# btmodel

##### Bradley-Terry Model Fitting Function

`btmodel`

is a basic fitting function for simple Bradley-Terry models.

- Keywords
- regression

##### Usage

```
btmodel(y, weights = NULL, type = c("loglin", "logit"), ref = NULL,
undecided = NULL, position = NULL, start = NULL, vcov = TRUE, estfun =
FALSE, …)
```

##### Arguments

- y
paircomp object with the response.

- weights
an optional vector of weights (interpreted as case weights).

- type
character. Should an auxiliary log-linear Poisson model or logistic binomial be employed for estimation? The latter is not available if undecided effects are estimated.

- ref
character or numeric. Which object parameter should be the reference category, i.e., constrained to zero?

- undecided
logical. Should an undecided parameter be estimated?

- position
logical. Should a position effect be estimated?

- start
numeric. Starting values when calling

`glm.fit`

.- vcov
logical. Should the estimated variance-covariance be included in the fitted model object?

- estfun
logical. Should the empirical estimating functions (score/gradient contributions) be included in the fitted model object?

- …
further arguments passed to functions.

##### Details

`btmodel`

provides a basic fitting function for Bradley-Terry models,
intended as a building block for fitting Bradley-Terry trees and
Bradley-Terry mixtures in the psychotree package, respectively. While
`btmodel`

is intended for individual paired-comparison data, the
eba package provides functions for aggregate data.

`btmodel`

returns an object of class `"btmodel"`

for which
several basic methods are available, including `print`

, `plot`

,
`summary`

, `coef`

, `vcov`

, `logLik`

, `estfun`

and `worth`

.

##### Value

`btmodel`

returns an S3 object of class `"btmodel"`

,
i.e., a list with components as follows.

paircomp object with the response

estimated parameters on log-scale (without the first parameter which is always constrained to be 0),

covariance matrix of the parameters in the model,

log-likelihood of the fitted model,

number of estimated parameters,

the weights used (if any),

number of observations (with non-zero weights),

character for model type (see above),

character for reference category (see above),

logical for estimation of undecided parameter (see above),

logical for estimation of position effect (see above),

character labels of the objects compared,

empirical estimating function (also known as scores or gradient contributions).

##### See Also

`pcmodel`

, `gpcmodel`

, `rsmodel`

,
`raschmodel`

, `plmodel`

, the eba package

##### Examples

```
# NOT RUN {
o <- options(digits = 4)
## data
data("GermanParties2009", package = "psychotools")
## Bradley-Terry model
bt <- btmodel(GermanParties2009$preference)
summary(bt)
plot(bt)
options(digits = o$digits)
# }
```

*Documentation reproduced from package psychotools, version 0.5-1, License: GPL-2 | GPL-3*