AICcmodavg (version 1.0)

evidence: Compute Evidence Ratio Between Two Models

Description

This function compares two models of a candidate model set based on their evidence ratio (i.e., ratio of Akaike weights). The default computes the evidence ratio of the Akaike weights between the top-ranked model and the second-ranked model. You must supply a model selection table of class 'aictab' as the first argument.

Usage

evidence(aic.table, model.high = "top", model.low = "second.ranked")

Arguments

aic.table

a model selection table of class 'aictab' such as that produced by 'aictab'. The table may be sorted or not, as the function sorts the table internally.

model.high

the top-ranked model (default), or alternatively, the name of another model as it appears in the model selection table.

model.low

the second-ranked model (default), or alternatively, the name of a lower-ranked model such as it appears in the model selection table.

Value

• 'evidence' produces an object of class 'evidence' with the following components:
• Model.high
  the model specified in 'model.high'.
• Model.low
  the model specified in 'model.low'.
• Ev.ratio
  the evidence ratio between the two models compared.

Details

The default compares the Akaike weights of the top-ranked model to the second-ranked model in the candidate model set. The evidence ratio can be interpreted as the number of times a given model is more parsimonious than a lower-ranked model. If one desires an evidence ratio that does not involve a comparison with the top-ranking model, the name of the required model must be specified in the 'model.high' argument.

References

Burnham, K. P., Anderson, D. R. (2002) Model Selection and Multimodel Inference: a practical information-theoretic approach. Second edition. Springer: New York.

See Also

AICc, aictab, c_hat, modavg, importance, confset, modavgpred

Examples

##run example from Burnham and Anderson (2002, p. 183) with two
##non-nested models
data(pine)
Cand.set <- list( )
Cand.set[[1]] <- lm(y ~ x, data = pine)
Cand.set[[2]] <- lm(y ~ z, data = pine)

##assign model names
Modnames <- c("raw density", "density corrected for resin content")

##compute model selection table
aicctable.out <- aictab(cand.set = Cand.set, modnames = Modnames)

##compute evidence ratio
evidence(aic.table = aicctable.out, model.low = "raw density")
evidence(aic.table = aicctable.out) #gives the same answer
##round to 4 digits after decimal point
print(evidence(aic.table = aicctable.out, model.low = "raw density"),
digits = 4)


##run models for the Orthodont data set in nlme
require(nlme)

##set up candidate model list
Cand.models <- list()
Cand.models[[1]] <- lme(distance ~ age, data = Orthodont, method = "ML")
##random is ~ age | Subject
Cand.models[[2]] <- lme(distance ~ age + Sex, data = Orthodont, random =
~ 1, method = "ML")
Cand.models[[3]] <- lme(distance ~ 1, data = Orthodont, random = ~ 1,
method = "ML")

##create a vector of model names
Modnames <- paste("mod", 1:length(Cand.models), sep = "")


##compute AICc table
aic.table.1 <- aictab(cand.set = Cand.models, modnames = Modnames,
second.ord = TRUE)

##compute evidence ratio between best model and second-ranked model
evidence(aic.table = aic.table.1)

##compute the same value but from an unsorted model selection table
evidence(aic.table = aictab(cand.set = Cand.models,
modnames = Modnames, second.ord = TRUE, sort = FALSE))

##compute evidence ratio between second-best model and third-ranked
##model  
evidence(aic.table = aic.table.1, model.high = "mod1",
model.low = "mod3")