topic Re: GLM confidence limits for group specific intercepts and slopes in Statistical Procedures

GLM confidence limits for group specific intercepts and slopes

smar — Fri, 18 Sep 2020 11:11:16 GMT

I am using proc GLM with dummy variables coding for different groups and a continuous variable. Then, I can get coeffcients and CI for all variables and interactions.

I then compute group-specific intercept and slopes for the 0-group as follows:

intercept + ca t0

cont + cont*cat 0

How then can I get the corresponding CI?

Example:

data tmp;
    input cont cat outcome;
    datalines;
1.1 0 0.8
1.5 0 0.6
2.1 0 0.6
5.1 0 0.2
2.1 1 0.9
1.1 1 0.7
1.4 1 0.8
4.7 1 0.3
;
run;

proc glm data=tmp;
    class cat;
    model outcome = cont | cat / solution clparm;
run;

Parameter	Estimate	Standard Error	t Value	Pr > \|t\|	95% Confidence	Limits
Intercept	0.989189	0.128196	7.72	0.0015	0.633259	1.34512
cont	-0.13514	0.04707	-2.87	0.0454	-0.26582	-0.00445
cat 0	-0.10905	0.178144	-0.61	0.5735	-0.60366	0.385561
cat 1	0	.	.	.	.	.
cont*cat 0	0.000383	0.06342	0.01	0.9955	-0.1757	0.176466
cont*cat 1	0	.	.	.	.	.

Re: GLM confidence limits for group specific intercepts and slopes

PaigeMiller — Fri, 18 Sep 2020 11:13:52 GMT

These are essentially the confidence intervals for predicted values.

So you need to add the desired levels of conc and cat to your dataset, with missing values for outcome, and then the OUTPUT statement data set will contain the desired confidence intervals.

Re: GLM confidence limits for group specific intercepts and slopes

smar — Fri, 18 Sep 2020 11:27:20 GMT

I am afraid predicted values CI are not what I am looking for.

To be more precise, let's assume my model is as follows:

outcome = b0 + b1 * group + (b2 + b3*group) * x

with "group" being a binary variabe.

I am looking for the CIs of the group-specific intercept (b0 + b1*group) and the group-specific slopes (b2 + b3*group) with no regard to the value of x.

Re: GLM confidence limits for group specific intercepts and slopes

PaigeMiller — Fri, 18 Sep 2020 11:38:45 GMT

Okay, then you need to re-parameterize the model so that each of these terms of interest is an individual term in the model.

model outcome = cat cont*cat / solution clparm;

The group specific slopes are the cont*cat terms. The group specific intercepts are the cat term.

Re: GLM confidence limits for group specific intercepts and slopes

smar — Fri, 18 Sep 2020 12:10:14 GMT

I accepted the answer a bit fast (because I am mainly interested in the slopes).

Your solution works for slopes, but the intercept still have to be added to "cat".

Is there a workaround for that?

Output:

Intercept	0.9891891892	0.12819646	7.72	0.0015	0.6332587543	1.3451196241
cat 0	-.1090473452	0.17814433	-0.61	0.5735	-.6036552868	0.3855605963
cat 1	0.0000000000	.	.	.	.	.
cont*cat 0	-.1347517730	0.04250296	-3.17	0.0338	-.2527589074	-.0167446387
cont*cat 1	-.1351351351	0.04707033	-2.87	0.0454	-.2658233265	-.0044469437

Re: GLM confidence limits for group specific intercepts and slopes

PaigeMiller — Fri, 18 Sep 2020 14:39:53 GMT

Add the NOINT option into the MODEL statement.