Standard error is 0 in "Solution for Fixed Effects" in PROC MIXED when using transformed variable

[confooseddesi89]

Hello,

I am running PROC MIXED on an outcome variable called Reaction_Time and the predictors Day, Day*Day (quadratic trajectory), Sleepiness, Day*Sleepiness, Day*Day*Sleepiness, and Time. See the code below for my analysis:

Proc Mixed data=SR.Cog NOCLPRINT NOITPRINT COVTEST METHOD=ML; 
CLASS Participant; 
MODEL Reaction_Time = Day Day*Day Sleepiness Day*Sleepiness Day*Day*Sleepiness Time / SOLUTION; 
RANDOM intercept / TYPE=AR(1) SUBJECT=Participant; run;

When using such code I have no issues with the SAS output. However, if I substitute Response_Speed, the inversely transformed variable of Reaction_Time (that is, 1/Reaction_Time), in place of Reaction_Time, the "Solution for Fixed Effects" produces standard errors of 0 for my effects for "Day*Day*Sleepiness" and "Time." See the attached screenshot of my output:

The "t Values" are consequently infinity, and the p-values are < .0001. As you can see, in "Type 3 Tests of Fixed Effects," this phenomenon does not seem to be occurring; the p-values are over .0001. I tried searching online for standard errors of 0; it was mentioned that the model may be overparameterized. I'm not sure why this would be the case, as the model ran just fine with the non-transformed variable (Reaction_Time). Can someone clarify and help me fix this error?

Thanks!

confooseddesi89

[PaigeMiller · Accepted solution]

I'm guessing your scaling of variables is very different and the zero happens because of arithmetic underflow.

[confooseddesi89]

That was it! Changed the scaling of my variable (multiplied by 1000) and I didn't get 0 standard errors anymore. Thanks!