In sibling models with categorical outcomes the question arises of how best to calculate the intraclass correlation, ICC. We show that, for this purpose, the random effects linear probability model is preferable to a random effects non-linear probability model, such as a logit or probit. This is because, for a binary outcome, the ICC derived from a random effects linear probability model is a non-parametric estimate of the ICC, equivalent to a statistic called Cohen’s κ. Furthermore, because κ can be calculated when the outcome has more than two categories, we can use the random effects linear probability model to compute a single ICC in cases with more than two outcome categories. Lastly, ICCs are often compared between groups to show the degree to which sibling differences vary between groups: we show that when the outcome is categorical these comparisons are invalid. We suggest alternative measures for this purpose.

中文翻译：

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同级模型，分类结果和类内相关

在具有分类结果的同级模型中，出现了一个问题，即如何最好地计算类内相关性（ICC）。我们证明，为此目的，随机效应线性概率模型优于诸如logit或probit之类的随机效应非线性概率模型。这是因为，对于一个二元结果，从线性概率模型随机效应产生的ICC是国际刑事法院的非参数估计，相当于一个叫科恩的统计κ。此外，因为κ可以在结果具有两个以上类别时进行计算，在具有两个以上结果类别的情况下，我们可以使用随机效应线性概率模型来计算单个ICC。最后，ICC经常在组之间进行比较，以显示组之间兄弟姐妹差异的变化程度：我们表明，当结果是绝对分类时，这些比较是无效的。我们建议为此目的采取其他措施。