Hosmer et al. (2013: 327) advise that in a logistic regression model with a single random (group-level) effect, the so-called intra-cluster correlation is an estimate of the proportion of the overall variability accounted for by the random (group-level) effect. The formula that they provide for comp…

[image] blokeman: If left to my own devices I’d probably calculate the average of the three ICCs, I’m not sure what you mean by “per regresison equation”. Is it just a discrete (as opposed to truly multinomial) regression? If you want the posterior standard deviation of a parameter, you nee…

[image] Bob_Carpenter: I’m not sure what you mean by “per regresison equation”. Is it just a discrete (as opposed to truly multinomial) regression? Sorry, that must have been an erroneous wording (I’ve edited it now). It’s multinomial. With 4 outcome categories, the model is composed of 3 bin…

[image] blokeman: With 4 outcome categories, the model is composed of 3 binary logistic regressions, each comparing one non-reference outcome with the reference outcome. Why not use multi-logit? It’s the usual approach for multiple categories. There’s a discussion in the manual regression ch…

There is an icc()-function in the sjstats-package , which can be used for stanreg or brms objects. However, for non-Gaussian models, it is recommended to calculate the ICC based on the posterior predictions (I think this was stated by @Bob_Carpenter or @bgoodri ). You can use the ppd-argument to calc…

[image] Rstanarm: extracting variance components rstanarm Outside of a Gaussian, linear, no link function model, the idea of a decomposition of variance does not make sense. The general, correct, and Bayesian way to do things is PPD <- posterior_predict(post) vars <- appl…

Thanks for the input, strengejacke. I tried the package you’re referring to. And indeed, its author defines ICC identically to what I’ve understood it to mean: “the proportion of the variance explained by the grouping structure in the population”. But the output of the icc() function is cryptic to m…

I’ll take a shot at calculating it myself. Maybe people can tell me something I’m doing wrong: Reminder: it’s a categorical logit model with 4 outcome categories and one random effect. ll.re <- log_lik(mod, re_formula = NULL)#Posterior predictive LLs using random effect ll.fe <- log_lik(mod, re_fo…

The ICC also depends on whether you calculate the mean or median of posterior draws. See argument typical in icc(). And the “ICC” based on the posterior predictive distribution is not necessarily close to a “classical” ICC.

Thank you. I find that using the median instead of the mean yields the same result (to two decimal places). Might I infer that since that was the only thing that raised a comment, you see no error in the rest of the procedure?

For the classical ICC, you get tau.00 from VarCorr(). I’m not sure whether using the log-likelihood is the appropriate approach.

Calculating Intra-Cluster Correlation (ICC) for the Group-Level Effect in a Multinomial GLMM

Modeling

strengejacke July 16, 2018, 8:32am 6

Here’s the link to the discussion.

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Calculating Intra-Cluster Correlation (ICC) for the Group-Level Effect in a Multinomial GLMM

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