4
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Here is the R code :

library(lme4)
fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
confint(fm1)

Computing profile confidence intervals ...
                 2.5 %     97.5 %
.sig01       14.3815760  37.715996
.sig02       -0.4815007   0.684986
.sig03        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 ) :

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 ?

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  • 1
    $\begingroup$ For the variance components, those are profile likelihood CIs. An explanation of how such CIs are constructed is given here: stats.stackexchange.com/q/9833/1934 $\endgroup$ – Wolfgang Jul 25 '15 at 12:52
  • $\begingroup$ 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 . $\endgroup$ – user81411 Jul 26 '15 at 5:05
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    $\begingroup$ Those are Wald-type CIs. They usually perform terribly for variance components, so that's why the confint() function doesn't calculate them this way. Profile CIs are obtained via iterative methods - there is no closed-form equation. $\endgroup$ – Wolfgang Jul 26 '15 at 8:03
  • $\begingroup$ @Wolfgang If I want to calculate the confidence interval of variance component based on asymptotic standard normal distribution (not profile) , how can I calculate them ? $\endgroup$ – user81411 Jul 26 '15 at 12:47
  • $\begingroup$ @Wolfgang Could you please give me some reference of "Why does wald type CI give poor estimates for variance component?" $\endgroup$ – user81411 Jul 30 '15 at 12:27

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