Unexpected R matrix in PROC MIXED if ref=first

ckx — Thu, 15 Jan 2026 14:27:16 GMT

I’d always assumed that if the option “order=internal” is used on the PROC MIXED statement, that the rows of an R matrix would be ordered according to the values of the time variable. It turns out that the rows of R have the same order as the time variable in the fixed effects. If “time(ref=first)” is used in the CLASS statement then the first category will be placed in the LAST row of R, as it is for the fixed effects.

The attached SAS program estimates a model using the ARH(1) covariance structure twice, first with “time(ref=first)”, then with “time(ref=last)”. Data are from https://stats.oarc.ucla.edu/wp-content/uploads/2016/02/repeat-1.txt, the model is:

Title1 "arh(1) structure, time(ref=first)";
ods output R=R1;
proc mixed data=long order=internal;
  class exertype time(ref=first);
  model pulse = exertype time exertype*time / solution;
  repeated time / subject=id type=arh(1) R;
run;
ods output close;

Using “time(ref=first)”, I get the following covariance pattern estimates and R matrix:

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
Var(1)	id	83.2217
Var(2)	id	120.57
Var(3)	id	35.9136
ARH(1)	id	0.5022

Estimated R Matrix for Subject 1
Row	Col1	Col2	Col3
1	35.9136	13.7881	33.0464
2	13.7881	83.2217	50.3053
3	33.0464	50.3053	120.57

R[1,1] corresponds with Var(3) in the covariance estimates, R[2,2] with Var(1), R[3,3] with Var(2). The order of the TIME variable in the fixed effects is 2, 3, 1 and that order seems to be used for the covariance parameter estimates as well.

The same model using “time(ref=last)” in the class statement produces the following covariance parameter estimates and R matrix:

Covariance Parameter Estimates
Cov Parm	Subject	Estimate
Var(1)	id	35.7683
Var(2)	id	87.1927
Var(3)	id	115.50
ARH(1)	id	0.5101

Estimated R Matrix for Subject 1
Row	Col1	Col2	Col3
1	35.7683	28.4861	16.7237
2	28.4861	87.1927	51.1893
3	16.7237	51.1893	115.50

Diagonal values of R now correspond with values for Var(1) to Var(3) from the covariance parameter estimates.

Is this a known "feature" for time variables using repeated measures in PROC MIXED? The R matrix will not be as expected if the default "ref=last" is not used for the time variable and the covariance pattern assumes ordered categories.

Re: Unexpected R matrix in PROC MIXED if ref=first

jiltao — Thu, 15 Jan 2026 14:45:28 GMT

Please refer to this usage note:

http://support.sas.com/kb/69066

Especially #2.

As noted in the usage note, a workaround would be to create another variable, such as time1, which is a copy of time, and use time1 in the REPEATED statement. For example,

proc mixed data=long order=internal; class exertype time(ref=first) time1; model pulse = exertype time exertype*time / solution; repeated time1 / subject=id type=arh(1) R; run;

Hope this helps.

Jill

Re: Unexpected R matrix in PROC MIXED if ref=first

ckx — Thu, 15 Jan 2026 15:31:39 GMT

Thanks Jill, for the quick reply with a workaround as well!

topic Re: Unexpected R matrix in PROC MIXED if ref=first in Statistical Procedures

Unexpected R matrix in PROC MIXED if ref=first

Re: Unexpected R matrix in PROC MIXED if ref=first

Re: Unexpected R matrix in PROC MIXED if ref=first