# LME and multiple comparisons

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Chen Gafni on 17 Jun 2016
Answered: Paul on 5 Aug 2020
Hello, I have a model with several categorical fixed factors, each having several levels. Fitlme reports confidence intervals and p values for n-1 levels of each fixed factor compared to a selected reference. How can I determine these values for other combinations of factor levels? (e.g., level 1 vs. level 2, level 1 vs. level 3, level 2 vs. level 3).
Thanks, Chen

Peng Li on 5 Aug 2020
If I understand your question correctly, you were asking a post hoc comparison issue? coefTest method of LinearMixedModel object could help with this. basically you need a comtrast matrix to indicate which two levels you'd like to compare.
Here is reference page for coefTest.

Paul on 5 Aug 2020
Hi Chen,
You talk about confidence intervals and p-values, and how you can get those for other combinations/comparisons of levels. The answer about p-values I have given recently, here.
With regards to confidence intervals I'm not sure I can give you a satisfying answer, but I first want to ask you to clarify your question a bit more. Do you mean the confidence interval of the difference between level 1 and level 2, for example? There are ways to calculate this, but I'm not sure if this is at all useful in practice. I found it hard to determine a best way of doing this, and I found I had very little need for it in the end, so I never figured out exactly how to do it.
If you could explain what kind of confidence bounds you are talking about, exactly, and what you want to use them for, I can see if I can help you.
Best,
Paul

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