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#' @importFrom utils flush.console
glmmPQL.fit <- function(X, y, Z, weights = rep(1, NROW(y)), start = NULL,
etastart = NULL, mustart = NULL,
offset = rep(0, NROW(y)), family = gaussian(),
control = glmmPQL.control(...),
sigma = NULL, sigma.fixed = FALSE, ...) {
matchCall <- as.list(match.call(expand.dots = FALSE))
dots <- names(matchCall[["..."]])
dots <- intersect(dots, setdiff(names(formals(glm)), "control"))
fit0 <- do.call("glm.fit", c(list(X, y, weights, start = start,
etastart = etastart, mustart = mustart,
offset = offset, family = family,
control = glm.control()),
matchCall[dots]))
w <- fit0$prior.weights
# QR missing from glm.fit if ncol(X) = 0
QR <- qr(X)
R <- qr.R(QR)
rank <- QR$rank
p <- ncol(R)
nm <- colnames(R)[seq(length = rank)]
if (rank < p) {
X0 <- X[,colnames(R)[-seq(length = rank)]]
X <- X[, nm]
}
empty <- !length(X)
if (empty) {
alpha <- numeric(0)
Xa <- matrix(0, length(y), 1)
}
eta <- fit0$linear.predictors
residuals <- fit0$residuals
Y <- eta + residuals - offset #working response
wy <- fit0$weights # iterative weights
wY <- sqrt(wy) * Y
wZ <- sqrt(wy) * Z
ZWy <- crossprod(wZ, wY)
ZWZ <- crossprod(wZ, wZ)
if (!empty) {
wX <- sqrt(wy) * X
XWy <- crossprod(wX, wY)
XWX <- crossprod(wX, wX)
ZWX <- crossprod(wZ, wX)
E <- chol(XWX)
J <- backsolve(E, t(ZWX), transpose = TRUE)
f <- backsolve(E, XWy, transpose = TRUE)
ZSy <- ZWy - crossprod(J, f)
ZSZ <- ZWZ - crossprod(J, J)
}
if (is.null(sigma)) sigma <- 0.1
logtheta <- log(sigma^2)
conv <- FALSE
for (i in 1:control$maxiter) {
## Update coefficients
for (j in 1:control$IWLSiter) {
IZWZD <- ZWZ * sigma^2
diag(IZWZD) <- 1 + diag(IZWZD)
A <- chol(IZWZD)
if (!empty) {
IZSZD <- ZSZ * sigma^2
diag(IZSZD) <- 1 + diag(IZSZD)
G <- chol(IZSZD)
g <- backsolve(G, ZSy, transpose = TRUE)
v <- backsolve(G, g)
B <- backsolve(A, sigma * ZWX, transpose = TRUE)
K <- chol(XWX - crossprod(B, B))
b <- backsolve(A, sigma * ZWy, transpose = TRUE)
c <- backsolve(K, XWy - t(B) %*% b, transpose = TRUE)
alpha <- backsolve(K, c)
Xa <- X %*% alpha
beta <- sigma^2 * v
}
else {
g <- backsolve(A, ZWy, transpose = TRUE)
v <- backsolve(A, g)
beta <- sigma^2 * v
}
eta <- c(Xa + Z %*% beta + offset)
## Update working response & weights
mu <- family$linkinv(eta)
mu.eta.val <- family$mu.eta(eta)
residuals <- (fit0$y - mu)/mu.eta.val
Y <- eta + residuals - offset
wy <- w * mu.eta.val^2/family$variance(mu)
wY <- sqrt(wy) * Y
wZ <- sqrt(wy) * Z
ZWy <- crossprod(wZ, wY)
ZWZ <- crossprod(wZ, wZ)
if (!empty) {
wX <- sqrt(wy) * X
XWy <- crossprod(wX, wY)
XWX <- crossprod(wX, wX)
ZWX <- crossprod(wZ, wX)
E <- chol(XWX)
J <- backsolve(E, t(ZWX), transpose = TRUE)
f <- backsolve(E, XWy, transpose = TRUE)
ZSy <- ZWy - crossprod(J, f)
ZSZ <- ZWZ - crossprod(J, J)
score <- c(crossprod(X, wy * residuals),
crossprod(Z, wy * residuals) - v)
diagInfo <- c(diag(XWX), diag(ZWZ))
if (all(diagInfo < 1e-20) ||
all(abs(score) <
control$tol * sqrt(control$tol + diagInfo))) {
if (sigma.fixed) conv <- TRUE
break
}
}
else {
score <- crossprod(Z, wy * residuals) - v
diagInfo <- diag(ZWZ)
if (all(diagInfo < 1e-20) ||
all(abs(score) <
control$tol * sqrt(control$tol + diagInfo))) {
if (sigma.fixed) conv <- TRUE
break
}
}
}
if (!sigma.fixed){
## Update sigma
## sigma^2 = exp(logtheta)
## One Fisher scoring iteration
IZWZD <- ZWZ * sigma^2
diag(IZWZD) <- 1 + diag(IZWZD)
A <- chol(IZWZD)
if (!empty) {
IZSZD <- ZSZ * sigma^2
diag(IZSZD) <- 1 + diag(IZSZD)
G <- chol(IZSZD)
g <- backsolve(G, ZSy, transpose = TRUE)
v <- backsolve(G, g)
h <- backsolve(G, ZSZ, transpose = TRUE)
H <- backsolve(G, h)
}
else {
g <- backsolve(A, ZWy, transpose = TRUE)
v <- backsolve(A, g)
h <- backsolve(A, ZWZ, transpose = TRUE)
H <- backsolve(A, h)
}
## Harville p326
score <- drop(-0.5 * sum(diag(H)) + 0.5 * crossprod(v, v)) *
sigma^2
Info <- 0.5 * sum(H^2) * sigma^4
if (control$trace) {
##B & K eq 5 - still not consistently increasing
cat("Iteration ", i,
". Score = ", abs(score) ,
"\n", sep = "")
flush.console()
}
## check for overall convergence
if (Info < 1e-20 ||
abs(score) < control$tol * sqrt(control$tol + Info)){
conv <- TRUE
break
}
## Cannot use beta to update t(YXa) %*% Vinv %*% YXa
ZWYXa <- crossprod(wZ, sqrt(wy) * (Y - Xa))
optfun <- function(logtheta) {
IZWZD <- ZWZ * exp(logtheta)
diag(IZWZD) <- 1 + diag(IZWZD)
A <- chol(IZWZD)
if (!empty) {
IZSZD <- ZSZ * exp(logtheta)
diag(IZSZD) <- 1 + diag(IZSZD)
G <- chol(IZSZD)
d <- backsolve(A, sqrt(exp(logtheta)) * ZWYXa,
transpose = TRUE)
sum(log(diag(G))) - 0.5 * crossprod(d, d)
}
else {
d <- backsolve(A, sqrt(exp(logtheta)) * ZWy,
transpose = TRUE)
sum(log(diag(A))) - 0.5 * crossprod(d, d)
}
}
optres <- optimize(optfun, c(-10, 10))
if (optfun(-10) < optfun(optres$minimum))
sigma <- 0
else {
if (abs(optres$minimum - (logtheta + score/Info)) > 0.1)
logtheta <- optres$minimum
else
logtheta <- logtheta + score/Info
sigma <- sqrt(exp(logtheta))
}
}
else if (conv)
break
}
if (!empty) varFix <- chol2inv(K)
else varFix <- matrix(, 0, 0)
rownames(varFix) <- colnames(varFix) <- colnames(X)
fit0$coef[nm] <- alpha
if (!sigma.fixed)
varSigma <- sigma^2/(4 * Info)
else
varSigma <- NA
glm <- identical(sigma, 0)
if (!empty) {
if (rank < p) QR <- qr(cbind(wX, sqrt(w) * X0))
else QR <- qr(wX)
R <- qr.R(QR)
}
list(coefficients = structure(fit0$coef, random = beta),
residuals = residuals,
fitted.values = mu,
#effect = ?
R = if (!empty) R,
rank = rank,
qr = if (!empty) QR,
family = family,
linear.predictors = eta,
deviance = if (glm) sum(family$dev.resids(y, mu, w)),
aic = if (glm)
family$aic(y, length(y), mu, w, sum(family$dev.resids(y, mu, w))) +
2 * rank,
null.deviance = if (glm) {
wtdmu <- family$linkinv(offset)
sum(family$dev.resids(y, wtdmu, w))
},
iter = ifelse(glm, NA, i),
weights = wy,
prior.weights = w,
df.residual = length(y) - rank,
df.null = if (glm) length(y) - sum(w == 0),
y = y,
sigma = sigma, sigma.fixed = sigma.fixed,
varFix = varFix, varSigma = varSigma, converged = conv)
}
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