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I would like to be able to perform a sample size calculation for an Ordinal Logistic regression with mixed effects. The proposed design would have two different tests each with 5 different items, each participant does both tests and each item. (i.e. wide format data would be: ten columns of data - five for test 1 and five for test 2. Each row is a different participant). The dependent variable is ordered categorical with three levels (0,1,2).

Reading information on GLMMs by Ben Bolker, Andrew Gelman, and others, I see that that it might be sensible to include 'test' as a fixed effect rather than random effect (not enough levels?), but with 'item' as a random effect?

My question is in two parts:

  1. Is the correct model for this type of data either a series of binomial contrasts using logistic GLMM or is an ordinal logistic GLMM possible? I cannot find information on the ordinal GLMM model and an R implementation?
  2. Is it possible to perform a power calculation via simulation for an ordinal GLMM or alternatively, should I do a separate power calculation for each binomial contrast?
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  • $\begingroup$ Can you make this more specific than 'can I have some advice'? Note that asking for code / code check is off topic here. $\endgroup$ – gung Aug 23 '16 at 13:31
  • $\begingroup$ @gung I'm sorry my question was unclear, I have edited, as you and others have suggested, to be more specific. Also, I am not looking for code checking, so I have removed from the question. $\endgroup$ – ReadBeard Aug 24 '16 at 8:04
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I think the answer can be found here: https://stackoverflow.com/questions/21082396/multinomial-logistic-multilevel-models-in-r

and more specifically, follow the calculation here: http://rpubs.com/bbolker/11703

The idea is that instead of fitting a single model, a series of binomial contrasts are used (i.e. dependent variable...model1: category 0 vs category 1; Model 2: category 0 vs category 2; and Model 3: category 1 vs category 2.)

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