btmix
Finite Mixtures of Bradley-Terry Models
Fit finite mixtures of Bradley-Terry models for paired comparisons data via maximum likelihood with the EM algorithm.
- Keywords
- mixture model, paired comparisons, Bradley-Terry model
Usage
btmix(formula, data, k, subset, weights,
nrep = 3, cluster = NULL, control = NULL,
verbose = TRUE, drop = TRUE, unique = FALSE, which = NULL,
type = c("loglin", "logit"), ref = NULL, undecided = NULL,
position = NULL, ...)FLXMCbtreg(formula = . ~ ., type = c("loglin", "logit"), ref = NULL,
undecided = NULL, position = NULL, ...)
Arguments
- formula
Symbolic description of the model (of type
y ~ 1
ory ~ x
).- data, subset
Arguments controlling formula processing.
- k
A vector of integers indicating the number of components of the finite mixture; passed in turn to the
k
argument ofstepFlexmix
.- weights
An optional vector of weights to be used in the fitting process; passed in turn to the
weights
argument offlexmix
.- nrep
Number of runs of the EM algorithm.
- cluster
Either a matrix with
k
columns of initial cluster membership probabilities for each observation; or a factor or integer vector with the initial cluster assignments of observations at the start of the EM algorithm. Default is random assignment intok
clusters.- control
An object of class
"FLXcontrol"
or a named list; controls the EM algorithm and passed in turn to thecontrol
argument offlexmix
.- verbose
A logical; if
TRUE
progress information is shown for different starts of the EM algorithm.- drop
A logical; if
TRUE
andk
is of length 1, then a singleraschmix
object is returned instead of astepRaschmix
object.- unique
A logical; if
TRUE
, thenunique()
is called on the result; for details seestepFlexmix
.- which
number of model to get if
k
is a vector of integers longer than one. If character, interpreted as number of components or name of an information criterion.- type
Character. Should an auxiliary log-linear Poisson model or logistic binomial be employed for estimation? The latter is only available if not 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?
- …
Currently not used.
Details
Internally stepFlexmix
is called with suitable arguments to fit the finite mixture model with
the EM algorithm.
FLXMCbtreg
is the flexmix
-driver for
Bradley-Terry mixture models.
The interface is designed along the same lines as raschmix
which is introduced in detail in Frick et al. (2012). However, the
btmix
function has not yet been fully tested and may change in
future versions.
Value
Either an object of class "btmix"
containing the best model
with respect to the log-likelihood (if k
is a scalar) or the
one selected according to which
(if specified and k
is a
vector of integers longer than 1) or an object of class
"stepBTmix"
(if which
is not specified and k
is a
vector of integers longer than 1).
References
Bradley, R.A., and Terry, M.E. (1952). Rank Analysis of Incomplete Block Designs. I. The Method of Paired Comparisons. Biometrika, 39(3/4), 324--345.
D<U+001B2CAC> M. (2011). Bradley Terry Mixture Models: Theory, Implementation in R and Validation. Diploma Thesis, Ludwig-Maximilians-Universit<e4>t M<U+2E8E896E>.
Frick, H., Strobl, C., Leisch, F., and Zeileis, A. (2012). Flexible Rasch Mixture Models with Package psychomix. Journal of Statistical Software, 48(7), 1--25. http://www.jstatsoft.org/v48/i07/.
Gr<U+2EB200AE>, and Leisch, F. (2008). FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters. Journal of Statistical Software, 28(4), 1--35. http://www.jstatsoft.org/v28/i04/.
Leisch, F. (2004). FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R. Journal of Statistical Software, 11(8), 1--18. http://www.jstatsoft.org/v11/i08/.
See Also
Examples
# NOT RUN {
# }
# NOT RUN {
## Data
data("GermanParties2009", package = "psychotools")
## omit single observation with education = 1
gp <- subset(GermanParties2009, education != "1")
gp$education <- factor(gp$education)
## Bradley-Terry mixture models
suppressWarnings(RNGversion("3.5.0"))
set.seed(1)
## fit models for k = 1, ..., 4 with concomitant variables
cm <- btmix(preference ~ gender + education + age + crisis,
data = gp, k = 1:4, nrep = 3)
## inspect results
plot(cm)
## select model
cm4 <- getModel(cm, which = "4")
## inspect mixture and effects
library("lattice")
xyplot(cm4)
effectsplot(cm4)
effectsplot(cm4, selection = "education")
## vis effects package directly
if(require("effects")) {
eff4 <- allEffects(cm4)
plot(eff4)
}
# }
# NOT RUN {
# }