Dear Christoph,
I done that and more. You'll find the functions below my signature. It
is mainly based on stepAIC from MASS. But it does more.
AICc = c(TRUE, FALSE) determines whether to use AICc or AIC
Furthermore it does not only refines the 'best' model but all good
models. A good model is defined as a model which has a AIC(c) values
that differs less that delta from the best model. Delta is by default 2,
but you can set it yourself. Delta = 0 would do the same thing a stepAIC
from MASS. Bandwidth controles the minimum number of models to refine.
Bandwidth = 10 will refine the 10 best models, regardless of AIC.
Marginal is a named list to indicate marginality. marginal = list(A =
c("B", "C"), B = "C") means that A can only enter the model if B and C
are present and B can only enter the model if C is present. Likewise B
can only leave the model is A is not present and C if A nor B are
present.
joint allows to specify variables that must enter or leave the model
simultaneous. joint = list(c("X", "Y"), c("SinX", "CosX"))
HTH,
Thierry
------------------------------------------------------------------------
----
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature
and Forest
Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
methodology and quality assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium
tel. + 32 54/436 185
thierry.onkel...@inbo.be
www.inbo.be
To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to
say what the experiment died of.
~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data.
~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of
data.
~ John Tukey
stepAIC <- function (object, scope, scale = 0, direction = c("both",
"backward", "forward"), trace = 1, steps = 1000, use.start = FALSE, k =
2, bandwidth = 10, marginal = NULL, AICc = TRUE, delta = 2, joint =
NULL, positive.definite = FALSE, ...){
mydeviance <- function(x, ...) {
dev <- deviance(x)
if (!is.null(dev)){
dev
} else {
extractAIC(x, k = 0)[2]
}
}
cut.string <- function(string) {
if (length(string) > 1){
string[-1] <- paste("\n", string[-1], sep = "")
}
string
}
Terms <- terms(object)
object$formula <- Terms
if (inherits(object, "lme")){
object$call$fixed <- Terms
} else {
if (inherits(object, "gls")){
object$call$model <- Terms
} else {
object$call$formula <- Terms
}
}
if (use.start){
warning("'use.start' cannot be used with R's version of glm")
}
md <- missing(direction)
direction <- match.arg(direction)
backward <- direction == "both" | direction == "backward"
forward <- direction == "both" | direction == "forward"
if (missing(scope)) {
fdrop <- numeric(0)
fadd <- attr(Terms, "factors")
if (md){
forward <- FALSE
}
} else {
if (is.list(scope)) {
if(!is.null(fdrop <- scope$lower)){
fdrop <- attr(terms(update.formula(object, fdrop)),
"factors")
colnames(fdrop) <- sapply(strsplit(colnames(fdrop), ":",
fixed = TRUE), function(x) paste(sort(x), collapse = ":"))
fdrop <- fdrop[, order(colnames(fdrop))]
} else {
fdrop <- numeric(0)
}
if (!is.null(fadd <- scope$upper)){
fadd <- attr(terms(update.formula(object, fadd)),
"factors")
colnames(fadd) <- sapply(strsplit(colnames(fadd), ":",
fixed = TRUE), function(x) paste(sort(x), collapse = ":"))
fadd <- fadd[, order(colnames(fadd))]
}
} else {
if (!is.null(fadd <- scope)){
fadd <- attr(terms(update.formula(object, scope)),
"factors")
colnames(fadd) <- sapply(strsplit(colnames(fadd), ":",
fixed = TRUE), function(x) paste(sort(x), collapse = ":"))
fadd <- fadd[, order(colnames(fadd))]
}
fdrop <- numeric(0)
}
}
models <- vector("list", steps)
if (is.list(object) && (nmm <- match("nobs", names(object), 0)) > 0)
{
n <- object[[nmm]]
} else {
n <- length(residuals(object))
}
fit <- object
bAIC <- extractAIC(fit, scale, k = k, ...)
# bAIC <- extractAIC(fit, scale, k = k)
edf <- bAIC[1]
if(AICc){
bAIC <- bAIC[2] + (2 * edf + (edf * 1)) / (n - edf - 1)
} else {
bAIC <- bAIC[2]
}
if (is.na(bAIC)){
stop("AIC is not defined for this model, so stepAIC cannot
proceed")
}
Terms <- terms(fit)
# reorder the covariates in alphabetical order
response <- as.list(attr(Terms, "variables"))[[attr(Terms,
"response") + 1]]
if(length(attr(Terms, "factors")) > 0){
fixed <- sort(sapply(strsplit(colnames(attr(Terms, "factors")),
":", fixed = TRUE), function(x) paste(sort(x), collapse = ":")))
fixed <- paste(c(rownames(attr(Terms, "factors"))[attr(Terms,
"offset")], fixed), collapse = " + ")
fit <- update(fit, as.formula(paste(response, fixed, sep = " ~
")), evaluate = FALSE)
fit <- eval.parent(fit)
} else {
fixed <- "1"
}
Terms <- terms(fit)
nm <- 1
#append the basic model to the list of the results
models[[nm]] <- list(deviance = mydeviance(fit), df.resid = n - edf,
AIC = bAIC, formula = paste(response, fixed, sep = " ~ "), expanded =
FALSE, object = fit)
bestAIC <- bAIC
selection <- 1
while (nm < steps & length(selection) > 0) {
#create a list of formulas which have to be expanded
formulas <- sapply(models[selection], function(x){x$formula})
#create a vector with AIC values of the model to be expanded.
cAIC <- sapply(models[selection], function(x){x$AIC})
if(trace >= 1){
cat("\n")
cat(nm, "models tested.\n")
if(length(cAIC) > 1){
cat(length(cAIC), "models to expand. AIC range:",
round(range(cAIC[is.finite(cAIC)], na.rm = TRUE), 3), "\n\n")
} else {
cat("1 model to expand.\n\n")
}
}
#set the expanded flag on the models selected to expand
models[selection] <- lapply(models[selection], function(x){
x$expanded <- TRUE
if(is.infinite(x$AIC)){
x$AIC <- NA
}
x
})
#expand each selected model
for(i in seq_along(formulas)){
form <- formulas[i]
if(trace >= 2){
cat("Expand model", i, "\n",
cut.string(deparse(as.vector(formula(form)))), "\nAIC:",
round(cAIC[[i]], 3), " Best AIC:", round(bestAIC, 3), "AIC range:",
round(range(cAIC[is.finite(cAIC)], na.rm = TRUE), 3), "\n\n")
utils::flush.console()
}
#select the terms which can be added of dropped
Terms <- terms(as.formula(form))
ffac <- attr(Terms, "factors")
if (!is.null(sp <- attr(Terms, "specials")) && !is.null(st
<- sp$strata)){
ffac <- ffac[-st, ]
}
scope <- factor.scope(ffac, list(add = fadd, drop = fdrop),
marginal = marginal, joint = joint)
#to backward selection
if (backward && length(scope$drop)) {
#create all formulas of smaller models
rhs <- sapply(scope$drop, function(x){
newForm <- update.formula(form, as.formula(paste(".
~ . ", x, sep = "-")))
if(length(attr(terms(newForm),
"factors")) == 0){
paste(response,
paste(c(rownames(attr(Terms, "factors"))[attr(Terms, "offset")], 1),
collapse = " + "), sep = " ~ ")
} else {
if(ncol(attr(terms(newForm), "factors")) >
1){
fixed <-
paste(sort(sapply(strsplit(colnames(attr(terms(newForm), "factors")),
":", fixed = TRUE), function(x) paste(sort(x), collapse = ":"))),
collapse = " + ")
paste(response,
paste(c(rownames(attr(Terms, "factors"))[attr(Terms, "offset")], fixed),
collapse = " + "), sep = " ~ ")
} else {
paste(response,
paste(c(rownames(attr(Terms, "factors"))[attr(Terms, "offset")], 1),
collapse = " + "), sep = " ~ ")
}
}
})
#ignor smaller models which have allready been calculated
scope$drop <- scope$drop[sapply(rhs, function(rhst){
all(sapply(models[seq_len(nm)], function(x){
x$formula != rhst
}))
})]
#drop all suitable terms one by one
if(all(!is.na(scope$drop)) & length(scope$drop)){
for(sdrop in scope$drop){
newForm <- update.formula(form,
as.formula(paste(". ~ . ", sdrop, sep = "-")))
newObject <- update(fit, newForm, evaluate =
FALSE)
newObject <- try(eval.parent(newObject))
#check if the model gave an error or not
if(class(newObject) != "try-error"){
bAIC <- extractAIC(newObject, scale, k = k,
...)
# bAIC <- extractAIC(newObject, scale, k = k)
edf <- bAIC[1]
if(AICc){
bAIC <- bAIC[2] + (2 * edf + (edf * 1))
/ (n - edf - 1)
} else {
bAIC <- bAIC[2]
}
deviance <- mydeviance(newObject)
if(positive.definite &&
class(try(intervals(newObject))) == "try-error"){
bAIC <- ifelse(is.infinite(cAIC[i]), NA,
-Inf)
} else {
if(bestAIC > bAIC){
bestAIC <- bAIC
}
}
} else {
#set the AIC temporary to -Inf if the model gave an error. This will be
reset later on to NA. It is set to -Inf so the model will have the
lowest AIC and will be expanded.
edf <- n
bAIC <- ifelse(is.infinite(cAIC[i]), NA,
-Inf)
newObject <- NULL
deviance <- NA
}
if(ncol(attr(terms(newForm), "factors")) > 1){
#sort the terms in the model alphabetical or make the NULL model
newFixed <-
sort(sapply(strsplit(colnames(attr(terms(newForm), "factors")), ":",
fixed = TRUE), function(x) paste(sort(x), collapse = ":")))
newFixed <- paste(c(rownames(attr(Terms,
"factors"))[attr(Terms, "offset")], newFixed), collapse = " + ")
expanded <- FALSE
} else {
newFixed <- paste(c(rownames(attr(Terms,
"factors"))[attr(Terms, "offset")], 1), collapse = " + ")
expanded <- TRUE
bAIC <- ifelse(is.infinite(bAIC), NA, bAIC)
}
nm <- nm + 1
models[[nm]] <- list(deviance = deviance,
df.resid = n - edf, AIC = bAIC, formula = paste(response,
paste(newFixed, collapse = " + "), sep = " ~ "), expanded = expanded,
object = newObject)
if(trace >= 3){
cat("Model", nm, "Drop: ", sdrop, "\n",
cut.string(deparse(as.vector(as.formula(paste(response, newFixed, sep =
" ~ "))))), "\nAIC: ", round(bAIC, 3), " Best AIC: ", round(bestAIC, 3),
"\n\n")
utils::flush.console()
}
}
}
}
if (forward && length(scope$add)) {
rhs <- sapply(scope$add, function(x){
selection <- which(colnames(attr(Terms, "factors"))
== x)
fixed <-
paste(sort(sapply(strsplit(c(colnames(attr(Terms, "factors")), x), ":",
fixed = TRUE), function(x) paste(sort(x), collapse = ":"))), collapse =
" + ")
paste(response, paste(c(rownames(attr(Terms,
"factors"))[attr(Terms, "offset")], fixed), collapse = " + "), sep = " ~
")
})
scope$add <- scope$add[sapply(rhs, function(rhst){
all(sapply(models[seq_len(nm)], function(x){
x$formula != rhst
}))
})]
if(all(!is.na(scope$add)) & length(scope$add)){
for(sadd in scope$add){
newForm <- update.formula(form,
as.formula(paste(". ~ . ", sadd, sep = "+")))
newObject <- update(fit, newForm, evaluate =
FALSE)
newObject <- try(eval.parent(newObject))
if(class(newObject) != "try-error"){
bAIC <- extractAIC(newObject, scale, k = k,
...)
# bAIC <- extractAIC(newObject, scale, k = k)
edf <- bAIC[1]
if(AICc){
bAIC <- bAIC[2] + (2 * edf + (edf * 1))
/ (n - edf - 1)
} else {
bAIC <- bAIC[2]
}
deviance <- mydeviance(newObject)
if(positive.definite &&
class(try(intervals(newObject))) == "try-error"){
bAIC <- ifelse(is.infinite(cAIC[i]), NA,
-Inf)
} else {
if(bestAIC > bAIC){
bestAIC <- bAIC
}
}
} else {
edf <- NA
deviance <- NA
bAIC <- ifelse(is.infinite(cAIC[i]), NA,
-Inf)
newObject <- NULL
}
newFixed <-
sort(sapply(strsplit(colnames(attr(terms(newForm), "factors")), ":",
fixed = TRUE), function(x) paste(sort(x), collapse = ":")))
newFixed <- paste(c(rownames(attr(terms(fit),
"factors"))[attr(terms(fit), "offset")], newFixed), collapse = " + ")
nm <- nm + 1
models[[nm]] <- list(deviance = deviance,
df.resid = n - edf, AIC = bAIC, formula = paste(response, newFixed, sep
= " ~ "), expanded = FALSE, object = newObject)
if(trace >= 3){
cat("Model", nm, "Add: ", sadd, "\n",
cut.string(deparse(as.vector(as.formula(paste(response, newFixed, sep =
" ~ "))))), "\nAIC: ", round(bAIC, 3), " Best AIC: ", round(bestAIC, 3),
"\n\n")
utils::flush.console()
}
}
}
}
}
models[seq_len(nm)] <-
models[seq_len(nm)][order(sapply(models[seq_len(nm)],
function(x){x$AIC}))]
selection <- which(sapply(models[seq_len(nm)], function(x){
(x$AIC - bestAIC < delta) | is.infinite(x$AIC)
}) == TRUE)
if(length(selection) < bandwidth){
selection <- seq_len(min(c(nm, bandwidth)))
}
unselect <- seq_len(nm)[!seq_len(nm) %in% selection]
models[unselect] <- lapply(models[unselect], function(x){
x$object <- NULL
x
})
selection <- selection[sapply(models[selection],
function(x){!x$expanded})]
}
if(nm > steps){
cat("Warning: algorithm did not converge")
models[[1]]$Converged <- FALSE
} else {
models[[1]]$Converged <- TRUE
}
models[sapply(models, function(x){
!is.null(x)
})]
}
factor.scope <- function (factor, scope, marginal = NULL, joint = NULL)
{
drop <- scope$drop
add <- scope$add
if (length(factor) && !is.null(drop)) {
facs <- factor
if (length(drop)) {
nmdrop <- colnames(drop)
nmfac <- colnames(factor)
nmfac0 <- sapply(strsplit(nmfac, ":", fixed = TRUE),
function(x) paste(sort(x), collapse = ":"))
nmdrop0 <- sapply(strsplit(nmdrop, ":", fixed = TRUE),
function(x) paste(sort(x), collapse = ":"))
where <- match(nmdrop0, nmfac0, 0)
if (any(!where)){
stop(gettextf("lower scope has term(s) %s not included
in model", paste(sQuote(nmdrop[where == 0]), collapse = ", ")), domain
= NA)
}
facs <- factor[, -where, drop = FALSE]
nmdrop <- nmfac[-where]
} else {
nmdrop <- colnames(factor)
}
if (ncol(facs) > 1) {
keep <- rep.int(TRUE, ncol(facs))
f <- crossprod(facs > 0)
for (i in seq(keep)){
keep[i] <- max(f[i, -i]) != f[i, i]
}
nmdrop <- nmdrop[keep]
}
keep <- unique(unlist(lapply(strsplit(nmdrop, ":", fixed =
TRUE), function(x){
whereMarginal <- match(x, names(marginal))
if(!all(is.na(whereMarginal))){
if(length(x) == 1){
marginal[[whereMarginal]]
} else {
lowerOrderTerms <- lapply(seq_along(whereMarginal),
function(z){
if(is.na(whereMarginal[z])){
x[z]
} else {
c(x[z], marginal[[whereMarginal[z]]])
}
})
lowerOrder <- apply(expand.grid(lowerOrderTerms), 1,
function(z){
paste(sort(z), collapse = ":")
})
lowerOrder[!lowerOrder %in% paste(sort(x), collapse
= ":")]
}
}
})))
nmdrop <- nmdrop[!nmdrop %in% keep]
if(length(joint) & length(nmdrop)){
nmdrop <- sapply(strsplit(nmdrop, ":", fixed = TRUE),
function(sdrop){
whereJoint <- sapply(joint, function(x){
!all(!sdrop %in% x)
})
if(sum(whereJoint) > 0){
if(length(sdrop) == 1){
paste(unlist(joint[whereJoint]), collapse = "-")
} else {
whichJoint <- !sdrop %in%
unlist(joint[whereJoint])
paste(sdrop[whichJoint],
unlist(joint[whereJoint]), sep = ":", collapse = "-")
}
} else {
paste(sdrop, collapse = ":")
}
})
nmdrop <- unique(nmdrop)
}
} else {
nmdrop <- character(0)
}
if (!length(add)){
nmadd <- character(0)
} else {
nmfac <- colnames(factor)
nmadd <- colnames(add)
if (!is.null(nmfac)) {
nmfac0 <- sapply(strsplit(nmfac, ":", fixed = TRUE),
function(x) paste(sort(x), collapse = ":"))
nmadd0 <- sapply(strsplit(nmadd, ":", fixed = TRUE),
function(x) paste(sort(x), collapse = ":"))
where <- match(nmfac0, nmadd0, 0)
if (any(!where)){
stop(gettextf("upper scope does not include model
term(s) %s", paste(sQuote(nmfac[where == 0]), collapse = ", ")), domain
= NA)
}
nmadd <- nmadd[-where]
add <- add[, -where, drop = FALSE]
}
if (ncol(add) > 1) {
keep <- rep.int(TRUE, ncol(add))
f <- crossprod(add > 0)
for (i in seq(keep)){
keep[-i] <- keep[-i] & (f[i, -i] < f[i, i])
}
nmadd <- nmadd[keep]
}
if(length(nmadd)){
keep <- sapply(strsplit(nmadd, ":", fixed = TRUE),
function(x){
whereMarginal <- match(x, names(marginal))
if(!all(is.na(whereMarginal))){
if(length(x) == 1){
all(!marginal[[whereMarginal]] %in% nmadd)
} else {
lowerOrderTerms <-
lapply(seq_along(whereMarginal), function(z){
if(is.na(whereMarginal[z])){
x[z]
} else {
c(x[z], marginal[[whereMarginal[z]]])
}
})
lowerOrder <-
apply(expand.grid(lowerOrderTerms), 1, function(z){
paste(sort(z), collapse = ":")
})
lowerOrder <- lowerOrder[!lowerOrder %in%
paste(sort(x), collapse = ":")]
all(!lowerOrder %in% nmadd)
}
} else {
TRUE
}
})
nmadd <- nmadd[keep]
}
if(length(nmadd) & length(joint)){
nmadd <- sapply(strsplit(nmadd, ":", fixed = TRUE),
function(sadd){
whereJoint <- sapply(joint, function(x){
!all(!sadd %in% x)
})
if(sum(whereJoint) > 0){
whichJoint <- !sadd %in% unlist(joint[whereJoint])
if(length(sadd) == 1){
paste(unlist(joint[whereJoint]), collapse = "+")
} else {
paste(sadd[whichJoint],
unlist(joint[whereJoint]), sep = ":", collapse = "+")
}
} else {
paste(sadd, collapse = ":")
}
})
nmadd <- unique(nmadd)
}
}
list(drop = nmdrop, add = nmadd)
}
-----Oorspronkelijk bericht-----
Van: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org]
Namens Dr. Christoph Scherber
Verzonden: donderdag 30 april 2009 13:51
Aan: r-help@r-project.org
Onderwerp: [R] stepAICc
Dear R users,
Would it be difficult to change the code of stepAIC (from the MASS
library) to use AICc instead of AIC?
It would be great to know of someone has tried this already.
Best wishes
Christoph.
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