# Compute Evidence Ratio Between Two Models 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`, `dictab`, `ictab` as the first argument. 1.1 ```r 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`, `dictab`, or `ictab`. 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. ## Returns `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. ## References Burnham, K. P., Anderson, D. R. (2002) **Model Selection and Multimodel Inference: a practical information-theoretic approach**. Second edition. Springer: New York. ## Author(s) Marc J. Mazerolle ## See Also `AICc`, `aictab`, `bictab`, `c_hat`, `confset`, `importance`, `modavg`, `modavgShrink`, `modavgPred` ## Examples ```r ##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) ```

evidence function