Basically I have questions about three different "proc glimmix" code's model setup. ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- Data description; The "mydata" is like a 44 days(Day=1,2,3...44) by 24 subjects(PID=1,2,3...24) observations total dataset and it only contains 5 columns each(Missed, PID, Day, Q, Z). The data are complete, balanced(each subjects have 1,2,3...44 days). "Missed" is the binary(0/1) response and only "Q" and "Z" are continuous data("Z" here is the subejct-level data, which means for the same subject "PID 1", it should be the same value of "-1.05643" for all days). ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- My problems: (1) proc glimmix data=mydata pconv=1e-4;
class PID Day;
model Missed=Q Z/s dist=binomial link=logit;
random Q/subject=pid;
random _residual_/ subject= pid(day) type=ar(1);
run; (2) proc glimmix data=mydata pconv=1e-4;
class PID Day;
model Missed=Q Z/s dist=binomial link=logit;
random Q/subject=pid;
random _residual_/ subject= day(pid) type=ar(1);
run; (3) proc glimmix data=mydata pconv=1e-4;
class PID Day;
model Missed=Q Z/s dist=binomial link=logit;
random Q/subject=pid;
random day / subject= pid type=ar(1) residual;
run; I want to know the mathematical formulas of the above three codes actually fitting. Basically I am not very sure what is the meaning of "R-side" on mathematical formula of NON-Gaussian GLMM. BTW, I can run those code((1) and (2) do not get the "Standard Error" of "AR(1)" of table "Covariance Parameter Estimates") and I can see (1) and (2) actually giving the same results, except for (3). So I become more confused... ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- For example, if the code is like below without R-side; proc glimmix data=mydata pconv=1e-4;
class PID Day;
model Missed=Q Z/s dist=binomial link=logit;
random Q/subject=pid;
run; Then, its mathematical model should be(Y_{j,t} here is the value of Missed): On the other hand, I know the one of repeated measure if it is LMM(Gaussian): proc glimmix data=mydata1;
class PID Day;
model yjt=Q Z/ s dist=normal;
random q/subject=pid;
random day / subject= pid type=ar(1) residual;
run; ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- I am strungling of it for a while and cannot find out any answers about these kind of questions. The questions may be short but I just attach all the information in case of any confusion. I am really looking forward that someone can help me and am very appreciated of it. Thank you.
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