R: Estimated Abilities from a Bradley-Terry Model

BTabilities {BradleyTerry2} | R Documentation

## 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)

### Arguments

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

### 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`.

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 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`.

### Author(s)

David Firth and Heather Turner

### 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)

    ### baseball example

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

[Package BradleyTerry2 version 1.0-6 Index]