predictAvg {wiqid}

Predict average values from multiple fitted models

Description

Produce model-averaged estimates of predictions from multiple models of the same type fitted with a function in the wiqid package.

Usage

predictAvg(modList, newdata, parameter, ci=0.95, type=c("link", "response"), IC=AICc)

Arguments

modList

a list of fitted model objects of class wiqid.

newdata

a data frame with columns for each of the covariates in the model. Unused columns are ignored. Missing values are not allowed. See Details.

parameter

character; the name of the parameter to predict; this will appear on the left hand side of one of the formulae in the model.

ci

the confidence interval to use.

type

the type of prediction required. The default is on the scale of the linear predictors; the alternative "response" is on the scale of the response variable. Thus if the parameter is a probability, the default predictions are on the logit or probit scale and type = "response" gives the predicted probabilities. May be abbreviated.

IC

the information criterion function to use to calculate model weights.

Details

The function calls predict with each of the models in modList in turn to obtain predictions (estimates and SEs). The information criterion specified by IC is applied to each model to get model weights, and these are used to average the estimates.

The algorithm to calculate the SEs (and hence CIs) of the model-averaged estimates follows Anderson (2008, p.111).

Value

Returns a matrix with four columns (estimate, SE, lower and upper confidence limits) and a row for each row in newdata. If newdata has row names, these will be used for the output. Attributes give information on the link used and the confidence level.

Author(s)

Mike Meredith.

References

Anderson, D.R. (2008) Model based inference in the life sciences: a primer on evidence. Springer Science + Business Media, New York NY.

Examples

data(toves)

# Extract detection histories
DH <- toves[, 1:4]

# Fit some models
m.1 <- occSS(DH, psi ~ x1, data=toves)
m.12 <- occSS(DH, psi ~ x1 + x2, data=toves)
m.13 <- occSS(DH, psi ~ x1 + x3, data=toves)
m.123 <- occSS(DH, psi ~ x1 + x2 + x3, data=toves)
m.23 <- occSS(DH, psi ~ x2 + x3, data=toves)
AICtable(AICc(m.1, m.12, m.13, m.123, m.23))

# Covariate x1 is essential, x3 is unnecessary, and there's
#   doubt about x2, as the difference in AICc between m.1 and m.12
#   is small.
# We'll use m.1 and m.12 to get model-averaged estimates  of 'psi' for
#   the first 10 sites in the data set.

newdata <- toves[1:10, ]

psi.ma <- predictAvg(list(m.1, m.12), newdata, "psi", type="response")

# Get estimates for the individual models and plot
psi.1 <- predict(m.1, newdata, parameter="psi", type="response")
psi.12 <- predict(m.12, newdata, parameter="psi", type="response")

require(graphics)
plot(1:10, psi.ma[,1], xlab="Site number", ylab="psi", pch=16, cex=1.5,
    las=1, ylim=0:1, xlim=c(0.5, 10.5))
arrows(1:10, psi.ma[,3], 1:10, psi.ma[,4], angle=90, length=0.03, code=3, lwd=2)
# Add values from psi.1 and psi.12
points(1:10 - 0.2, psi.1[,1], col='red')
arrows(1:10 - 0.2, psi.1[,3], 1:10 - 0.2, psi.1[,4],
    angle=90, length=0.03, code=3, col='red')
points(1:10 + 0.2, psi.12[,1], pch=2, col='blue')
arrows(1:10 + 0.2, psi.12[,3], 1:10 + 0.2, psi.12[,4],
    angle=90, length=0.03, code=3, col='blue')