mlogit {mlogit} | R Documentation |
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, ...) ## S3 method for class 'mlogit' print(x, digits = max(3, getOption("digits") - 2), width = getOption("width"), ...) ## S3 method for class 'mlogit' summary(object, ...) ## S3 method for class 'summary.mlogit' print(x, digits = max(3, getOption("digits") - 2), width = getOption("width"), ...) ## S3 method for class 'mlogit' print(x, digits = max(3, getOption("digits") - 2), width = getOption("width"), ...) ## S3 method for class 'mlogit' logLik(object, ...) ## S3 method for class 'mlogit' residuals(object, outcome = TRUE, ...) ## S3 method for class 'mlogit' fitted(object, outcome = TRUE, ...) ## S3 method for class 'mlogit' predict(object, newdata, returnData = FALSE, ...) ## S3 method for class 'mlogit' df.residual(object, ...) ## S3 method for class 'mlogit' terms(x, ...) ## S3 method for class 'mlogit' model.matrix(object, ...) ## S3 method for class 'mlogit' update(object, new, ...)
x, object |
an object of class |
formula |
a symbolic description of the model to be estimated, |
new |
an updated formula for the |
newdata |
a |
returnData |
if |
data |
the data: an |
subset |
an optional vector specifying a subset of observations, |
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 |
, |
digits |
the number of digits, |
width |
the width of the printing, |
outcome |
a boolean which indicates, for the |
... |
further arguments passed to |
For how to use the formula argument, see mFormula
.
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 |
expanded.formula |
the formula (a |
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 Behavior, in P. Zarembka ed., Frontiers in Econometrics, New-York: Academic Press.
McFadden, D. (1974) “The Measurement of Urban Travel Demand”, Journal of Public Economics, 3, pp. 303-328.
Train, K. (2004) Discrete Choice Modelling, with Simulations, Cambridge University Press.
mlogit.data
to shape the data. multinom
from
package nnet
performs the estimation of the multinomial logit
model with individual specific variables. mlogit.optim
for 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 <- mlogit.data(Fishing, varying = c(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) library("nnet") summary(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", choice="mode", 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, shape = "long", chid.var = "individual", alt.var="mode", choice = "choice") ## An heteroscedastic logit model data("TravelMode", package = "AER") hl <- mlogit(choice ~ wait + travel + vcost, TravelMode, shape = "long", chid.var = "individual", alt.var = "mode", method = "bfgs", heterosc = TRUE, tol = 10) ## 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, shape='long', alt.var='mode', 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, shape = "long", chid.var = "individual", alt.var = "mode", probit = TRUE) ## End(Not run) ## a mixed logit model ## Not run: rpl <- mlogit(mode ~ price+ catch | income, Fishing, varying = 2:9, shape = 'wide', rpar = c(price= 'n', catch = 'n'), correlation = TRUE, halton = NA, R = 10, tol = 10, print.level = 0) 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, choice='ch', varying = 1:12, ranked=TRUE, shape="wide", reflevel="PC")