Nothing
BImm <- function(fixed.formula,random.formula=NULL,Z=NULL,nRandComp=NULL,m,data=list(),maxiter=100){
if ((is.null(random.formula))&(is.null(Z))){
stop("Random part of the model must be especified")
}
if ((is.null(random.formula)==FALSE)&(is.null(Z))==FALSE){
stop("Random part of the model has been specified twice")
}
if ((is.null(Z)==FALSE)&(is.null(nRandComp))){
stop("Number of random components must be specified")
}
if ((is.null(Z))&(is.null(nRandComp)==FALSE)){
stop("Number of random components must be specified only when Z is defined")
}
if (is.null(Z)==FALSE){
if (dim(Z)[2]!=sum(nRandComp)){
stop("The number of random effects in each random component must match with the number of columns of the design matrix Z")
}
}
if (maxiter!=as.integer(maxiter)){
stop("maxiter must be integer")
}
if(maxiter<=0){
stop("maxiter must be positive")
}
if (sum(as.integer(m)==m)==length(m)){
} else{
stop("m must be integer")
}
if (min(m)<=0){
stop("m must be positive")
}
#Fixed effects design matrix:
fixed.mf <- model.frame(formula=fixed.formula, data=data)
X <- model.matrix(attr(fixed.mf, "terms"), data=fixed.mf)
q <- dim(X)[2]
#Outcome variable:
y <- model.response(fixed.mf)
nObs <- length(y)
#Balanced data
if(length(m)==1){
balanced <- "yes"
m. <- rep(m,nObs)
} else{
m. <- m
if (sum(m[1]==m)==length(m)){
balanced <- "yes"
} else{
balanced <- "no"
}
}
if (sum(as.integer(y)==y)==length(y)){
} else {
stop("y must be integer")
}
if ((length(m)==1) | (length(m)==length(y))){
} else{
stop("m must be a number, or a vector of the length of y")
}
if (max(y-m)>0 | min(y) < 0){
stop("y must be bounded between 0 and m")
}
#Specifiying random effects structure
if (is.null(random.formula)){
nComp <- length(nRandComp) #Number of random components, number of u,v...
nRand <- dim(Z)[2] #Number of random effects, number of u_i,v_i,..
namesRand <- as.character(seq(1,nComp,1))
} else {
#Random effects design matrix:
random.mf <- model.frame(formula=update(random.formula,~.-1), data=data)
nComp <- dim(random.mf)[2] #Number of random components, number of u,v...
nRandComp <- NULL #Number of random effects in each random components, number of u_i in u.
Z <- NULL
for(i in 1:nComp){
z <- model.matrix(~random.mf[,i]-1)
Z <- cbind(Z,z)
nRandComp <- c(nRandComp,dim(z)[2])
}
nRand <- dim(Z)[2] #Number of random effects, number of u_i,v_i,..
namesRand <- names(random.mf)
}
# Initial values
iter=0
while.iter <- 0
beta <- BIreg(fixed.formula,m,data)$coefficients
all.sigma <- rep(1,nRand)
oldall.sigma <- rep(Inf,nRand)
eta <- X%*%beta
oldeta <- rep(Inf,nObs)
while (max(abs(oldall.sigma-all.sigma))>0.001){
oldall.sigma<- all.sigma
oldeta <- rep(Inf,nObs)
while (max(abs(eta-oldeta))>0.001){
oldeta <- eta
# Relevant to the working vector
p <- 1/(1+exp(-(eta)))
mu <- m.*p
g. <- m./(mu*(m.-mu))
yw <- eta + (g.*(y-mu))
W <- diag(c((m.*p*(1-p))))
#Variance-covariance matrix of random effects
d <- d. <- NULL
for (i in 1:nComp){
d <- c(d,rep(all.sigma[i],nRandComp[i]))
d. <- c(d.,rep(1/(all.sigma[i]),nRandComp[i]))
}
D <- diag(d)
D. <- diag(d.)
u <- solve(t(Z)%*%W%*%Z+D.)%*%t(Z)%*%W%*%(yw-X%*%beta)
beta <- solve(t(X)%*%W%*%X)%*%t(X)%*%W%*%(yw-Z%*%u)
eta <- X%*%beta+Z%*%u
}
# Calculating the variance component sigmau
t <- 0
t1 <- NULL
t2 <- NULL
sig. <- NULL
for (l in 1:nComp){
t1 <- t+1
t2 <- t+nRandComp[l]
D. <- (1/all.sigma[l])*diag(nRandComp[l])
sig.. <- as.numeric((1/nRandComp[l])*(t(u[seq(t1,t2)])%*%u[seq(t1,t2)]+sum(diag(solve(t(Z[,seq(t1,t2)])%*%W%*%Z[,seq(t1,t2)]+D.)))))
sig. <- cbind(sig.,sqrt(sig..))
t <- t+nRandComp[l]
}
all.sigma <- sig.
iter=iter+1
cat("Iteration number:", iter,"\n")
if (iter==maxiter){
print("The maximum number of iterations was reached without convergence")
conv <- "no"
out <- list(conv=conv)
return(out)
}
}
conv <- "yes"
# Returning the final values
d <- NULL
for (l in 1:nComp){
d. <- all.sigma[l]*rep(1,nRandComp[l])
d <- c(d,d.)
}
D <- diag(d)
W. <- diag(1/diag(W))
V <- W.+Z%*%D%*%t(Z)
# Beta
fixed.coef <- beta
V. <- solve(V)
fixed.vcov <- solve(t(X)%*%V.%*%X)
# Random efffects u
random.coef <- u
sigma.coef <- all.sigma
P <- V.- V.%*%X%*%fixed.vcov%*%t(X)%*%V.
Fisher.randvar <- -(1/2)*4*(sigma.coef^2)*(sum(diag(P%*%Z%*%t(Z)%*%P%*%Z%*%t(Z))))
sigma.var <- -1/Fisher.randvar
# fitted values and residuals
fitted <- 1/(1+exp(-eta))
# Deviance
# See Pawitan book
#deviance <- 2*log(2*pi)+log(det(solve(W)))+t(yw-eta)%*%W%*%(yw-eta)+log(det(solve(D.)))+t(u)%*%D.%*%u+log(det(t(Z)%*%W%*%Z+D.))
# Breslow's approach
deviance <- sum(log(diag(V)))+log(det(t(X)%*%V.%*%X))+t(yw-X%*%beta)%*%V.%*%(yw-X%*%beta)
df <- nObs-length(fixed.coef)-1
# output
out <- list(fixed.coef=fixed.coef,fixed.vcov=fixed.vcov,
random.coef=random.coef,sigma.coef=sigma.coef,sigma.var=sigma.var,
fitted.values=fitted,conv=conv,
deviance=deviance, df=df,conv=conv,
nRand=nRand,nRandComp=nRandComp,namesRand=namesRand,
iter=iter,nObs=nObs,
y=y,X=X,Z=Z,
balanced=balanced,m=m)
class(out) <- "BImm"
out$call <- match.call()
out$formula <- formula
out
}
print.BImm <- function(x,...){
cat("Call: \t")
print(x$call)
cat("\nFixed effects estimation:\n")
print(t(x$fixed.coef))
cat("\n")
cat("\nStandard deviation of normal random effects:\n")
for (i in 1:length(x$namesRand)){
cat(x$namesRand[i], x$sigma.coef[i])
cat("\n")
}
cat("\nDeviance of the model:",x$deviance)
cat("\nNumber of iterations:",x$iter)
if(x$balanced=="yes"){
cat("\nBalanced data, maximum score in the trials:", x$m,"\n")
} else {
cat("\nNo balanced data.\n")
}
}
summary.BImm <- function(object,...){
# Fixed
se <- sqrt(diag(object$fixed.vcov))
tval <- object$fixed.coef/se
TAB <- cbind(object$fixed.coef,se,tval,2*pnorm(-abs(tval)))
colnames(TAB) <- c("Estimate","StdErr","t.value","p.value")
#Sigma
sigma.table <- cbind(object$sigma.coef,sqrt(object$sigma.var))
rownames(sigma.table) <- object$namesRand
colnames(sigma.table) <- c("Estimate","StdErr")
out <- list(call=object$call,fixed.coefficients=TAB,
random.coef=object$random.coef,sigma.table=sigma.table,
fitted.values=object$fitted.values,residuals=object$residuals,
deviance=object$deviance, df=object$df,
nRand=object$nRand,nComp=object$nComp,nRandComp=object$nRandComp,namesRand=object$namesRand,
iter=object$iter,nObs=object$nObs,
y=object$y,X=object$X,Z=object$Z,
balanced=object$balanced,m=object$m,
conv=object$conv)
class(out) <- "summary.BImm"
out
}
print.summary.BImm <- function(x,...){
cat("Call:\t")
print(x$call)
cat("\nFixed effects coefficients:\n")
cat("\n")
printCoefmat(x$fixed.coefficients,P.values=TRUE,has.Pvalue=TRUE)
cat("\n---------------------------------------------------------------\n")
cat("Random effects dispersion parameter(s):\n")
cat("\n")
print(x$sigma.table)
cat("\n---------------------------------------------------------------\n")
cat("Deviance of the model:",x$deviance,"; with", x$df,"degrees of freedom.")
cat("\nNumber of observations:",x$nObs)
cat("\nNumber of iterations:", x$iter)
if(x$balanced=="yes"){
cat("\nBalanced data, maximum score in the trials:", x$m)
} else {
cat("\nNo balanced data.")
}
cat("\nNumber of random effects in each random component:",x$nRandComp,"\n")
cat("\n")
}
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