Solved – Reporting confidence interval of linear mixed model in R

confidence intervalmixed modelr

Hi I have a question regarding interpreting the confidence interval of linear mixed model in R

So I have a model like this 

a2 <- lmer(RT ~ Trial + (1 + Trial | ID), data = d2)

summary(a2)

Linear mixed model fit by REML ['lmerMod']
Formula: RT ~ Trial + (1 + Trial | ID)
   Data: d2

REML criterion at convergence: 21952.6

Scaled residuals: 

    Min      1Q    Median      3Q     Max 
-6.5799   -0.4538  -0.0546  0.4154  5.6741 

Random effects:

 Groups   Name        Variance Std.Dev. Corr 
 ID       (Intercept)  3.780   1.944         
          Trial        2.928   1.711    -0.20
 Residual             18.938   4.352         
Number of obs: 3701, groups:  ID, 205

Fixed effects:
            Estimate Std. Error t value
(Intercept)   3.4625     0.1542  22.450
Trial         0.3462     0.1426   2.427

Correlation of Fixed Effects:
      (Intr)
Trial -0.145

And then i calculate the confidence interval 

> confint(a2, oldNames = FALSE)
Computing profile confidence intervals ...
                               2.5 %      97.5 %
sd_(Intercept)|ID         1.70924477  2.19902280
cor_Trial.(Intercept)|ID -0.37359403 -0.01528644
sd_Trial|ID               1.48596866  1.95348922
sigma                     4.24882612  4.45891618
(Intercept)               3.15960363  3.76556626
Trial                     0.06594692  0.62636130

I'm not sure what each row in the confidence interval represents. When asked to report the confidence interval of Trial I thought it was (0.07, 0.63) but turns out it should be (1.49, 1.95). Why is that ?

Best Answer

Assuming that Trial is a dichotomous variable taking values 0 and 1, then

  • The 95% confidence interval for Trial (0.07 - 0.63) is for the difference of the average RT between Trial=1 and Trial=0.
  • The 95% confidence interval for sd_Trial|ID (1.49 - 1.95) is for the standard deviation of the random subject-specific differences between Trial=1 and Trial=0.