If I have multiple group within person, how could I conduct repeated ANOVA?

[SAS-questioner]

I have dataset like follows:

Person  GroupA GroupB GroupC DV

  1             A            F           1        30

  1             A            F            2       40

  1             A            N           1       20

  1             A            N           2       15  

  1             B            F           1        25

  1             B            F            2       24

  1             B            N           1       22

  1             B            N           2       17

  2.............A             F           1       12

  2.......................................................

In this case, I want to compare the mean difference between A, B, C. How could I conduct the repeated ANOVA?

PROC MIXED;
CLASS person groupA groupB groupC;
MODEL DV = groupA|groupB|groupC;
REPEATED / SUBJECT=person TYPE=CS;
run;

Does the above code look correct? But I saw some example that I think should put "repeated groupA groupB groupc/SUBJECT=person" because those groups are repeated within persons, but I can't put more than one repeated effects. Could anyone help me with it? Thank you!

[Ksharp]

Which variable is your Visit Number variable ? if GroupC was, I think you should code like :

REPEATED / SUBJECT=person*groupB*groupC TYPE=CS;

Or Calling @SteveDenham @StatDave

[SAS-questioner]

When you are saying the visit number variable do you mean the time variable? Actually I don't have time variable in my dataset, but all the group A B and C are nested within each person.

[SteveDenham]

If there are only 2 levels for each of the factors A, B and C, you may want to consider calling at least one effect RANDOM.  The other two could then be fit as doubly repeated measures using the Kronecker product UN@UN as the type.  The subject= will be slightly different for each of these.

Here is an example for that (no guarantees as to whether this will work or not, without having the data to fit)::

PROC MIXED;
CLASS person groupA groupB groupC;
MODEL DV = groupA|groupB|groupC;
RANDOM intercept/subject=GroupC;
REPEATED groupA GroupB/ SUBJECT=person*groupC TYPE=UN@UN;
run;

Another method would be to concatenate the factors essentially making this a one-way ANOVA, and use LSMESTIMATE statements to with a JOINT option to get F tests of interest.  You would have to either switch to PROC GLIMMIX or use a STORE statement followed by PROC PLM.

SteveDenham

[SAS-questioner]

Hi, thank you for your reply and suggestions, but the group A, B, and C have more than three levels, can I put all three of them in the repeated statement? Or I saw there is one procedure call the proc genmod, can I use this instead without putting the repeated statements? 

[SAS-questioner]

I guess the proc genmod doesn't work because it didn't produce the F test result, and I can't check the mean difference among all those factors. Do you mean if the group A, B, and C are more than three factors, I should use proc glimmix to conduct the repeated ANOVA?

[jiltao]

There are several ways to model the correlations in your data. I am not sure what the variables GroupA, GroupB, and GroupC are, but one of the straightforward models would be modeling the correlations through random effects. For example,

PROC MIXED;
CLASS person groupA groupB groupC;
MODEL DV = groupA|groupB|groupC;
RANDOM intercept GroupA GroupB GroupC GroupA*GroupB GroupA*GroupC GroupB*GroupC/subject=person;
run;

Some of the random interaction effects might or might be present in your data. If you get zero estimated variance for some of the random effects, you might consider taking them out of the RANDOM statement.

[SAS-questioner]

I tried your method, and I didn't see any of the random effect in the output page, I only saw the Type three test of fixed effects. Does that look good?

                                  Type 3 Tests of Fixed Effects

                                                   Num     Den
                      Effect                    DF      DF    F Value    Pr > F

                      group A                    3      12       0.81    0.5112
                      group B                    2       8       4.00    0.0626
                      groupA*groupB              6      24       0.58    0.7460
                      group C                    3      12       0.99    0.4298
                      groupA*groupC              9      36       0.82    0.5985
                      groupB*groupC              6      24       1.33    0.2815
                      A*B*C                     18      72       1.76    0.0489

[jiltao]

Did you get the Covariance Parameter Estimates table in the output?

[SAS-questioner]

Sorry, yes, I get the covariance parameter estimate in the table. But will the "Estimated G matrix is not positive definite" affect the result?

[jiltao]

What is in this Covariance Parameter Estimates table? Can you send it here?

[SAS-questioner]

Below is the covariance parameter table, should I remove those with zeros and run the analysis again to avoid the negative definite? 

                                   Covariance Parameter Estimates

                            Cov Parm                 Subject     Estimate

                            Intercept               specimen      2.1541
                            Group A                 specimen      0.7469
                            Group B                 specimen           0
                            Group C                 specimen           0
                            GroupA*GroupB           specimen     0.04165
                            GroupA*GroupC           specimen      5.0689
                            GroupB*GroupC           specimen           0
                            Residual                              0.1730

[SteveDenham]

You should re run, leaving out Group B, Group C and the interaction Group B by Group C in the random statement.  A possible cause for the zero estimates is that the ML estimates are negative, and so using REML results in a zero value.  This would occur if all of the variability in these three factors is already explained by Group A and it's interactions.  However, it usually turns out that the standard errors of estimates are only minimally affected by leaving these in, and leaving them in results in denominator degrees of freedom that reflect your design.  The issue now is that you are "splitting" the variability due to these factors between fixed and random effects.  A possibility would be to exclude these factors from the RANDOM statement.

SteveDenham

[jiltao]

I agree with you Steve. For the ddf concerns, I would add the ddfm=kr option in the MODEL statement.

[SAS-questioner]

Thank you so much! I have one more question, if I check the dependent variable is not normally distributed, could I still use the proc mixed?