Hi Paige, the first post is in the "SAS Programming" forum, which was probably not the best place for the issue (and accordingly, very little discussion). The second post is in the "Statistical Procedures" forum, where there is more discussion. The solution that I am pursuing is essentially a Chow test as mentioned in an earlier.response: 1) duplicate the sample where the duplicate sample uses the alternative measurements for the variables; 2) assign a dummy variable to distinguish observations between the two samples; 3) interact the dummy variable with the X1 and X2 variables such that the model becomes: Y = X1 + X2 + D*X1 + D*X2. The coefficients for the interactive variables pick up the differential response between the two samples. Using a duplicate sample raises the issue of independence/clustering of observations. So, I evaluate the statistical significance of the coefficients using two-way (by subject and by time) cluster robust standard errors. Please offer any suggestions or criticisms of this approach.  Thank you,  Rick ... View more

Paige, in detail, Model 1 looks like this: Y/Z = X1/Z + X2/Z, where X, Y and Z are variables (no constants). So, for a given observation, Y, X1 and X2 are scaled by the same value. Same for Model 2 just a different scalar (i.e., instead of Z, substitute say W, which is a variable not a constant). I think I have a solution that will work.  Thank you!!  Rick ... View more

Yes Paige, you are correct. There may be a much simpler solution (famous last words) ... I'm thinking now that I could use two samples: one for each measurement.  Then simply use a dummy variable to pick up the difference in the coefficients. Thanks for your time, I really appreciate it!  Rick ... View more

Not sure if that works if you also rescale the dependent variable. ... View more

Probably best to purge this issue of any existing statistical procedures, and start with a clean slate. Think of the variables (both Y and X) for both models as consisting of a numerator and a denominator. The numerators are identical for both models. The denominators represent an attempt to scale the numerators, and the denominators are different for the two models. Goal is to compare the coefficients between the two models. Does this help frame the issue?  Thanks for you help guys!  Rick ... View more

Hi Paige, the difference between the variables in the two models is simply how we scale them (i.e., deflate them). Thanks for your help!  Rick ... View more

The two models are fit to the same dataset. However, the measurement of Y, X1 and X2 are different (I tried to highlight this idea with prime notation, Y', X1' and X2'). Thank you for your suggestion. ... View more

Thank you!  ODS GRAPHICS ON is helpful! ... View more

Thank you! ODS HTML does the trick.  ... View more

Thank you Steve!  I will definitely follow your advice!  Rick ... View more