Multinomial logit model
Estimation by maximum likelihood of the multinomial logit model, with alternative-specific and/or individual specific variables.
mlogit( formula, data, subset, weights, na.action, start = NULL, alt.subset = NULL, reflevel = NULL, nests = NULL, un.nest.el = FALSE, unscaled = FALSE, heterosc = FALSE, rpar = NULL, probit = FALSE, R = 40, correlation = FALSE, halton = NULL, random.nb = NULL, panel = FALSE, estimate = TRUE, seed = 10, ... )
formula |
a symbolic description of the model to be estimated, |
data |
the data: an |
subset |
an optional vector specifying a subset of
observations for |
weights |
an optional vector of weights, |
na.action |
a function which indicates what should happen when
the data contains |
start |
a vector of starting values, |
alt.subset |
a vector of character strings containing the subset of alternative on which the model should be estimated, |
reflevel |
the base alternative (the one for which the coefficients of individual-specific variables are normalized to 0), |
nests |
a named list of characters vectors, each names being a nest, the corresponding vector being the set of alternatives that belong to this nest, |
un.nest.el |
a boolean, if |
unscaled |
a boolean, if |
heterosc |
a boolean, if |
rpar |
a named vector whose names are the random parameters
and values the distribution : |
probit |
if |
R |
the number of function evaluation for the gaussian
quadrature method used if |
correlation |
only relevant if |
halton |
only relevant if |
random.nb |
only relevant if |
panel |
only relevant if |
estimate |
a boolean indicating whether the model should be
estimated or not: if not, the |
seed |
the seed to use for random numbers (for mixed logit and probit models), |
... |
further arguments passed to |
For how to use the formula argument, see Formula().
The data argument may be an ordinary data.frame. In this case,
some supplementary arguments should be provided and are passed to
mlogit.data(). Note that it is not necessary to indicate the
choice argument as it is deduced from the formula.
The model is estimated using the mlogit.optim().
function.
The basic multinomial logit model and three important extentions of this model may be estimated.
If heterosc=TRUE, the heteroscedastic logit model is estimated.
J - 1 extra coefficients are estimated that represent the scale
parameter for J - 1 alternatives, the scale parameter for the
reference alternative being normalized to 1. The probabilities
don't have a closed form, they are estimated using a gaussian
quadrature method.
If nests is not NULL, the nested logit model is estimated.
If rpar is not NULL, the random parameter model is estimated.
The probabilities are approximated using simulations with R draws
and halton sequences are used if halton is not
NULL. Pseudo-random numbers are drawns from a standard normal and
the relevant transformations are performed to obtain numbers drawns
from a normal, log-normal, censored-normal or uniform
distribution. If correlation = TRUE, the correlation between the
random parameters are taken into account by estimating the
components of the cholesky decomposition of the covariance
matrix. With G random parameters, without correlation G standard
deviations are estimated, with correlation G * (G + 1) /2
coefficients are estimated.
An object of class "mlogit", a list with elements:
coefficients: the named vector of coefficients,
logLik: the value of the log-likelihood,
hessian: the hessian of the log-likelihood at convergence,
gradient: the gradient of the log-likelihood at convergence,
call: the matched call,
est.stat: some information about the estimation (time used, optimisation method),
freq: the frequency of choice,
residuals: the residuals,
fitted.values: the fitted values,
formula: the formula (a Formula object),
expanded.formula: the formula (a formula object),
model: the model frame used,
index: the index of the choice and of the alternatives.
Yves Croissant
McFadden D (1973). “Conditional Logit Analysis of Qualitative Choice Behaviour.” In Zarembka P (ed.), Frontiers in Econometrics, 105-142. Academic Press New York, New York, NY, USA.
McFadden D (1974). “The measurement of urban travel demand.” Journal of Public Economics, 3(4), 303 - 328. ISSN 0047-2727, https://www.sciencedirect.com/science/article/pii/0047272774900036.
Train K (2009). Discrete Choice Methods with Simulation. Cambridge University Press. https://EconPapers.repec.org/RePEc:cup:cbooks:9780521766555.
mlogit.data() to shape the data. nnet::multinom() from
package nnet performs the estimation of the multinomial logit
model with individual specific variables. mlogit.optim()
details about the optimization function.
## Cameron and Trivedi's Microeconometrics p.493 There are two
## alternative specific variables : price and catch one individual
## specific variable (income) and four fishing mode : beach, pier, boat,
## charter
data("Fishing", package = "mlogit")
Fish <- dfidx(Fishing, varying = 2:9, shape = "wide", choice = "mode")
## a pure "conditional" model
summary(mlogit(mode ~ price + catch, data = Fish))
## a pure "multinomial model"
summary(mlogit(mode ~ 0 | income, data = Fish))
## which can also be estimated using multinom (package nnet)
summary(nnet::multinom(mode ~ income, data = Fishing))
## a "mixed" model
m <- mlogit(mode ~ price + catch | income, data = Fish)
summary(m)
## same model with charter as the reference level
m <- mlogit(mode ~ price + catch | income, data = Fish, reflevel = "charter")
## same model with a subset of alternatives : charter, pier, beach
m <- mlogit(mode ~ price + catch | income, data = Fish,
alt.subset = c("charter", "pier", "beach"))
## model on unbalanced data i.e. for some observations, some
## alternatives are missing
# a data.frame in wide format with two missing prices
Fishing2 <- Fishing
Fishing2[1, "price.pier"] <- Fishing2[3, "price.beach"] <- NA
mlogit(mode ~ price + catch | income, Fishing2, shape = "wide", varying = 2:9)
# a data.frame in long format with three missing lines
data("TravelMode", package = "AER")
Tr2 <- TravelMode[-c(2, 7, 9),]
mlogit(choice ~ wait + gcost | income + size, Tr2)
## An heteroscedastic logit model
data("TravelMode", package = "AER")
hl <- mlogit(choice ~ wait + travel + vcost, TravelMode, heterosc = TRUE)
## A nested logit model
TravelMode$avincome <- with(TravelMode, income * (mode == "air"))
TravelMode$time <- with(TravelMode, travel + wait)/60
TravelMode$timeair <- with(TravelMode, time * I(mode == "air"))
TravelMode$income <- with(TravelMode, income / 10)
# Hensher and Greene (2002), table 1 p.8-9 model 5
TravelMode$incomeother <- with(TravelMode, ifelse(mode %in% c('air', 'car'), income, 0))
nl <- mlogit(choice ~ gcost + wait + incomeother, TravelMode,
nests = list(public = c('train', 'bus'), other = c('car','air')))
# same with a comon nest elasticity (model 1)
nl2 <- update(nl, un.nest.el = TRUE)
## a probit model
## Not run:
pr <- mlogit(choice ~ wait + travel + vcost, TravelMode, probit = TRUE)
## End(Not run)
## a mixed logit model
## Not run:
rpl <- mlogit(mode ~ price + catch | income, Fishing, varying = 2:9,
rpar = c(price= 'n', catch = 'n'), correlation = TRUE,
alton = NA, R = 50)
summary(rpl)
rpar(rpl)
cor.mlogit(rpl)
cov.mlogit(rpl)
rpar(rpl, "catch")
summary(rpar(rpl, "catch"))
## End(Not run)
# a ranked ordered model
data("Game", package = "mlogit")
g <- mlogit(ch ~ own | hours, Game, varying = 1:12, ranked = TRUE,
reflevel = "PC", idnames = c("chid", "alt"))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.