# 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' or 'boot.wt' as the first argument.

### Usage

1 | ```
evidence(aic.table, model.high = "top", model.low = "second.ranked")
``` |

### Arguments

`aic.table` |
a model selection table of class |

`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 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.

### Value

`evidence`

produces an object of class `evidence`

with the
following components:

`Model.high` |
the model specified in |

`Model.low` |
the model specified in |

`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`

, `c_hat`

,
`confset`

, `importance`

, `modavg`

,
`modavgShrink`

, `modavgPred`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 | ```
##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 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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