brmultinom {brglm2}  R Documentation 
brmultinom
is a wrapper of brglmFit
that fits
multinomial regression models using implicit and explicit bias
reduction methods. See Kosmidis & Firth (2011) for details.
brmultinom( formula, data, weights, subset, na.action, contrasts = NULL, ref = 1, model = TRUE, x = TRUE, control = list(...), ... )
formula 
a formula expression as for regression models, of the form

data 
an optional data frame in which to interpret the variables occurring
in 
weights 
optional case weights in fitting. 
subset 
expression saying which subset of the rows of the data should be used in the fit. All observations are included by default. 
na.action 
a function to filter missing data. 
contrasts 
a list of contrasts to be used for some or all of the factors appearing as variables in the model formula. 
ref 
the reference category to use for multinomial regression. Either an integer, in which case levels(response)[ref] is used as a baseline, or a character string. Default is 1. 
model 
logical. If true, the model frame is saved as component 
x 
should the model matrix be included with in the result
(default is 
control 
a list of parameters for controlling the fitting
process. See 
... 
arguments to be used to form the default 'control' argument if it is not supplied directly. 
The models brmultinom
handles are also known as
baselinecategory logit models (see, Agresti, 2002, Section 7.1),
because they model the logodds of every category against a
baseline category. The user can control which baseline (or
reference) category is used via the ref
. By default
brmultinom
uses the first category as reference.
The maximum likelihood estimates for the parameters of baselinecategory logit models have infinite components with positive probability, which can result in problems in their estimation and the use of inferential procedures (e.g. Wad tests). Albert and Andreson (1984) have categorized the possible data patterns for such models into the exclusive and exhaustive categories of complete separation, quasicomplete separation and overlap, and showed that infinite maximum likelihood estimates result when complete or quasicomplete separation occurs.
The adjusted score approach to bias reduction that
brmultinom
implements (type = "AS_mean"
) is an
alternative to maximum likelihood that results in estimates with
smaller asymptotic bias that are also *always* finite, even in
cases of complete or quasicomplete separation.
brmultinom
is a wrapper of brglmFit
that fits
multinomial logit regression models through the 'Poisson trick' (see, for
example, Palmgren, 1981; Kosmidis & Firth, 2011).
The implementation relies on the construction of an 'extended'
model matrix for the loglinear model and constraints on the sums
of the Poisson means. Specifically, a loglinear model is fitted on
a Kronecker product
(https://en.wikipedia.org/wiki/Kronecker_product) of the
original model matrix X
implied by the formula, augmented by
nrow(X)
dummy variables.
The extended model matrix is sparse, and the Matrix package is used for its effective storage.
While brmultinom
can be used for analyses using
multinomial regression models, the current implementation is more
of a 'proof of concept' and is not expected to scale well with
either of nrow(X)
, ncol(X)
or the number of levels in
the categorical response.
Ioannis Kosmidis ioannis.kosmidis@warwick.ac.uk
Kosmidis I, Kenne Pagui E C, Sartori N (2020). Mean and median bias reduction in generalized linear models. *Statistics and Computing*, **30**, 4359 doi: 10.1007/s11222019098606
Agresti A (2002). *Categorical data analysis* (2nd edition). Wiley Series in Probability and Statistics. Wiley.
Albert A, Anderson J A (1984). On the Existence of Maximum Likelihood Estimates in Logistic Regression Models. *Biometrika*, **71** 1–10, doi: 10.2307/2336390
Kosmidis I, Firth D (2011). Multinomial logit bias reduction via the Poisson loglinear model. *Biometrika*, **98**, 755759 doi: 10.1093/biomet/asr026
Palmgren, J (1981). The Fisher Information Matrix for Log Linear Models Arguing Conditionally on Observed Explanatory Variables. *Biometrika*, **68**, 563566 doi: 10.1093/biomet/68.2.563
multinom
, bracl
for adjacent category logit models for ordinal responses
data("housing", package = "MASS") # Maximum likelihood using nnet::multinom houseML1nnet < nnet::multinom(Sat ~ Infl + Type + Cont, weights = Freq, data = housing) # Maximum likelihood using brmultinom with baseline category 'Low' houseML1 < brmultinom(Sat ~ Infl + Type + Cont, weights = Freq, data = housing, type = "ML", ref = 1) # The estimates are numerically the same as houseML0 all.equal(coef(houseML1nnet), coef(houseML1), tolerance = 1e04) # Maximum likelihood using brmultinom with 'High' as baseline houseML3 < brmultinom(Sat ~ Infl + Type + Cont, weights = Freq, data = housing, type = "ML", ref = 3) # The fitted values are the same as houseML1 all.equal(fitted(houseML3), fitted(houseML1), tolerance = 1e10) # Bias reduction houseBR3 < update(houseML3, type = "AS_mean") # Bias correction houseBC3 < update(houseML3, type = "correction")