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I have a data set with the following structure.

The response is ordinal.

There is an experimental factor (with two treatment levels, each treatment level applied to a different sample of subjects).

Each subject within each treatment group is then given both conditions of a different experimental factor. And each subject's ordinal response to each level of the second factor is measured across several time points with the between subject and within subject treatments continuing over the span of these time points.

My question is twofold. First is how to conceive the model for this structure. From one perspective it seems that this can be viewed as a split-plot design with the first factor being applied at the whole-plot level and the second experimental factor and time "operating" at the subplot level.

It seems that repeated measures considerations need to come into play as well.

But it also seems like the conceptual framework of statistical longitudinal analysis can be applied here as well. Then the first experimental factor is part of the between clusters level of analysis (with subjects being the clusters) and the second experimental factor and time being at the within clusters level of analysis.

Perhaps "split plot" and "repeated" versus cluster is an unnecessary distinction. But I haven't found any references that suggest that these are two sides of the same coin, which is why I am posing the question here.

The second part of my query concerns an appropriate R library for the analysis. It seems like an R library equivalent to the SAS Glimmix functionality is what I am looking for. I just came across the R mixor package and am taking a closer look at it. But if anyone has other suggestions I would welcome them.

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