# How is the confidence interval for variance component in "lmer" function computed ?

#### Cynderella

##### New Member
Here is the R code :

Code:
    library(lme4)
fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
confint.merMod(fm1,oldNames=FALSE)
And the output is

Code:
                                   2.5 %     97.5 %
sd_(Intercept)|Subject        14.3814761  37.715996
cor_Days.(Intercept)|Subject  -0.4815007   0.684986
sd_Days|Subject                3.8011641   8.753383
sigma                         22.8982669  28.857997
(Intercept)                  237.6806955 265.129515
Days                           7.3586533  13.575919

I understand how the confidence interval for "(Intercept)" and "coefficient of Days " are calculated (though it is **not profile** confidence intervals ) :

Code:
    res=summary(fm1)
ans=coefficients(res)
estimate = ans[,1]
se = ans[,2]

ci.int = estimate[1]+qnorm(c(.025,.975))*se[1]
[1] 238.0292 264.7810

ci.day = estimate[2]+qnorm(c(.025,.975))*se[2]
[1]  7.437595 13.496977
But I don't know how are the confidence interval of "sig01" , "sig02" , "sig03" , "sigma" calculated ?

I am trying to calculate the confidence interval (whether it is profiled or not) of variance component in that manner that I have calculated for "(Intercept)" and "Days", that is , confidence interval of variance component based on asymptotic standard normal distribution .

Thank you very much. Regards.