Hello Sarah. The examples included in this SPSS Technical Report may be helpful:

https://csass.ucsc.edu/self-study%20courses/SPSSMixed.pdf

Cheers,

Bruce

Check out the link below on the IBM site.

https://www.ibm.com/docs/en/spss-statistics/27.0.0?topic=models-linear-mixed-subjects-repeated

Especially here

Repeated

The variables specified in this list are used to identify repeated observations. For example, a single variable Week might identify the 10 weeks of observations in a medical study, or Month and Day might be used together to identify daily observations over the course of a year.

Abolfazl Ghoodjani, what you posted implies that the REPEATED sub-command is used only when there are repeated measures (or other correlated data points). That is not completely correct. As the Command Syntax Reference manual says:

"The REPEATED subcommand specifies the residual covariance matrix in the mixed-effects model. If no REPEATED subcommand is specified, the residual covariance matrix assumes the form of a scaled identity matrix with the scale being the usual residual variance."

Source: https://www.ibm.com/docs/en/spss-statistics/27.0.0?topic=mixed-repeated-subcommand-command

Furthermore, the attached SPSS syntax file includes an example with an independent groups design (Male vs Female with no repeated measures at all) where the REPEATED sub-command is used to allow (and model) heterogeneous variances. (People who do not have SPSS can view the syntax file with any text editor.) Here is an excerpt:

* Now allow unequal variances via /REPEATED sub-command.

MIXED Y BY Male

/FIXED=Male | SSTYPE(3)

/PRINT=SOLUTION R

/REPEATED=Male | SUBJECT(UniqueID) COVTYPE(DIAG)

/EMMEANS = tables(Male)

.

* Notice that this result matches the unequal variances F-tests from ONEWAY.

Given that REPEATED can be used when there are no repeated measures at all, as in this example, I wish the SPSS programmers had come up with a different name for the sub-command, as calling it REPEATED has caused many people no end of confusion. But it's not going to change now, so we have to live with it!

HTH.

PS- When I wrote that syntax, I had a version of SPSS that had not yet added the ROBUST subcomand to UNIANOVA/GLM. That would be another way to model variance heterogeneity nowadays.

https://www.ibm.com/docs/en/spss-statistics/27.0.0?topic=unianova-robust-subcommand-command

Bruce Weaver Excellent and thank you.