[R] How to calculate Intraclass-coefficient in 2-level Linear Mixed-Effects models?
Christine A.
adrion at ibe.med.uni-muenchen.de
Thu Jan 31 16:25:43 CET 2008
Dear R-users,
consider a 2-level linear mixed effects model (LME) with random intercept
AND random slope for level 1 AND 2. Does anybody know how to calculate
Intraclass-coefficient (ICC) for highest (innermost) level 2 ??? In the
literature, I did not find an example for these kind of komplex models.
For 1-level Random-Intercept models it would be easy:
ICC = variance due to the clustering variable / (variance due to the
clustering variable + variance remaining) = sigma^2_RandomIntercept /
(sigma^2_RIntercept + sigma^2_error)
My data are similar to Pixel-Data from R-package nlme:
=> Please assume an adequate model is the following (although you really do
not need the Random Slope on Level "Side within Dog" here... and an adequate
model is also different concerning fixed effects):
-----------------------------------------------------------------------------------
m1 <- lme(pixel ~ day + I(day^2), data = Pixel,
random = list(Dog = ~ day, Side = ~ day))
Linear mixed-effects model fit by REML
Data: Pixel
AIC BIC logLik
904.27 927.71 -443.13
Random effects:
----------------
Formula: ~day | Dog
Structure: General positive-definite, Log-Cholesky parametrization
StdDev Corr
(Intercept) 31.494 (Intr)
day 1.0720 -0.786
Formula: ~day | Side %in% Dog
Structure: General positive-definite, Log-Cholesky parametrization
StdDev Corr
(Intercept) 15.09 (Intr)
day 0.0000249 0
Residual 14.534
Fixed effects: pixel ~ day
Value Std.Error DF t-value p-value
(Intercept) 1093.22 10.9566 81 99.777 0.0000
day -0.15 0.4912 81 -0.303 0.7629
Correlation:
(Intr)
day -0.668
----------------------------------------------------------------------------------------------
There are 2 nested grouping factors: "Dog" (=Level 1) and "Side within Dog"
(=Level 2).
A LME could be used to calculate the intraclass correlation coefficient
(ICC) as a measure of concordance of pixel intensity in between left and
right Side .
Can anybody help me with the correct formula, i.e. do you have to include
variance component estimator for level 1 ("Dog"), too?
Is it something like this:
ICC = (sigma2_RandomSlope-Dog + sigma2_RandomSlope-SidewithinDog) /
(sigma2_RandomSlope-Dog + sigma2_RandomSlope-SidewithinDog + sigma2_error)
Any hints would be appreciated!
Many thanks in advance.
Christine Adrion,
University of Munich
--
View this message in context: http://www.nabble.com/How-to-calculate-Intraclass-coefficient-in-2-level-Linear-Mixed-Effects-models--tp15204786p15204786.html
Sent from the R help mailing list archive at Nabble.com.
More information about the R-help
mailing list