BradleyTerry2 (version 1.1.4)

BTabilities: Estimated Abilities from a Bradley-Terry Model

Description

Computes the (baseline) ability of each player from a model object of class "BTm".

Usage

BTabilities(model)

Value

A two-column numeric matrix of class c("BTabilities", "matrix"), with columns named "ability" and "se"; has one row for each player; has attributes named "vcov", "modelcall", "factorname" and (sometimes --- see below) "separate". The first three attributes are not printed by the method print.BTabilities.

Arguments

model

a model object for which inherits(model, "BTm") is TRUE

Author

David Firth and Heather Turner

Details

The player abilities are either directly estimated by the model, in which case the appropriate parameter estimates are returned, otherwise the abilities are computed from the terms of the fitted model that involve player covariates only (those indexed by model$id in the model formula). Thus parameters in any other terms are assumed to be zero. If one player has been set as the reference, then predict.BTm() can be used to obtain ability estimates with non-player covariates set to other values, see examples for predict.BTm().

If the abilities are structured according to a linear predictor, and if there are player covariates with missing values, the abilities for the corresponding players are estimated as separate parameters. In this event the resultant matrix has an attribute, named "separate", which identifies those players whose ability was estimated separately. For an example, see flatlizards().

References

Firth, D. (2005) Bradley-Terry models in R. Journal of Statistical Software, 12(1), 1--12.

Turner, H. and Firth, D. (2012) Bradley-Terry models in R: The BradleyTerry2 package. Journal of Statistical Software, 48(9), 1--21.

See Also

BTm(), residuals.BTm()

Examples

### citations example

##  Convert frequencies to success/failure data
citations.sf <- countsToBinomial(citations)
names(citations.sf)[1:2] <- c("journal1", "journal2")

##  Fit the "standard" Bradley-Terry model
citeModel <- BTm(cbind(win1, win2), journal1, journal2, data = citations.sf)
BTabilities(citeModel)

##  Compute probabilities journal i (row) beats journal j (column)
alpha <- exp(BTabilities(citeModel)[,1])
alpha/outer(alpha, alpha, "+")

### baseball example

data(baseball) # start with baseball data as provided by package

##  Fit mode with home advantage
baseball$home.team <- data.frame(team = baseball$home.team, at.home = 1)
baseball$away.team <- data.frame(team = baseball$away.team, at.home = 0)
baseballModel2 <- BTm(cbind(home.wins, away.wins), home.team, away.team,
                      formula = ~ team + at.home, id = "team",
                      data = baseball)

##  Estimate abilities for each team, relative to Baltimore, when
##  playing away from home:  
BTabilities(baseballModel2)

##  Compute probabilities team i (row) beats team j (col), when 
##  playing away from home
alpha <- exp(BTabilities(baseballModel2)[,1])
alpha/outer(alpha, alpha, "+")