MuMIn (version 1.0.0)

QAIC: Quasi AIC(c))

Description

Calculates quasi AIC (or quasi AICc) for one or several fitted model objects. This function is provided mainly as an example of custom rank function for use with model.avg and dredge

Usage

QAIC(object, ..., chat)
QAICc(object, ..., chat)

Arguments

object

a fitted model object.

...

optionally more fitted model objects.

chat

c - hat

Value

• If just one object is provided, returns a numeric value with the corresponding QAIC; if more than one object are provided, returns a data.frame with rows corresponding to the objects.

encoding

utf-8

See Also

AICc quasi family used for models with over-dispersion. AIC, BIC) may also be used as a custom rank function in dredge and model.avg.

Examples

# Based on "example(predict.glm)"
require(graphics)

budworm <- data.frame(ldose = rep(0:5, 2), numdead = c(1, 4, 9, 13, 18, 20, 0,
	2, 6, 10, 12, 16), sex = factor(rep(c("M", "F"), c(6, 6))))
budworm$SF = cbind(numdead = budworm$numdead, numalive = 20 - budworm$numdead)

budworm.lg <- glm(SF ~ sex*ldose, data = budworm, family = quasibinomial)

dd <- dredge(budworm.lg, rank = "QAIC", chat = summary(budworm.lg)$dispersion)
# Average all models
budworm.avg <- model.avg(get.models(dd, seq(nrow(dd))), method="NA")
#model.avg(mod[[1]], mod[[2]], rank = "QAIC", rank.args = list(chat = 1))

plot(c(1,32), c(0,1), type = "n", xlab = "dose",
     ylab = "prob", log = "x")
text(2^budworm$ldose, budworm$numdead/20, as.character(budworm$sex))
ld <- seq(0, 5, 0.1)

newdata <- data.frame(ldose=ld, sex=factor(rep("M", length(ld)),
	levels=levels(budworm$sex)))

# Predictions from global model / Males
pred.lg <- predict(budworm.lg, newdata, se.fit=TRUE, type="response")
matplot(2^ld, cbind(pred.lg$fit, pred.lg$fit - (2 * pred.lg$se.fit),
	pred.lg$fit + (2 * pred.lg$se.fit)), add=TRUE, type="l", col=1)

# Predictions from averaged model / Males
pred.avg <- predict(budworm.avg, newdata, se.fit=TRUE, type="response")
matplot(2^ld, cbind(pred.avg$fit, pred.avg$fit - (2 * pred.avg$se.fit),
	pred.avg$fit + (2 * pred.avg$se.fit)), add=TRUE, type="l", col=2)

newdata$sex[] <- "F"

# Predictions from global model / Females
pred.lg <- predict(budworm.lg, newdata, se.fit=TRUE, type="response")
matplot(2^ld, cbind(pred.lg$fit, pred.lg$fit - (2 * pred.lg$se.fit),
	pred.lg$fit + (2 * pred.lg$se.fit)), add=TRUE, type="l", col=1)

# Predictions from averaged model / Females
pred.avg <- predict(budworm.avg, newdata, se.fit=TRUE, type="response")
matplot(2^ld, cbind(pred.avg$fit, pred.avg$fit - (2 * pred.avg$se.fit),
	pred.avg$fit + (2 * pred.avg$se.fit)), add=TRUE, type="l", col=2)

legend("bottomright", legend=c("full", "averaged"), title="Model",
	   col=1:2, lty=1)