I am simulating data from the model . Three conditions are varied in the simulation:

(1) number of groups (NG: three conditions, NG = 30, 50, 100),

(2) group size (GS: three conditions, GS = 5, 30, 50),

(3) intraclass correlation (ICC: three conditions, ICC = 0.1, 0.2, 0.3).

So I wrote a function to simulate data from the model:

Code:

```
# J = number of groups
# n_j = group size
simu <- function(J,n_j,g00,g10,g01,g11,sig2_0,sig01,sig2_1){
N <- sum(rep(n_j,J)) #sample size
x <- rnorm(N) #level 1 (individual) level variable
z <- rnorm(J) #level 2 (group) level variable
#generate (u_0j,u_1j) from bivariate normal
mu <- c(0,0)
sig <- matrix(c(sig2_0,sig01,sig01,sig2_1),ncol=2)
u <- rmvnorm(J,mean=mu,sigma=sig)
b_0j <- g00 + g01*z + u[,1]
b_1j <- g10 + g11*z + u[,2]
y <- rep(b_0j,each=n_j)+rep(b_1j,each=n_j)*x + rnorm(N,0,0.5)
sim_data <- data.frame(Y=y,X=x,Z=rep(z,each=n_j),group=rep(1:J,each=n_j))
} # end of function simu
```

Code:

```
CI <- function(J,n_j,g00,g10,g01,g11,sig2_0,sig01,sig2_1){
dat <- simu(J,n_j,g00,g10,g01,g11,sig2_0,sig01,sig2_1)
lmer_obj <- lmer(Y~X+Z+X:Z+(X|group),data=dat)
res <- summary(lmer_obj)
estim <- coefficients(res)
se <- coefficients(res)
ci <- data.frame(intercept=estim[1] + qnorm(c(.025,.975))*se[1],
X=estim[2] + qnorm(c(.025,.975))*se[2],Z=estim[3] + qnorm(c(.025,.975))*se[3],
XZ=estim[4] + qnorm(c(.025,.975))*se[4])
indicator <- ifelse((ci[1,]<c(g00,g10,g01,g11) & ci[2,]>c(g00,g10,g01,g11)),0,1)
}
```

(1) sig01 = 0 , since in the paper , it is mentioned that "To simplify the simulation model, the covariance between the two u-terms is assumed equal to zero."

(2) sig2_0 = sig2_1 , in the paper , it is mentioned that "Busing (1993) shows that the effects for the intercept variance \(\sigma_{00}\) and the slope variance \(\sigma_{11}\) are similar; hence, we chose to set the value of \(\sigma_{11}\) equal to \(\sigma_{00}\) .

Now , I checked for a combination :

Code:

```
cond4 <- replicate(1000,CI(30,30,1,.3,.3,.3,(1/18),0,(1/18)))
nonc4 <- apply(cond4,1:2,mean)
```

Code:

```
intercept X Z XZ
1 0 0 0 0
```

Where am I doing mistake ?

Any HELP is APPRECIATED .

Many thanks! Regards .