topic Re: proc glm - categorical variable 2 levels but don't want interaction tested for each level in Statistical Procedures

proc glm - categorical variable 2 levels but don't want interaction tested for each level

mihoyoshi — Wed, 05 Feb 2020 18:54:41 GMT

Hi, I am trying to run proc glm (on SAS 9.4 TS Level 1M5) with a continuous dependent variable (log10biomarker) and 1 continuous independent variable (log10root) and 1 categorical independent variable (Species: either Kanlow or Summer). I would like to test for the separate effects of log10root and Species, but also for the interaction between the two independent variables. I have tried the code (below), specifying that Species is a categorical variable with the statement Class. And no dummy coding was necessary as the dataset lists either "Kanlow" or "Summer" in every cell (i.e. not say, "0" for Kanlow and "1" for Summer). However, the output (attached) shows that the interaction is tested for Kanlow and Summer individually. Instead, I want to simply test the interaction log10root * Species on log10biomarker (i.e. does the effect of log10root on log10biomarker change based on whether the species is Kanlow or Summer).

proc glm data=Rootmicr.Initial;
Class Species;
by Group;
model log10biomarker = log10root | Species / solution;
ods output ParameterEstimates=Rootmicr.IniDepthSpecIntxnGLMparmestim;
run;

Re: proc glm - categorical variable 2 levels but don't want interaction tested for each level

PaigeMiller — Wed, 05 Feb 2020 19:13:47 GMT

This is the correct output when you have an interaction between a class x-variable and a continuous x-variable.

The interaction is statistically significant (Pr > F is less than 0.05), and the area you have highlighted indicates the different slopes of log10root to predict log10biomarker, depending on which species is used.

Re: proc glm - categorical variable 2 levels but don't want interaction tested for each level

mihoyoshi — Wed, 05 Feb 2020 19:17:39 GMT

I see. Any thoughts on why there are no values in the parameter estimates output for when Species=Summer?

Re: proc glm - categorical variable 2 levels but don't want interaction tested for each level

PaigeMiller — Wed, 05 Feb 2020 19:55:44 GMT

That's how SAS has chosen to parameterize the model.

I wrote a short description about this (in a slightly different situation, although the same principle applies here)

Interpreting Multivariate Linear Regression with Categorical Variables

Re: proc glm - categorical variable 2 levels but don't want interaction tested for each level

Rick_SAS — Wed, 05 Feb 2020 21:06:19 GMT

Species=Summar is the reference level. Because you've included an intercept term, the GLM can only estimate DIFFERENCES between levels. For the mathematical details, see "Singular parameterizations, generalized inverses, and regression estimates"

Re: proc glm - categorical variable 2 levels but don't want interaction tested for each level

mihoyoshi — Wed, 05 Feb 2020 22:27:08 GMT

I ran this:

proc glm data=Rootmicr.Initial;
Class Species;
by Group;
model log10biomarker = log10root | depthnum | Species / solution;
lsmeans Species / stderr pdiff cov out=adjmeans;;
ods output ParameterEstimates=Rootmicr.IniDepthSpecIntxnGLMparmestim;
run;

How does one interpret this part of the output?

The SAS System

The GLM Procedure

Least Squares Means

Group=Universa

Species log10biomarker LSMEAN StandardError H0:LSMEAN=0 H0:LSMean1=LSMean2Pr > |t| Pr > |t|KanlowSummer

1.18374631	0.30934731	0.0010	0.2874
1.58113183	0.19197711	<.0001

Re: proc glm - categorical variable 2 levels but don't want interaction tested for each level

StatDave — Mon, 17 Feb 2020 19:59:24 GMT

There is only a single interaction estimated, and that is the -4.08 value. What is confusing you is just the fact that your Species variable is a CLASS (categorical) predictor and is represented in the model with two dummy-coded (0,1-coded) variables. However, since Species has two levels, it has only 1 degree of freedom and therefore only 1 estimable parameter. The second parameter is restricted to zero. Similarly, the interaction has only 1 degree of freedom (1 for log10root times 1 for Species equals 1). Again, the second is restricted to zero. The significant -4.08 interaction suggests that the effect of log10root differs between the two Species.