# Testing Parameters of Mixed Model .

#### Cynderella

##### New Member
This pdf illustrates nicely how is to test the random effect of multilevel model . But I am simulating data from a two-level model and estimating the parameters of the model for various combination of the parameters. For each condition , I generated 1000 simulated data sets. I have used R for both simulation and estimation. The codes are following :

Code:
simfun <- function(J,n_j,g00,g10,g01,g11,sig2_0,sig01,sig2_1){
N <- sum(rep(n_j,J))

x <- rnorm(N)
z <- rnorm(J)

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,sqrt(0.5))
sim_data <- data.frame(Y=y,X=x,Z=rep(z,each=n_j),group=rep(1:J,each=n_j))

}

fit <- function(J,n_j,g00,g10,g01,g11,sig2_0,sig01,sig2_1){
dat <- simfun(J,n_j,g00,g10,g01,g11,sig2_0,sig01,sig2_1)
model <- lmer(Y~X+Z+X:Z+(X||group),data=dat)
}

c4 <- replicate(10,fit(30,30,1,.3,.3,.3,(1/18),0,(1/18))) #I will replicate it 1000 times. but for now it is replicated 10 times
Now I want to test the both fixed effect and random effects . But not understanding how is to test all of them simultaneously .

To test both fixed effect and random effects , I modified the last function fit as :

Code:
fit <- function(J,n_j,g00,g10,g01,g11,sig2_0,sig01,sig2_1){
dat <- simfun(J,n_j,g00,g10,g01,g11,sig2_0,sig01,sig2_1)
model <- lmer(Y~X+Z+X:Z+(X||group),data=dat)

full <- lmer(Y~X+Z+X:Z+(X||group),data=dat,control=lmerControl(optCtrl=list(maxfun=20000)))

#Testing significance of random intercept
null.U0 <- update(full, .~.-(1 | group))
dev.U0 <- as.numeric(2*(logLik(full)-logLik(null.U0)))
p.U0 <- 0.5*(1-pchisq(dev.U0,1))

#Testing significance of random slope
null.U1 <- update(full, .~.-(0 + X | group))
dev.U1 <- as.numeric(2*(logLik(full)-logLik(null.U1)))
p.U1 <- 0.5*(1-pchisq(dev.U1,1))

#Testing significance of intercept of fixed part
null.int <- update(full, .~.-1)
dev.int <- as.numeric(2*(logLik(full)-logLik(null.int)))
p.int <- (1-pchisq(dev.U1,1))

#Testing significance of X of fixed part
null.x <- update(full, .~.-X)
dev.x <- as.numeric(2*(logLik(full)-logLik(null.x)))
p.x <- (1-pchisq(dev.x,1))

#Testing significance of Z of fixed part
null.z <- update(full, .~.-X)
dev.z <- as.numeric(2*(logLik(full)-logLik(null.z)))
p.z <- (1-pchisq(dev.z,1))

#Testing significance of interaction part
null.xz <- update(full, .~.-X:Z)
dev.xz <- as.numeric(2*(logLik(full)-logLik(null.xz)))
p.xz <- (1-pchisq(dev.xz,1))

pvals <- data.frame(p.U0=p.U0,p.U1=p.U1,p.int=p.int,p.x=p.x,p.z=p.z,p.xz=p.xz)
}

c1 <- replicate(10,fit(30,5,1,.3,.3,.3,(1/18),0,(1/18)))
colMeans(apply(c1,2,unlist))
Is it correct procedure to test the fixed and random effect part simultaneously? But I think I am introducing the multiplicity error. How can I adjust this by Bonferroni Correction ?