# Comparing coefficients in logistic regression

I have some problems I need help with. I am running a binary logistic regression.

DV: Brand choice (0/1)
IV1: Attitude towards product (p<0.05)
IV2: Price sensitivity (p<0.05)


(Both IV1 and IV2 are measured on the same scale)

I have found that “Attitude towards product” is more powerful ($β=1.308$) than “Price sensitivity” ($β=0.956$) in predicting brand choice. However, according to my thesis supervisor, in order to claim this fact, I need to run an additional test. That is, I need to find out if this difference is significant. So, what I want to know is if: $β_{Attitude}> β_{Price}$ (or if $β_{Attitude}≠ β_{Price}$) and if this is statistically significant. I have been searching a lot, but I cannot find how I am supposed to test this. Does anybody have any ideas??

I have read that it is possible to run a t-test (with brand choice as grouping variable) and look at the t-values and if the t-value is higher for “Attitude towards product” is higher, then it is the stronger one. However, I have 3 groups (conditions) so I’m not sure that I can run a t-test. Can I use an ANOVA instead and look at the F-values?

I also came across some information that I could include an interaction-term (Attitude*Price) and that the p-value for each interaction term gives me a significance test for the difference in those coefficients. Is this a valid method??

What you need is a postestimation test, which tests for significance of difference between two regression models, one of which is nested, i.e., it results from the first regression model plus some restrictions. In your case, the restriction would be $β₁ > β₂$, Null Hypothesis is $β₁ − β₂ = 0$.