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I want to create an interaction term in SPSS on two continuous variables (ticket price and household income) in order to use this interaction term in a multiple regression model and test whether my main effects or interaction effects model is better.

Do I:

  1. Compute a new variable for each IV (the score minus the mean) and then an interaction term between these new variables?

  2. Or compute an interaction term between the original IVs? (I have 105 observations)

  3. Or do I re-code each of the IVs into categories e.g. low, med, high income/ticket price and then compute an interaction term that multiplied the two new categorical variables?

I had just created a new categorical variable for income (low,mid, high) and left the ticket price as is, but now I'm doing option 1 as I read this online.

Scortchi - Reinstate Monica
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1 Answers1

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First see When conducting multiple regression, when should you center your predictor variables & when should you standardize them?—there's no substantive† difference between models 1 & 2, both containing two linear terms plus an interaction term.

Second see What is the benefit of breaking up a continuous predictor variable?—discretizing continuous variables as in model 3 isn't generally a good idea. If your concern is to allow for curvilinear relationships you might consider a full second-order model for the expected response,

$$\operatorname{E}Y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_{11} x_1^2 + \beta_{22} x_2^2 + \beta_{12} x_1 x_2$$

where $x_1$ & $x_2$ are your predictors, & the $\beta$s the coefficients to be estimated; this has five regression degreees of freedom. For only one more degree of freedom than the eight you would spend on modelling the interaction between two three-level categorical variables you could even try a full third-order model, but at increased risk of over-fitting.

† By that I mean one model is just a reëxpression of the other—the predictors are redefined through an affine transformation & the interpretation of the coefficents changes accordingly, but the predictions & inferences remain the same.

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Scortchi - Reinstate Monica
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    +1, I'll just add that there are substantive differences between model 1 and 2 if you are interpreting individual coefficients. For instance, @Lora, know that $\beta_1$ in the model $$\operatorname{E}Y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_{3} x_1x_2$$ Is the marginal effect of $x_1$ when $x_2$ is 0. So if 0 is the mean, you'll get a different value than if 0 is whatever it is in the original data, which may be meaningless (such as having an income of 0... which I guess may not be totally meaningless). – le_andrew Apr 20 '15 at 17:33
  • @le_andrew: Thanks for that clarification - I was trying to mean too much with "substantive". – Scortchi - Reinstate Monica Apr 22 '15 at 20:18