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 model weights). The default computes the evidence ratio of the model weights between the top-ranked model and the second-ranked model. You must supply a model selection table of class 'aictab', 'bictab', 'boot.wt', or 'dictab' as the first argument.

Usage

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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 or of classes bictab, boot.wt, or dictab. 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.

Details

The default compares the model 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 label of the required model must be specified in the model.high argument 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.

Author(s)

Marc J. Mazerolle

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, bictab, c_hat, confset, importance, modavg, modavgShrink, modavgPred

Examples

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##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)


##example with bictab
## Not run: 
##compute model selection table
bictable.out <- bictab(cand.set = Cand.set, modnames = Modnames)
##compute evidence ratio
evidence(bictable.out, model.low = "raw density")

## End(Not run)


##run models for the Orthodont data set in nlme package
## Not run: 
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")
detach(package:nlme)

## End(Not run)

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