topic Re: Testing significance of change in R^2 values between models in multiple linear regression in Statistical Procedures

Testing significance of change in R^2 values between models in multiple linear regression

abarnett313 — Sun, 29 Oct 2017 20:23:53 GMT

Greetings,

I am conducting an analysis using multiple linear regression in which variables are entered into the model in five blocks, and I would like to determine if the change in R^2 values between the blocks is significant (similar to a likelihood-ratio test for logistic regression). The model are as follows:

Model 1: pcr = g1 g2 race

Model 2: pcr = g1 g2 race x1 x2

Model 3: pcr = g1 g2 race x1 x2 x3 x4 x5

Model 4: pcr = g1 g2 race x1 x2 x3 x4 x5 x6

Model 5: pcr = g1 g2 race x1 x2 x3 x4 x5 x6 x7

g1, g2, and g3 are categorical variables. x1-7 are continuous variables. Here's the code I'm using:

proc glm data=scales; class g2 g1 race; model pcr=race g1 g2 /solution ; title 'Block 1';run;

proc glm data=scales; class g2 g1 race; model pcr=x1 x2 race g1 g2 /solution ; title 'Block 2'; run;

proc glm data=scales; class g2 g1 race; model pcr=x1 x2 x3 x4 x5 race g1 g2 /solution ; title 'Block 3'; run;

proc glm data=scales; class g2 g1 race; model pcr=x1 x2 x3 x4 x5 x6 race g1 g2 /solution ; title 'Block 4'; run;

proc glm data=scales; class g2 g1 race; model pcr=x1 x2 x3 x4 x5 x6 x7 race g1 g2 /solution; title 'Block 5'; run;

I have tried to use proc glmselect, too, but the issue that I am having is that I do not want the program to select and report the best model only, and I only want the variables to enter the model in the order specified above. I'm using SAS Enterprise Guide v4.3.

Any help in terms of how to test the significance of the change in R^2 values (or confirmation that it is not possible to do so in SAS) would be much appreciated.

Thanks!

abarnett313

Re: Testing significance of change in R^2 values between models in multiple linear regression

PaigeMiller — Sun, 29 Oct 2017 20:47:47 GMT

You want to use the "Extra Sum of Squares" method, which is explained here:

http://www.jerrydallal.com/LHSP/extra.htm

This is relatively easy to do in SAS.

Re: Testing significance of change in R^2 values between models in multiple linear regression

abarnett313 — Wed, 01 Nov 2017 16:03:37 GMT

Thank you -- this is exactly what I was seeking! Is there a way to have SAS calculate the extra sum of squares, or does it need to be done by hand?

Re: Testing significance of change in R^2 values between models in multiple linear regression

PaigeMiller — Wed, 01 Nov 2017 19:26:39 GMT

You have your PROC GLM or PROC REG or whatever output the sum of squares to SAS data sets, using ODS OUTPUT.

Then it should be relatively simple to combine the SS from each model into a single data step, and do the math in the data step.

Re: Testing significance of change in R^2 values between models in multiple linear regression

abarnett313 — Thu, 02 Nov 2017 15:19:27 GMT

Ah, that makes sense. Thank you!