residuals.BTm {BradleyTerry2}

Residuals from a Bradley-Terry Model

Description

Computes residuals from a model object of class "BTm". In additional to the usual options for objects inheriting from class "glm", a "grouped" option is implemented to compute player-specific residuals suitable for diagnostic checking of a predictor involving player-level covariates.

Usage

## S3 method for class 'BTm'
residuals(
  object,
  type = c("deviance", "pearson", "working", "response", "partial", "grouped"),
  by = object$id,
  ...
)

Arguments

object

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

type

the type of residuals which should be returned. The alternatives are: "deviance" (default), "pearson", "working", "response", and "partial".

by

the grouping factor to use when type = "grouped".

...

arguments to pass on other methods.

Details

For type other than "grouped" see residuals.glm().

For type = "grouped" the residuals returned are weighted means of working residuals, with weights equal to the binomial denominators in the fitted model. These are suitable for diagnostic model checking, for example plotting against candidate predictors.

Value

A numeric vector of length equal to the number of players, with a "weights" attribute.

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(), BTabilities()

Examples

##
##  See ?springall
##
springall.model <- BTm(cbind(win.adj, loss.adj),
                       col, row, 
                       ~ flav[..] + gel[..] + 
                       flav.2[..] + gel.2[..] + flav.gel[..] + (1 | ..),
                       data = springall)
res <- residuals(springall.model, type = "grouped")
with(springall$predictors, plot(flav, res))
with(springall$predictors, plot(gel, res))
##  Weighted least-squares regression of these residuals on any variable
##  already included in the model yields slope coefficient zero:
lm(res ~ flav, weights = attr(res, "weights"),
   data = springall$predictors)
lm(res ~ gel, weights = attr(res, "weights"),
   data = springall$predictors)