
Note: I am sending this again because I got an email saying that it was not delivered. In case it was delivered initially, I apologise for the double-posting. 



Dear all, I am running a very simple mixed effects model using lmer. I get the following results:

Random
 effects: Groups   Name        Variance Std.Dev. id       (Intercept) 
7.4223   2.7244   Residual             1.9767   1.4060  
Number of obs: 8080, groups: id, 2020


Apparently,
 a very good question is whethe0r the estimate of the parameters of the 
random effect are indeed bigger than zero. So, I used the bootstrap 
method described by Faraway where the distribution of likelihood rations
 is built between a model with and withot the random effect. I get a 
probbility p<0.0001, so the random effect estimates are significant. I
 also confirmed these findings using the library("RLRsim"). 


So
 far so good, but one of the reviewers asked me to give 95% confidence 
intervals. I spent three hours on the internet searching for good 
solutions and decided that I should use the following:

sm1 <- mcmcsamp(mlm.1.1g, n=1000, saveb = TRUE)
lme4::HPDinterval(sm1)


However, the 95% lower and upper bounds do not indclude the estimate!!!! See below:

> r$sigma  lower    upper
[1,] 1.977582 2.058084
attr(,"Probability")
[1] 0.95

How is this possible? 

Also,
 I assume that the ST shows the ratio of [random effect variance]/[total
 variance]. In this case, my ICC is 7.42/(7.42+1.97)=0.79 but see the 
foloowing:

> r$ST  lower     upper
[1,] 0.6905202 0.7342866
attr(,"Probability")
[1] 0.95
My
 empirical ICC is not included in the confidence interval. Apparently, I
 am missing something but after spending a lot of time, I need to ask 
you offer me some of your experience. 
Thank you for your time

Jason


 
Dr. Iasonas Lamprianou
Department of Social and Political Sciences
University of Cyprus
	[[alternative HTML version deleted]]

