Running an MLR model with an interaction term

[ValSki]

Hi Everyone,

First time poster here. I am using SAS Studio and have run into a puzzling finding when attempting to run a multiple linear regression (MLR) model with and without an interaction term included. In Image 1, NSIDSC is contributing to the model when consulting the parameter estimates table and in Image 2 (the analysis with the interaction term), it appears to not be contributing. 

Question is, what does this mean? Why does this happen? And, how would I interpret this?

Any help on the matter would be greatly appreciated. Thank you!

Image 1Image 2

[PGStats]

From the little you have given us, it appears that in the first model you are estimating a single slope (-1.54) for both CCCF1 groups. In the second model, you are estimating separate slopes (-1.49, -1.60) for each group.

[PaigeMiller]

We'd probably need to see the full output, and the code in order to give you a complete answer. As to "why is this happening", different models will produce different results, its as simple as that.

[ValSki]

Hello Paige,

Thank you for replying. Here are the codes for the two analyses I was running. I've also attached the full output for the two. 

Without interaction term (image 1) and with (image 2): 

proc glmselect data=WORK.IMPORT outdesign(addinputvars)=Work.reg_design;
class DHH_SEX CCCF1 SPT_01 INCGHH / param=glm;
model PMHDSCR=NSIDSC DHH_SEX CCCF1 SPT_01 INCGHH / showpvalues selection=none;
run;

proc reg data=Work.reg_design alpha=0.05 plots(only)=(diagnostics residuals
observedbypredicted);
where DHH_SEX is not missing and CCCF1 is not missing and SPT_01 is not
missing and INCGHH is not missing;
ods select DiagnosticsPanel ResidualPlot ObservedByPredicted;
model PMHDSCR=&_GLSMOD /;
run;
quit;

proc glmselect data=WORK.IMPORT outdesign(addinputvars)=Work.reg_design;
class CCCF1 DHH_SEX SPT_01 INCGHH / param=glm;
model PMHDSCR=NSIDSC*CCCF1 NSIDSC CCCF1 DHH_SEX SPT_01 INCGHH / showpvalues
selection=none;
run;

proc reg data=Work.reg_design alpha=0.05 plots(only)=(diagnostics residuals
observedbypredicted);
where CCCF1 is not missing and DHH_SEX is not missing and SPT_01 is not
missing and INCGHH is not missing;
ods select DiagnosticsPanel ResidualPlot ObservedByPredicted;
model PMHDSCR=&_GLSMOD /;
run;
quit;

proc delete data=Work.reg_design;
run;

[PaigeMiller]

This is a great example of why I always avoid regression variable selection methods, such as PROC GLMSELECT when you have x-variables that are correlated with one another. The correlation between the x-variables means that two different models can have no resemblance to one another when you look at the parameter estimates.

So, that's the interpretation ... the correlation between the x-variables causes these models to be very different. Also, in Model 1, you have the interaction NSIDSC*CCCF1 entered into the model before the main effect of NSIDSC, and so the main effect of NSIDSC cannot be estimated. The order makes a difference here.

Confusing? Yes. That's where multiple linear regression takes you, to confusing-land, when you have correlated x-variables.

So what is the solution? I suggest a solution that does not have these drawbacks, which performs better in the case of correlation x-variables, and the above confusion is minimized. The order of the variables has no impact, and the coefficients don't swing wildly because of the presence or non-presence of a term in the model. That solution is called Partial Least Squares regreesion, which can be found in SAS PROC PLS.

[ValSki]

All the predictors, including the interaction are run simultaneously. I tried to rearrange the order of my predictors, as I suspected the order is influencing the results but regardless of the set-up, NSIDSC still gave me a zero slope. I'll have to take a look into using proc pls instead. Hopefully, that will help. 

[PGStats]

You are right that parameter estimates may change when you change the order of terms in the model. Try, for example:

ods select ParameterEstimates;
proc glm data=sashelp.heart plots=none;
class sex;
model weight = sex*height height sex / solution;
run; quit;

ods select ParameterEstimates;
proc glm data=sashelp.heart plots=none;
class sex;
model weight = height sex sex*height / solution;
run; quit;

The two models are mathematically equivalent. But because glm is overparameterized, some terms must be declared redundant. The two models only differ in the choice of redundant terms.

[PaigeMiller]

---

@ValSki wrote:

All the predictors, including the interaction are run simultaneously. I tried to rearrange the order of my predictors, as I suspected the order is influencing the results but regardless of the set-up, NSIDSC still gave me a zero slope. I'll have to take a look into using proc pls instead. Hopefully, that will help. 

---

It did NOT give you an NSIDSC slope of zero. It said it could not estimate the slope for NSIDSC. There is a difference.

[PGStats]

Why use proc GLMSELECT (without selection and with param=GLM) and proc REG instead of proc GLM? What's the advantage?