estimate continuous - categorical interaction

[DDK]

Hello,

Probably a very simple question for the slightly experienced statisticians.

I want to use the estimate statement to calculate the parameter estimate of an interaction of a continuous variable with a categorical variable in PROC MIXED. I understand that one of the betas in the 'solutions for fixed effects' is set at 0 or the reference (at least I thought I understood).

Lets say I have:

proc mixed data=test.components;

class treatment homogeneous;

model bwcomp=treatment  homogeneous husacomp treatment*husacomp;

estimate  'test'  husacomp 1 treatment*husacomp 1 0

run;

The solution for fixed effects states for the estimates:

intercept	1.0609
Treatment A	-0.8602
Treatment B	0
Homogeneous mix	0.1577
Homogeneous uni	0
husacomp	0.7271
Husacomp*treatment A	-0.9016
Husacomp*treatment B	0

The estimate statement for Husacomp*treatment A will give the estimate -0.1745, which is 0.7271-0.9016. If I run the estimate statement for B it will give 0.7271.

If I run the following model:

proc mixed data = test.components;

class treatment homogeneous;

model bwcomp = treatment  homogeneous husacomp treatment*husacomp homogeneous*husacomp;

estimate  'test'  husacomp 1 treatment*husacomp 1 0

run;

I get:

intercept	1.0102
Treatment A	-0.7845
Treatment B	0
Homogeneous mix	0.1762
Homogeneous uni	0
husacomp	0.5788
Husacomp*treatment A	-0.8719
Husacomp*treatment B	0
Husacomp*homogeneous mix	0.3269
Husacomp*homogeneous uni	0

And the estimate statement returns -0.1297 for for Husacomp*treatment A. I don't seem to understand how this number is achieved. I'm probably doing something stupid and am missing out on something. I'm not too versed with the estimate statement and if anyone could help me, it would be appreciated.

[SteveDenham · Accepted solution]

OK, I think I see what the problem might be.  Correct me if I am wrong in this assumption, but I believe husacomp is a continuous variable and you want to know how to include a unit change in husacomp in the estimate.  In the second model, I am certain that something is going on with homogeneous*husacomp.  The best diagnostic I can offer right off the top of my head is to add the E option to your ESTIMATE statement--I think there is a term in the L matrix that is not captured with just the coefficients you entered (no guarantee on this, though).  Try it and see if that is at all possible.

A quick calculation shows that the result is .5788 + (-0.8719) + 0.5 * (0.3269), so it looks like the L matrix is averaging over the coefficients for homogeneous*husacomp, in order to "remove" any effects there.

Steve Denham

[lvm]

There have been several posts, with answers, on the coding and meaning of interactions of factors and continuous variables.

[DDK]

Thank you SteveDenham for the  useful and very helpful answer (indeed husacomp is a continuous variable). I see how to manually calculate it now. When the e option is entered for the second model I get:

Effect	treatment	homogeneous	Row1
Intercept
treatment	HuSA
treatment	PBS
homogeneous		mix
homogeneous		uniform
husacomp			1
husacomp*treatment	HuSA		1
husacomp*treatment	PBS
husacomp*homogeneous		mix	0.5
husacomp*homogeneous		uniform	0.5

 Which would mean (as I understand it) that with the estimate statement from the second model I am purely looking at what the effect is of a 1 unit increase in husacomp in the HuSA group (the class variable) on BWcomp (which is what I was interested in, to specifically indicate what the effect was of that interaction). 

(I know that there are other posts handling interactions, but I did not seem to get (or likely, understand) the answer from those posts.)