all the ICCs - #59
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"ICC" names a family of coefficients that share a form -- a ratio of a variance component to a total variance -- but answer different questions and carry different names in different literatures. Implement the widest set computable from a mixed model or a table of ratings, all behind the existing `icc` entry point, and document the taxonomy. Variance partitioning (extends the existing behaviour): - `conditional=true` includes var(Xβ) in the denominator, giving the conditional (unadjusted) ICC alongside the adjusted one. - `slopes=:mean` averages the random-effects variance over observations following Johnson (2014), so the ICC is defined for random-slope models rather than silently summing the diagonal of Σ. - `method=` selects the GLMM observation-level variance: the Nakagawa et al. (2017) `:delta`, `:lognormal` and `:trigamma` approximations for Poisson, and `:theoretical` vs `:observation_level` for binomial. - `method=:simulation` partitions variance on the response scale by simulating from the fitted model, following Goldstein et al. (2002). - `groupmean=true` gives the group-mean reliability that the organizational literature calls ICC(2) after Bliese (2000). Inter-rater reliability (new): passing a long-format table of ratings computes the six Shrout & Fleiss (1979) / McGraw & Wong (1996) coefficients with their exact F-based intervals, reproducing the published Shrout & Fleiss Table 2 values and psych::ICC's intervals. Following Liljequist et al. (2019), the default reports all six together with the variance components and a rater-bias F test, rather than requiring a model to be chosen in advance. BREAKING: two changes to existing results, both deliberate. - Random-slope ICCs change, because the Johnson (2014) average replaces the sum of the random-effect variances (sleepstudy `(1+days|subj)`: 0.477 -> 0.709). Pass `slopes=:diagonal` to recover the old values. - Poisson ICCs change, because the observation-level variance was hardcoded to 1.0, which is not one of the standard estimators. The default is now Nakagawa's `:lognormal`. Also fixes an ordering bug in the bootstrap group-mean path, where the guard for a missing `model` ran after the `_group_size` call it was meant to protect. Co-Authored-By: Claude Fable 5 <[email protected]>
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