Longitudinal study - how to plot the outcome with CI against time

[Ksharp]

That is G-Side random effect with SUBJECT_ID variable.

If you can get model convergency you need some skill to adjust parameters of model . Check this:
https://support.sas.com/resources/papers/proceedings12/332-2012.pdf

in proc mixed, the random and repeated statements model G-Side and R-Side random effect separatedly.
Correspond to PROC GLIMMIX ,it should be:
G_Side effect:
random intercept / subject = Patient_ID;

R_Side effect:
random visit/ subject = Patient_ID residal ;
or
random _residual_/ subject = Patient_ID;

[TomHsiung]

Hello, @Ksharp 

I spent a couple of weeks learning the general linear mixed model. The model is in the form of the formula in the screenshot.

We can use the maximum likelihood method or matrix of variance-covariance to solve the point and interval estimation of the regression coefficients. What I don't understand is: What is the difference between the G- and R-side models? Both belong to the general linear mixed model, so they have the same model formula.

[Ksharp]

Ou. That is a large topic. I think @lvm  @SteveDenham  could give you more details about it.
G-side random effect is for estimate coefficient.
For example : if you take SEX as fixed and random effect,
then the actually coefficient = coefficient (of fixed effect) +coefficient (of random effect) .
here coefficient (of fixed effect) is the same for Both Male and Female,
while coefficient (of random effect) is different for Male and Female.

The horizontal level/direction has random coefficient.


R-side random is design for RESIDUAL term.
For examle : if you take VISIT as random effect ,the residual from each VISIT is diffent/random.

The vertical level/direction has random coefficient.


Check resources for more info:
https://stats.oarc.ucla.edu/other/mult-pkg/introduction-to-generalized-linear-mixed-models/
https://support.sas.com/kb/37/109.html
https://support.sas.com/kb/37/110.html
https://blogs.sas.com/content/iml/2019/12/03/longitudinal-data-response-profile-model.html
https://blogs.sas.com/content/iml/2019/12/05/longitudinal-data-mixed-model.html

[SteveDenham]

I realize this sort of jumping into the middle but I would suggest looking at the output file, especially the iteration history. If the history stops at 20 iterations with no other messages, then you have run up against the default maximum. If the history keeps rolling along and eventually has some other message, then there are some things to try. For a first attempt, I would suggest adding the following NLOPTIONS statement:

nloptions maxiter=1000 tech=nrridg;

For R-side models and a binary distribution, the ridged Newton-Raphson method often works better than the default quasi-Newton (QUANEW).

Good luck.

SteveDenham

[TomHsiung]

Thanks for the suggestion, sir. But I think I must first understand the G- and R-side models first. I know understand the formula of a general linear mixed model but the textbook I read does not discuss this topic in detail.

[TomHsiung]

Does R-side PROC GLIMMIX neglect the random effect (Z*u)?

PS: y = X*Beta + Z*u + error

[Ksharp]

Z*u is G-side random effect,
R-side random effect is in/included ERROR term.

[TomHsiung]

Thanks for the feedback. OK, if R-side model does not have the Zu matrix, then what is the difference between the mixed effect model and a regular linear model?

PS: R-side model: Y = X*beta + error is the same to the regular linear model: Y = X*beta + error. What makes the difference?

[Ksharp]

R-side random effect have the similar/same structure with G-side at some time.
You could take R-side random 's error term as:
error=Zu
here Zu has the similar/same structure with G-side random Zu.

E.X. the following two model(G-side and R-side) are the same model.
G-side:
proc imixed;
class subject;
model y=time;
random int/subject=subject;
run;

R-side:
proc mixed;
class subject;
model y=time;
repeated time/type=cs subject=subject;
run;

Except RANDOM constrain the correlation to be positive,whereas REPEATED leaves the correlation unconstrained.