Solved – Multilevel models: Meaning of random intercept

mixed modelrepeated measuressas

I am quite confused at the moment regarding multilevel models as implemented in SAS PROC MIXED. I am new to mixed models.

Let's say I have 2 treatments, a new treatment and a control. And let's say that I have a sample of n subjects, each is contributing 1, 2 or 3 samples, i.e., the treatment (new or control) is being applied in 1 to 3 places in the subject's body.

I can't understand the difference between:

Proc mixed data=...
class Treatment SubjectID;
model Y = Treatment;
Random SubjectID;
run;

and

Proc mixed data=...
class Treatment SubjectID;
model Y = Treatment;
Random intercept / subject = SubjectID;
run;

I can't figure out this intercept / slope issue and its meaning.

Best Answer

Continuing @Peter Flom's example, it is equivalent to write the following two blocks:

proc mixed data=rc;
   class Batch;
   model Y = ;
   random batch;
run;

proc mixed data=rc;
   class Batch;
   model Y = ;
   random int / subject=batch;
run;

This first block adds a random effect term for each level of batch. The second block adds a random intercept and specifies that it varies from 'subject' to 'subject'.

Related Solutions

Solved – Reporting results of linear mixed-effects model

This may not help answer your question, but I noticed that you have a repeated measure (Day) in your experiment, but you did not indicate that this was a repeated measure in your model. I would have thought the random term in your model to be as such:

mymodel <- lme(dv ~ Treatment*Day, random = ~1|Subject/Day, 
               data = mydf, na.action = na.omit,
               correlation = corAR1(form = ~1 |Subject/Day), method = "REML")

As for reporting the results, did you intend to report on the day on which you start seeing significant differences between the treatments? If so, then I think you'll need to look at/report on the contrasts on the interaction term as well. I'm a stats novice myself and basically have the same question as you do :-)

Andy Field's "Discovering Statistics Using R" explains how to report results from a linear mixed effects model in Ch14. I don't have the book at hand but can edit this post once I get my hands on it again.

Solved – Mixed model with partial nesting/partial repeating

You might find it useful to think about random effects factors that are nested (which is more common) and random effects factors that are crossed (which is less common). If teacher_id, student_id, and class_id are random effects factors, then I (like you) would think of class_id being nested within teacher_id, and student_id being crossed with class_id(teacher_id). Hence I would consider

    random teacher_id
        class_id(teacher_id)
        student_id
        student_id*class_id(teacher_id);

If the model uses a normal distribution, then student_id*class_id(teacher_id) would be omitted from the random statement because it would be the residual variance. Your model uses a binary distribution and so has no residual variance; ideally the random statement would include student_id*class_id(teacher_id).

Adding two more random terms to your model certainly is not going to help with the problem with model size. You might find success with the HPMIXED procedure: citing the documentation, "The HPMIXED procedure is specifically designed to cope with estimation problems involving a large number of fixed effects, a large number of random effects, or a large number of observations." Unfortunately, HPMIXED assumes normal distributions. But to the rescue come Xie and Madden (2014) who have written a macro %HPGLIMMIX for generalized linear mixed models:

http://www.jstatsoft.org/article/view/v058i08/v58i08.pdf

I have never used this macro, and I have no idea whether the extensive unbalance and incompleteness of this design structure will be problematic. So I wish you good luck!

Best Answer

Related Solutions

Solved – Reporting results of linear mixed-effects model

Solved – Mixed model with partial nesting/partial repeating

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