Hi , can anyone please explain me the following output produces in `R` when I ran the command `confint(lmer())` .

Here is the R code :

And the output is :

I have understood the last two row which are confidence interval for Intercept and Days , respectively . But what are those `sig01` , `sig02` , `sig03` , `sigma` ?

If I write down the model `Reaction ~ Days + (Days | Subject)` :

\(\text{Reaction}_{ij}=\beta_{0j}+\beta_{1j}\text{Days}_{ij}+e_{ij}\)

\(\beta_{0j}=\gamma_{00}+u_{0j}\)

\(\beta_{1j}=\gamma_{10}+u_{1j}\)

Combining the last two equations into first one , that is , by substituting the level-2 equation to level-1 equation, we have ;

\(\text{Reaction}_{ij}=\gamma_{00}+\gamma_{10}\text{Days}_{ij}+u_{0j}+u_{1j}\text{Days}_{ij}+e_{ij}\)

* Is `sig01` variance of \(u_{0j}\) ?

* Is `sig02` variance of \(u_{1j}\) ?

* Is `sig03` variance of \(e_{ij}\) ?

* What is `sigma` in the output of `confint` ?

Many Thanks! Regards .

Here is the R code :

Code:

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

Code:

```
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
```

If I write down the model `Reaction ~ Days + (Days | Subject)` :

\(\text{Reaction}_{ij}=\beta_{0j}+\beta_{1j}\text{Days}_{ij}+e_{ij}\)

\(\beta_{0j}=\gamma_{00}+u_{0j}\)

\(\beta_{1j}=\gamma_{10}+u_{1j}\)

Combining the last two equations into first one , that is , by substituting the level-2 equation to level-1 equation, we have ;

\(\text{Reaction}_{ij}=\gamma_{00}+\gamma_{10}\text{Days}_{ij}+u_{0j}+u_{1j}\text{Days}_{ij}+e_{ij}\)

* Is `sig01` variance of \(u_{0j}\) ?

* Is `sig02` variance of \(u_{1j}\) ?

* Is `sig03` variance of \(e_{ij}\) ?

* What is `sigma` in the output of `confint` ?

Many Thanks! Regards .

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