topic Re: If I have multiple group within person, how could I conduct repeated ANOVA? in Statistical Procedures

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

SAS-questioner — Tue, 22 Mar 2022 23:01:35 GMT

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!

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

Ksharp — Wed, 23 Mar 2022 12:39:35 GMT

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

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

SteveDenham — Wed, 23 Mar 2022 13:33:27 GMT

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

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

SAS-questioner — Wed, 23 Mar 2022 18:34:58 GMT

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?

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

SAS-questioner — Wed, 23 Mar 2022 18:36:35 GMT

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.

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

SAS-questioner — Wed, 23 Mar 2022 19:23:55 GMT

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?

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

jiltao — Wed, 23 Mar 2022 20:23:40 GMT

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.

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

SAS-questioner — Wed, 23 Mar 2022 20:56:48 GMT

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

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

jiltao — Wed, 23 Mar 2022 21:05:10 GMT

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

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

SAS-questioner — Wed, 23 Mar 2022 21:08:12 GMT

I saw the Estimated G matrix is not positive definite. Might be that's the reason it didn't show any random effects? Should I change something in the code?

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

SAS-questioner — Wed, 23 Mar 2022 21:10:08 GMT

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

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

jiltao — Wed, 23 Mar 2022 22:19:42 GMT

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

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

SAS-questioner — Wed, 23 Mar 2022 23:12:43 GMT

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

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

SteveDenham — Thu, 24 Mar 2022 13:48:23 GMT

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

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

StatsMan — Thu, 24 Mar 2022 15:14:47 GMT

Another possibility is to treat person as a block and make PERSON the single random effect in your model. Were these measures taken sequentially over time, or are they observational statistics on the combination of the fixed effects A,B, and C? If you go with this approach, then put A,B, and C on the model statement and use a single RANDOM statement with

random int / subject=person;

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

SAS-questioner — Thu, 24 Mar 2022 15:51:16 GMT

Thank you for your reply. Those measures were not taken sequentially over time, they just the observational statistics for each person. So do you think the random int/subject=person work as same as put all groups in the random like random interceptA B C A*B A*C B*C /subject=person? So the result is the repeated ANOVA instead of multilevel modeling?

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

jiltao — Thu, 24 Mar 2022 17:25:46 GMT

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

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

SAS-questioner — Thu, 24 Mar 2022 18:44:50 GMT

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?

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

SAS-questioner — Thu, 24 Mar 2022 19:49:19 GMT

By the way, how could I conduct the homogeneity of variance test in proc mixed for repeated ANOVA? Thank you!

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

SteveDenham — Thu, 24 Mar 2022 20:23:53 GMT

Remember that the assumption for ANOVA is that the errors are normally distributed, not the data. Someplace else in this thread you asked how to do that. An OUTPUT statement that puts all of the residuals in a data set, followed by the test for normality in PROC UNIVARIATE will work, but a QQ plot would be even better, as all known tests for normality suffer from dependency on sample size - if the dataset is large, then the test is over powered and will declare even small deviations from normality to be significant, and if the dataset is small it is under powered and could easily miss a true difference.

Somewhere else in this thread you ask about non-normal dependent variables. It would help to know what your dependent variable(s) is/are. Counts may have a Poisson, generalized Poisson or negative binomial distribution. Strict proportions of the events/trials type are, by default, binomial. Ratios of continuous variables that are continuous on the open interval (0,1) tend to have a beta distribution. PROC GLIMMIX (for conditional inference) and GENMOD (for marginal inference) are the right tools for this, so read through the examples for those two procedures.

So now it appears that the variables A, B and C are measures on each subject, rather than classification variables to which subjects are assigned at random. Is that the case? Without breaking any privacy issues, could you tell us what these variables are? I am leaning toward the approach given by @StatsMan of treating the subject as the random effect, clustering responses by subject. This approach could probably be done more directly with PROC GEE or GENMOD.

However, if there are assigned "treatments" included in these 3, that approach may need some additional thought. lA thorough description of design and variables would go a long way toward addressing all of these issues.

SteveDenham