See the most important interactions between variables when you have many variables

[Mathis1]

Hello there,

I'm looking to predict a price variable with around 8 variables (each of them being categorical and presenting multiple modalities). Before trying to analyse the two-way interaction , i'd like to see if i can find an interaction A*B that is more significant than others. So i can focus on this interaction to analyze it. Any advice ?

Thank you for your help !

🙂

[PaigeMiller]

I don't think there is a simple Yes or No answer to your question. It depends on the data, and it also depends on what you mean by "most important interaction" (which may or may not be different than where you say "most significant interaction"). Furthermore, in the context of building a model and interpreting the results, there are a lot of things that come into play. So that's my answer — my answer is that there is no simple answer and it depends.

[Ksharp]

Try PROC HPGENSELECT .

model y=a|b|c|d....... ;

[SteveDenham]

And if you only want to look at two way interactions, add "@2" to the model statement that @Ksharp  gave.

For example:

PROC HPGENSELECT data=<yourdatafile>;
CLASS a b c d; /* List all of your variables of interest here */
model y=a|b|c|d@2/distribution=normal; /* Again, include all your variables of interest */

You should probably have an include option to make sure that you include main effects and that the selection process only addresses the two way interactions.

And now for the caveat: Just because an interaction is "more significant" does not imply that it is more important from a process standpoint.  That is a matter of knowledge of the field, so be very cautious in proceeding.

SteveDenham

[PaigeMiller]

I agree with @SteveDenham. It's easy to get SAS to do the calculations and present them. It takes a lot more to interpret the model results and pick "most important" or "most significant".

[StatDave]

See this note on variable importance. One easy alternative discussed there is PROC ADAPTIVEREG. By default it fits a flexible model that is a selection of the most important effects among the possible main effects and the two-way interactions of the variables you specify in the MODEL statement. It includes a table of variable importance values it uses which are based on a GCV criterion that is explained in the procedure documentation. 

You also might want to be careful if you are planning to assume that your price response variable is normally distributed. Depending on how large those values are, its distribution might be pretty skewed so that a distribution like gamma or inverse Gaussian is more appropriate. Both are supported by ADAPTIVEREG as well as the normal. The RsquareV macro discussed in the note is also a possible way to assess importance.