[R-sig-ME] CLMM: Calculate ICC & Assessing Model Fit

Juho Kristian Ruohonen juho@kr|@t|@n@ruohonen @end|ng |rom gm@||@com
Wed Aug 19 15:35:00 CEST 2020

Just voicing two thoughts as a non-statistician:

1. Why do you feel you need a mixed model in the first place? It looks to
me like every Individual is contributing the same number of responses (i.e.
4). Thus, the individual-specific effects can be assumed to cancel each
other out, and no random effect is needed.
2. Why complicate things with a non-canonical link function? It looks to me
like a standard ordinal logistic regression model, with fixed effects only,
would do the job for you. Guides and textbooks abound on how to assess the
fit of such models.



ke 19. elok. 2020 klo 14.44 Sidoti, Salvatore A. (
sidoti.23 using buckeyemail.osu.edu) kirjoitti:

> To begin with, I'm not a fan of cross-posting. However, I posted my
> question on Stack Exchange more than two weeks ago, but I have yet to
> receive a sufficient answer:
> https://stats.stackexchange.com/questions/479600/data-with-ordinal-responses-calculate-icc-assessing-model-fit
> Here's what I've learned since then (hopefully):
> 1) ICC of a CLMM:
> Computed like this:
> (variance of the random effect) / (variance of the random effect + 1) If
> this is correct, I would love to see a reference/citation for it.
> 2) 95% Confidence Interval for the ICC from a CLMM Model To my current
> understanding, a confidence interval for an ICC is only obtainable via
> simulation. I've conducted simulations with GLMM model objects ('lme4'
> package) and the bootMer() function. Unfortunately, bootMer() will not
> accept a CLMM model ('ordinal' package).
> 3) Model Fit of a CLMM
> Assuming that the model converges without incident, the model summary
> includes a condition number of the Hessian ('cond.H'). This value should be
> below 10^4 for a "good fit". This is straightforward enough. However, I am
> not as sure about the value for 'max.grad', which needs to be "well below
> 1". The question is, to what magnitude should max.grad < 1 for a decent
> model fit? My reference is linked below (Christensen, 2019), but it does
> not elaborate further on this point:
> https://documentcloud.adobe.com/link/track?uri=urn:aaid:scds:US:b6a61fe2-b851-49ce-b8b1-cd760d290636
> 3) Effect Size of a CLMM
> The random variable's effect is determined by a comparison between the
> full model to a model with only the fixed effects via the anova() function.
> I found this information on the 'rcompanion' package website:
> https://rcompanion.org/handbook/G_12.html
> The output of this particular anova() will include a value named
> 'LR.stat', the likelihood ratio statistic. The LR.stat is twice the
> difference of each log-likelihood (absolute value) of the respective
> models. Is LR.stat the mixed-model version of an "effect size"? If so, how
> does one determine if the effect is small, large, in-between, etc?
> Cheers,
> Sal
> Salvatore A. Sidoti
> PhD Candidate
> Behavioral Ecology
> The Ohio State University
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