- outcome
the binomial response: either a numeric vector, a factor in
which the first level denotes failure and all others success, or a
two-column matrix with the columns giving the numbers of successes and
failures.
- player1
either an ID factor specifying the first player in each
contest, or a data.frame containing such a factor and possibly other
contest-level variables that are specific to the first player. If given in a
data.frame, the ID factor must have the name given in the id
argument. If a factor is specified it will be used to create such a
data.frame.
- player2
an object corresponding to that given in player1 for
the second player in each contest, with identical structure -- in particular
factors must have identical levels.
- formula
a formula with no left-hand-side, specifying the model for
player ability. See details for more information.
- id
the name of the ID factor.
- separate.ability
(if formula does not include the ID factor as
a separate term) a character vector giving the names of players whose
abilities are to be modelled individually rather than using the
specification given by formula.
- refcat
(if formula includes the ID factor as a separate term)
a character specifying which player to use as a reference, with the first
level of the ID factor as the default. Overrides any other contrast
specification for the ID factor.
- family
a description of the error distribution and link function to
be used in the model. Only the binomial family is implemented, with
either"logit", "probit" , or "cauchit" link. (See
stats::family() for details of family functions.)
- data
an optional object providing data required by the model. This
may be a single data frame of contest-level data or a list of data frames.
Names of data frames are ignored unless they refer to data frames specified
by player1 and player2. The rows of data frames that do not
contain contest-level data must correspond to the levels of a factor used
for indexing, i.e. row 1 corresponds to level 1, etc. Note any rownames are
ignored. Objects are searched for first in the data object if
provided, then in the environment of formula. If data is a
list, the data frames are searched in the order given.
- weights
an optional numeric vector of ‘prior weights’.
- subset
an optional logical or numeric vector specifying a subset of
observations to be used in the fitting process.
- na.action
a function which indicates what should happen when any
contest-level variables contain NAs. The default is the
na.action setting of options. See details for the handling of
missing values in other variables.
- start
a vector of starting values for the fixed effects.
- etastart
a vector of starting values for the linear predictor.
- mustart
a vector of starting values for the vector of means.
- offset
an optional offset term in the model. A vector of length equal
to the number of contests.
- br
logical. If TRUE fitting will be by penalized maximum
likelihood as in Firth (1992, 1993), using brglm::brglm(),
rather than maximum likelihood using glm(), when abilities are
modelled exactly or when the abilities are modelled by covariates and the
variance of the random effects is estimated as zero.
- model
logical: whether or not to return the model frame.
- x
logical: whether or not to return the design matrix for the fixed
effects.
- contrasts
an optional list specifying contrasts for the factors in
formula. See the contrasts.arg of model.matrix().
- ...
other arguments for fitting function (currently either
glm(), brglm::brglm(), or glmmPQL())