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List: r-sig-mixed-models
Subject: [R-sig-ME] Residual variance term in lmer with binomial error and observation-level random effect
From: Tina Wey <tina.wey () gmail ! com>
Date: 2013-09-20 17:24:12
Message-ID: CABrS_XEPnj5zhf2Oa5LFmL6=M-THRiQ5U5btRu1mdT6iD8_PEA () mail ! gmail ! com
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Hello,
I am calculating the repeatability of a random effect of individual in a
model using lmer and wanted to check that I'm understanding the residual
variance term correctly. I have seen similar questions previously posted,
but not quite answering my specific question clearly.
The outcome variable is a proportion (of two white blood cell types in a
sample), so I am using a binomial error distribution with logit link. I
have added an observation-level random effect to account for
overdispersion. A simplified version of the model is:
nl <- lmer (prop.test ~ # a proportion created from cbind (n, l)
(1|obs.id) # observation-level random effect
+ (1|uid) # individual random effect
+ (1|year) # random effect of year
+ date + age + sex # fixed effects
, data = NL.main
, family = "binomial"
)
>From the Nakagawa & Shielzeth 2010 Biological Reviews paper on this topic,
the residual variance for an additive overdispersion model of this type
should be the variance of the residual term + (pi^2)/3. From a previous
thread on this mailing list, I read that the observation-level random
effect gives the residual variance term. So two main questions:
1. Is the residual variance then calculated as: (variance explained by
obs.id) + (pi^2) / 3 ?
2. If so, then the repeatability of individual random effect in my model is
very small (0.02681726), yet significant at p = 0.002875. Is it strange to
have such a significant random effect with such a small intraclass
correlation coefficient? I do have a very large sample size (863
observations on 334 individuals), but still didn't know if this outcome was
suspicious...
Many thanks in advance!
Tina
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