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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??

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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 $β₁ − β₂ = 0$.

Examples for such postestimation tests are the Wald test or the Likelihood ratio test. I do not know which statistical package you use, but here is a link that describes those tests in STATA.

Interaction terms can be used to test for difference in coefficients for specific groups in your sample. The interaction is then constructed with a dummy variable that identifies the group which might feature a different coefficient in the regression model. I do not believe that an interaction term between price and attitude could help to answer your question.

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  • $\begingroup$ Thanks for your answer! I am using SPSS, so if you know (or have a link) on how to do this in SPSS, that would be helpful. $\endgroup$
    – GentlemanEddie
    Commented Sep 6, 2012 at 10:40
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    $\begingroup$ Adding to @mzuba 's good answer (+1), the reason an interaction won't test what you want is that an interaction tests whether the effect of one IV on the DV is different at different levels of the other IV. That isn't your question. I am not an SPSS person, but, at the least, you could run the two regression models, get the log likelihoods, subtract one from the other and then test using a chi-square with df = 1. But SPSS can almost certainly do this for you. You might also look at AIC and BIC, which penalize for the complexity of hte model $\endgroup$
    – Peter Flom
    Commented Sep 6, 2012 at 10:43
  • $\begingroup$ Thanks Peter! I just came across some additional information that if the variables are measured on the same scale (which they are), I can just look at the Exp(B) values and make comparisons and draw conclusions using those numbers (which is what I did in the first place). This would certainly make my life much easier;). Do you (or anyone else) know if this is a valid method?? $\endgroup$
    – GentlemanEddie
    Commented Sep 6, 2012 at 11:00
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    $\begingroup$ @user13879 Exponentiating the coefficients from a logistic regression just makes them interpretable as odds ratios - that can be useful for presenting results sometimes, but it doesn't actually test for differences between the two coefficients. $\endgroup$
    – Matt Parker
    Commented Sep 6, 2012 at 15:20
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For those still looking at this old post, I found an article by King that might be useful: (King, J.E. (2007). Standardized coefficients in logistic regression. Paper presented at the annual meeting of the Southwest Educational Research Association, San Antonio, TX. February, 1-12.)

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