CLMM: Calculate ICC & Assessing Model Fit

The 'cauchit' link was used in the example for stability. The other distributions that are available in the package produced warnings. My "real" data set uses the 'loglog' link for the clmm().

The distribution across the 9 levels appears rather haphazard, which dissuaded me from trying a GLMM:

https://photos.app.goo.gl/8BtBa9N6PtqbZ1fM8

Cheers,
Sal

-----Original Message-----
From: David Duffy <David.Duffy at qimrberghofer.edu.au>
Sent: Wednesday, August 19, 2020 10:59 PM
To: Sidoti, Salvatore A. <sidoti.23 at buckeyemail.osu.edu>
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] CLMM: Calculate ICC & Assessing Model Fit

It turns out that the statistical contribution of each animal in my 
study is quite profound, so a mixed model is essential in my case.

Do you really need the cauchit? What does the distribution across 9 levels of the trait look like? We regularly fit ordinal mixed models in genetic contexts, and one rule of thumb is that if there are more than 5 levels, then treating the variable as continuous usually gives much the same answers as the ordinal model, but interpretation of effects, variance explained etc is a lot more straightforward. Aside from residuals, one can get model goodness-of-fit chi-squares from the pairwise (and higher order) contingency tables (predicted v. observed) eg Visit1 v. Visit2 summed across all subjects (where the probit model parameters are the 8 thresholds and 1 polychoric correlation, so you have 64-9 degrees of freedom for whether a latent bivariate normal fits).

Cheers, David Duffy.