like this

log(odds ofasking for help) = 0,17*x6+0,346*w-0,06*w*x6

whete x6=1 if someone has psychotic symptoms and 0 otherwise, same for w.

Now, based on this model someone with both symptoms still has the highest odds of seeking help, only the log odds are 0,06 less then the sum of 0,17 and 0,346 which would be the log odds if the two factors had no interaction.

I hope this helps
rogojel
rogojel,

If you can, please add more detail to this. I am interested in this interpretation.

DrFurbs,

I typically don't get caught up in the interaction term value (that is why I am probing rogojel). What I typically do is calculate the OR for outcome based on anxiety when controlling for covariate, in subjects with depression. Then do the same thing for patients without depression. Since there is interaction, these two ORs will be different and you can look to see if the OR for depressed subjects is different from 1 and same for patients not depressed. So this is a way to examine how subjects vary based on the terms within the interaction term in lieu of interpreting the interaction term's beta coefficient.

Side point, your interpretation is also based on your study design and whether you have temporality in the occurrence of the study variables.

#### rogojel

##### TS Contributor
hi,
this is the way I believe it works : the odds of a person seeking help are described by the equation :

odds = exp( 0,17*x6 + 0,346*w -0,06*w*x6). So, the odds of a psychotic seeking help will be
exp(0,17) because x6 is 1 and w is 0.
Similarly the odds of an anxiety patient seeking help will be exp(0,346)
If a person has both disorders then according to the model the odds of him seeking help will be
exp(0,17+0,346-0,06) roughly exp(0,46).

What do you think?

regards

#### hlsmith

##### Less is more. Stay pure. Stay poor.
rogojel, you could be right, but that seems incorrect for some reason. Will look into it tomorrow.

#### DrFurbs

##### New Member
wow im really confused now. Would posting the full output help in interpretation?

@rogojel apologies if my question annoys you

But if the ORs of X6 is almost 4 and the OR of W (anxiety) is almost 5 and then the OR of the interaction is below 1 - surely this means a less likelihood. I get the equation isnt /is adding up. This is moderation right? The effect of W are reducing the strength of X6 on help-seeking?

@hlsmith

You said you dont focus on the interaction term value, however im not sure if this make any difference, the interaction term is actually vitally important as its the main hypothesis, i.e, a reduction in ORs (although you mention a way of doing it without focusing on interaction results).

#### hlsmith

##### Less is more. Stay pure. Stay poor.
You have a significant multiplicative interaction term. The way i describe shows how odds change in the presence of the other variable. It will actually show you what is going on, which can get masked or confused by looking solely at the term. I will post a whole bunch more tomorrow.

#### rogojel

##### TS Contributor
hi guys,
The interpretation I propose hinges on the equation I am using, and looking at it I think that it is probably incorrect. So, the first question would be, what is the equation you are fitting?
I think, that interpreting the interaction term should be fairly straightforward once we know the equation.
@DrFurbs : yepp, looking at the complete model might help. E.g. how are the IVs defined?
regards

#### DrFurbs

##### New Member
hi rogojel

All the variables in the model are binary (0, 1). The results are in this LINK

You really only need to start reading at the MODEL results and LOGISTIC REGRESSION ODDS RATIO RESULTS. Ignore the rest. I have commented out some stuff in the syntax using ! (im sure you know).

Let me know if you need anything else please.

Regards,

Dr.F

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I think you are getting too hung up on the terms. Another approach is to convert your coefficients into probabilities for all of the scenarios for the model. Currently you have W (0 reference level) when controlling for X6 (with 0 being its reference level). You can run all of the combinations of the model to get all four probabilities, so W=1|x6=1, w=0|x6=1, w=1|x6=0, w=0|x6=0. Then once you convert them into probabilities, plot them and connect the values for the first two term and connect the values for the second terms. Looking at these lines you can better understand how risk changes in the presence of x6, since one line with represent risk in W|x6 = 1 and the other will represent risk in W|X6 = 0.

What is the prevalence of your outcome variable in the sample?

#### rogojel

##### TS Contributor
Hi DrFurbos,
I will need to study that a bit, it has a lot of information. A question about the variables: do you have healthy people in the model? I mean in the restricted model we were discussing would w=0 and x6=0 mean a person with neither symptoms?

kind regards

#### DrFurbs

##### New Member
Hi Hlsmith

The prevalence is:

Code:
GP: Spoke with about a mental, nervous or emotional complaint in past 12 months

Frequency	Percent	Valid Percent	Cumulative Percent
Valid	no	6469	87.4	87.4	87.4
yes	934	12.6	12.6	100.0
Total	7403	100.0	100.0

#### rogojel

##### TS Contributor
hlsmith,
I think, if I do what you propose I will get the same result I was proposing earlier, namely that the odds of a person with both conditions asking for help is higher then the odds of a person with any one of the conditions asking for help.

Of course I would have to translate the probs back to odds.

#### DrFurbs

##### New Member
Hi DrFurbos,
I will need to study that a bit, it has a lot of information. A question about the variables: do you have healthy people in the model? I mean in the restricted model we were discussing would w=0 and x6=0 mean a person with neither symptoms?

kind regards
Yes, the binary variables are operationlized as :
0 = no disorder 1 = disorder.
y1 (the outcome variable) is spoke to a doctor: 0= no 1 = yes

#### rogojel

##### TS Contributor
my predictions would be like this , provided that I calculated correctly:
the odds ratio of a person with x6 and w looking for help would be about 10. In the absence of the interction the odds ratio would be about 18. I guess calculating the probabilities and working out the odds you should get the same tesult. In the odds ratio I took as a basis a person with both x6 and w equal to 0.

regards