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## compar.gee.R (2015-05-01)
## Comparative Analysis with GEEs
## Copyright 2002-2015 Emmanuel Paradis
## This file is part of the R-package `ape'.
## See the file ../COPYING for licensing issues.
compar.gee <-
function(formula, data = NULL, family = gaussian, phy,
corStruct, scale.fix = FALSE, scale.value = 1)
{
if (requireNamespace("gee", quietly = TRUE)) gee <- gee::gee
else stop("package 'gee' not available")
if (!missing(corStruct)) {
if (!missing(phy))
warning("the phylogeny was ignored because you gave a 'corStruct' object")
R <- vcv(corStruct, corr = TRUE)
} else {
R <- vcv(phy, corr = TRUE)
}
if (is.null(data)) data <- parent.frame()
else {
nmsR <- rownames(R)
if (!identical(rownames(data), nmsR)) {
if (!any(is.na(match(rownames(data), nmsR))))
data <- data[nmsR, ]
else {
msg <- if (missing(corStruct))
"the tip labels of the tree" else "those of the correlation structure"
msg <- paste("the rownames of the data.frame and", msg,
"do not match: the former were ignored in the analysis")
warning(msg)
}
}
}
effect.assign <- attr(model.matrix(formula, data = data), "assign")
for (i in all.vars(formula)) {
if (any(is.na(eval(parse(text = i), envir = data))))
stop("the present method cannot be used with missing data: you may consider removing the species with missing data from your tree with the function 'drop.tip'.")
}
id <- rep(1, dim(R)[1])
geemod <- do.call("gee", list(formula, id, data = data, family = family, R = R,
corstr = "fixed", scale.fix = scale.fix,
scale.value = scale.value))
W <- geemod$naive.variance
fname <-
if (is.function(family)) deparse(substitute(family)) else if (is.list(family)) family$family else family
if (fname == "binomial")
W <- summary(glm(formula, family = quasibinomial, data = data))$cov.scaled
N <- geemod$nobs
## <FIXME>
## maybe need to refine below in case of non-Brownian corStruct
if (!missing(corStruct)) phy <- attr(corStruct, "tree")
dfP <- sum(phy$edge.length)*N / sum(diag(vcv(phy))) # need the variances
## </FIXME>
## compute QIC:
Y <- geemod$y
MU <- geemod$fitted.values
Qlik <- switch(fname,
"gaussian" = -sum((Y - MU)^2)/2,
"binomial" = sum(Y*log(MU/(1 - MU)) + log(1 - MU)),
"poisson" = sum(Y*log(MU) - MU),
"Gamma" = sum(Y/MU + log(MU)),
"inverse.gaussian" = sum(-Y/(2*MU^2) + 1/MU))
Ai <- do.call("gee", list(formula, id, data = data, family = family,
corstr = "independence", scale.fix = scale.fix,
scale.value = scale.value))$naive.variance
QIC <- -2*Qlik + 2*sum(diag(solve(Ai) %*% W))
obj <- list(call = match.call(),
effect.assign = effect.assign,
nobs = N,
QIC = QIC,
coefficients = geemod$coefficients,
residuals = geemod$residuals,
fitted.values = MU,
family = geemod$family$family,
link = geemod$family$link,
scale = geemod$scale,
W = W,
dfP = dfP)
class(obj) <- "compar.gee"
obj
}
print.compar.gee <- function(x, ...)
{
nas <- is.na(x$coef)
coef <- x$coef[!nas]
cnames <- names(coef)
coef <- matrix(rep(coef, 4), ncol = 4)
dimnames(coef) <- list(cnames,
c("Estimate", "S.E.", "t", "Pr(T > |t|)"))
df <- x$dfP - dim(coef)[1]
coef[, 2] <- sqrt(diag(x$W))
coef[, 3] <- coef[, 1]/coef[, 2]
if (df < 0) {
warning("not enough degrees of freedom to compute P-values.")
coef[, 4] <- NA
} else coef[, 4] <- 2 * (1 - pt(abs(coef[, 3]), df))
residu <- quantile(as.vector(x$residuals))
names(residu) <- c("Min", "1Q", "Median", "3Q", "Max")
cat("Call: ")
print(x$call)
cat("Number of observations: ", x$nobs, "\n")
cat("Model:\n")
cat(" Link:", x$link, "\n")
cat(" Variance to Mean Relation:", x$family, "\n")
cat("\nQIC:", x$QIC, "\n")
cat("\nSummary of Residuals:\n")
print(residu)
if (any(nas))
cat("\n\nCoefficients: (", sum(nas), " not defined because of singularities)\n",
sep = "")
else cat("\n\nCoefficients:\n")
print(coef)
cat("\nEstimated Scale Parameter: ", x$scale)
cat("\n\"Phylogenetic\" df (dfP): ", x$dfP, "\n")
}
drop1.compar.gee <- function(object, scope, quiet = FALSE, ...)
{
fm <- formula(object$call)
trm <- terms(fm)
z <- attr(trm, "term.labels")
ind <- object$effect.assign
n <- length(z)
ans <- matrix(NA, n, 3)
for (i in 1:n) {
wh <- which(ind == i)
ans[i, 1] <- length(wh)
ans[i, 2] <- t(object$coefficients[wh]) %*%
solve(object$W[wh, wh]) %*% object$coefficients[wh]
}
df <- object$dfP - length(object$coefficients)
if (df < 0) warning("not enough degrees of freedom to compute P-values.")
else ans[, 3] <- pf(ans[, 2], ans[, 1], df, lower.tail = FALSE)
colnames(ans) <- c("df", "F", "Pr(>F)")
rownames(ans) <- z
if (any(attr(trm, "order") > 1) && !quiet)
warning("there is at least one interaction term in your model:
you should be careful when interpreting the significance of the main effects.")
class(ans) <- "anova"
attr(ans, "heading") <- paste("Single term deletions\n\n Model:",
as.character(as.expression(fm)), "\n")
ans
}
predict.compar.gee <-
function(object, newdata = NULL, type = c("link", "response"), ...)
{
type <- match.arg(type)
pred <- if (is.null(newdata)) object$fitted.values else {
frm <- formula(object$call$formula)[-2]
X <- model.matrix(frm, data = newdata)
beta <- object$coefficients
X[, names(beta), drop = FALSE] %*% beta
}
if (type == "link") return(pred)
f <- match.fun(object$family)
f(link = object$link)$linkinv(pred)
}
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