Average Effectiveness of Variables in Binary Logistic Model

Question

I have constructed a binary logistic model to check the effect of various variables on the probability of a consumer to buy. I have 5 different brands, and in the model I have 5 price variables which are specific to the brand (interaction between brand dummy and price). So my output looks like this:

                         Coefficient               P-value
Price_Brand_A                0.25                    0.02
Price_Brand_B                0.50                    0.01
Price_Brand_C                0.10                    0.09
Price_Brand_D                0.40                    0.15
Price_Brand_E                0.65                    0.02

What I would like to ask, is if it is correct to say something about the overall effect of price, and not specifically about the brands. For instance would it be correct to take the average of the coefficients and say that the average effect of price is equal to 0.38? Or is there some statistical procedure I should follow to report the overall effect of price? Also would the same apply for the P-value?

I am working with spss and I am new at modelling so any help would be appreciated.

Many Thanks

Answer 1

If you test an interaction hypothesis, you have to include a number of terms in your model. In this case, you would have to include:

• Base effect of price
• Base effects of brands (dummies)
• Interaction effects of brand dummies * price.

Since you have 5 brands, you will have to include 4 of the 5 dummy variables. The dummy you leave out will be your reference category. The same goes for the interaction terms. In this case, the base effect of price will be the effect of price for the reference category of brands. The base of dummies will be the difference between brands if the price would be 0. The interaction effects can be interpreted in two different ways. On way is to say that the effect of an interaction term would be the additional price effect of one brand, compared to the reference category of brands. The other way is to say that the interaction effect is the additional difference between the brand and the reference brand if price increases by one.

If you want to know what the average effect of price is, why would you include interaction terms? In that case, I would leave out the interactions in a first model, and then include the interactions to show that the average effect of price is not accurate if you would look at the effect for each brand.

Maybe you could post some more output? I think you got more out of it than you posted in your question?

Good luck!