# Interpretation of logistic regression results

#### daydreamerin

##### New Member
Hi all,

I'm doing empirical research for the first time and have the following setup:
• 1 dichotomous DV (purchase referral)
• 2 dichotomous IVs: Purchase type (good vs. service), Customization (standard vs. customized)
My hypothesis is that there is an interaction effect between the two IVs:Compared to services, customization will have a stronger effect on purchase referrals for material goods. I ran a binary logistic regression in SPSS with standard materials as the reference category and got significant results for the two main effects and the interaction. However, I am having difficulties with the interpretation of the interaction. Here is some of the output:

Purchase type: B = 1.824, exp(B) = 6.195
Customization: B = .937, exp(B) = 2.553
PT x CUSTOM: B = -.971, exp(B) = .379

So the likelihood to refer one’s purchase is 6.195 times higher for services than for material goods. But how do I figure out if the interaction effect is in the direction I hypothesized? I ran the regression a second time and used standard/services as the reference categories:

Purchase type: B = -1.824, exp(B) = .161
Customization: B = -.033, exp(B) = .967
PT x CUSTOM: B = .971, exp(B) = 2.639

So I get a negative regression coefficient and a low Odds ratio when I look at customized services compared to standard material goods, and a positive regression coefficient and way higher Odds ratio when I compare customized material goods to standard services right? Can I correctly assume that the interaction effect is in the way I predicted?

Can somebody tell me how to correctly interpret this and if there is a way that I could maybe even visualize this?!

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Well you also have your intercept, which would be when both predictors are set to zero, then purchage type when custom set to zero, vice versa, and then the when both set to 1. It is all about making sure you know which variable group is set as the reference, we can't tell from your post. Can you post your output?

#### noetsi

##### Fortran must die
I would not chose logistic regression as my first empirical analysis.

This, which is basically the relative impact, is incredibly hard to do with regression (I have been trying to find a good way to do it for a decade now without success). You can say that the DV moves more for one variable than another.

"Compared to services, customization will have a stronger effect on purchase referrals for material goods."

I don't understand exactly what you are trying to say about the interaction. I don't think there is a quantitative way to say that the interaction effect is greater on one main effect than the other if that is what you mean.

#### daydreamerin

##### New Member
Well you also have your intercept, which would be when both predictors are set to zero, then purchage type when custom set to zero, vice versa, and then the when both set to 1. It is all about making sure you know which variable group is set as the reference, we can't tell from your post. Can you post your output?
Yes, of course! I attached the output for the two regressions and included a picture with the reference category settings.

My codings are:
Purchase type 0 = Material good
Purchase type 1 = Service
Customization 0 = Standardized
Customization 1 = Customized

In this first picture I am seeing the effects for customized service compared to standard goods right?

Whereas here in this second picture I set the reference to last (= 1?) for purchase type, so I am seeing the effects of customized goods compared to standard services no?

#### daydreamerin

##### New Member
I would not chose logistic regression as my first empirical analysis.

This, which is basically the relative impact, is incredibly hard to do with regression (I have been trying to find a good way to do it for a decade now without success). You can say that the DV moves more for one variable than another.

"Compared to services, customization will have a stronger effect on purchase referrals for material goods."

I don't understand exactly what you are trying to say about the interaction. I don't think there is a quantitative way to say that the interaction effect is greater on one main effect than the other if that is what you mean.
Oh actually I just wanted to do a simple ANOVA, but my supervisor wants me to do a logistic regression

What I am trying to prove is that the effect of customization on purchase referrals depends on what kind of purchase the person made (a material good or a service).
More specifically, I found that the number of people who would recommend their purchase in each of my four categories (standard material, standard service, customized material, customized service) basically did not change at all from standard services (n = 63) to customized services (n = 65), but it doubled going from standard material goods (n = 20) to customized material goods (n = 45).

#### noetsi

##### Fortran must die
"What I am trying to prove is that the effect of customization on purchase referrals depends on what kind of purchase the person made (a material good or a service)."

that is pretty much the definition of interaction then, one variable's impact on the DV varies at levels of another predictor.

Other than a statistical test of the interaction term, you normally show the interaction by showing how one variable impacts the DV at different levels of the other predictor. This is a lot easier to do when the interacting predictor has a few levels (is categorical). But its not simple at all when the DV has only two levels. I have never seen anyone do that although I guess in theory it would be the same. But it would be not easy to show as it would with an interval DV.