| Title: | Multinomial Logit Models |
|---|---|
| Description: | Maximum Likelihood estimation of random utility discrete choice models, as described in Kenneth Train (2009) Discrete Choice Methods with Simulations <doi:10.1017/CBO9780511805271>. |
| Authors: | Yves Croissant [aut, cre] |
| Maintainer: | Yves Croissant <[email protected]> |
| License: | GPL (>=2) |
| Version: | 1.0-3 |
| Built: | 2024-06-25 05:03:55 UTC |
| Source: | https://github.com/r-forge/mlogit |
mlogit provides a model description interface (enhanced formula-data), a very versatile estimation function and a testing infrastructure to deal with random utility models.
For a gentle and comprehensive introduction to the package, see the package's vignettes.
a sample of 4654 individuals
A dataframe containing :
choice: choice of a vehicule amoung 6 propositions,
college: college education?,
hsg2: size of household greater than 2?
coml5: commulte lower than 5 miles a day?,
typez: body type, one of regcar (regular car), sportuv (sport utility vehicule), sportcar, stwagon (station wagon), truck, van, for each proposition z from 1 to 6,
fuelz: fuel for proposition z, one of gasoline, methanol, cng (compressed natural gas), electric.,
pricez: price of vehicule divided by the logarithme of income,
rangez: hundreds of miles vehicule can travel between refuelings/rechargings,
accz: acceleration, tens of seconds required to reach 30 mph from stop,
speedz: highest attainable speed in hundreds of mph,
pollutionz: tailpipe emissions as fraction of those for new gas vehicule,
sizez: 0 for a mini, 1 for a subcompact, 2 for a compact and 3 for a mid–size or large vehicule,
spacez: fraction of luggage space in comparable new gas vehicule,
costz: cost per mile of travel (tens of cents) : home recharging for electric vehicule, station refueling otherwise,
stationz: fraction of stations that can refuel/recharge vehicule.
Journal of Applied Econometrics data archive.
McFadden D, Train K (2000). “Mixed MNL Models for Discrete Response.” Journal of Applied Econometrics, 15(5), 447–470. ISSN 08837252, 10991255.
a sample of 2798 individuals
A dataframe containing :
id: individuals identifiers,
choice: one of heinz41, heinz32, heinz28, hunts32,
disp.z: is there a display for brand z ?
feat.z: is there a newspaper feature advertisement for brand z?
price.z: price of brand z.
Journal of Business Economics and Statistics web site.
Jain DC, Vilcassim NJ, Chintagunta PK (1994). “A Random-Coefficients Logit Brand-Choice Model Applied to Panel Data.” Journal of Business & Economic Statistics, 12(3), 317-328.
Functions that extract the correlation structure of a mlogit object
cor.mlogit(x) cov.mlogit(x)cor.mlogit(x) cov.mlogit(x)
x |
an |
These functions are deprecated, use vcov. instead.
A numerical matrix which returns either the correlation or the covariance matrix of the random parameters.
Yves Croissant
a sample of 3292 individualscross-section
A dataframe containing :
id: individuals identifiers,
choice: one of sunshine, keebler, nabisco, private,
disp.z: is there a display for brand z?
feat.z: is there a newspaper feature advertisement for brand z?
price.z: price of brand z.
Journal of Business Economics and Statistics web site.
Jain DC, Vilcassim NJ, Chintagunta PK (1994). “A Random-Coefficients Logit Brand-Choice Model Applied to Panel Data.” Journal of Business & Economic Statistics, 12(3), 317-328.
Paap R, Franses PH (2000). “A dynamic multinomial probit model for brand choice with different long-run and short-run effects of marketing-mix variables.” Journal of Applied Econometrics, 15(6), 717-744.
Functions used to describe the characteristics of estimated random parameters
stdev(x, ...) rg(x, ...) med(x, ...) ## S3 method for class 'rpar' mean(x, norm = NULL, ...) ## S3 method for class 'rpar' med(x, norm = NULL, ...) ## S3 method for class 'rpar' stdev(x, norm = NULL, ...) ## S3 method for class 'rpar' rg(x, norm = NULL, ...) ## S3 method for class 'mlogit' mean(x, par = NULL, norm = NULL, ...) ## S3 method for class 'mlogit' med(x, par = NULL, norm = NULL, ...) ## S3 method for class 'mlogit' stdev(x, par = NULL, norm = NULL, ...) ## S3 method for class 'mlogit' rg(x, par = NULL, norm = NULL, ...) qrpar(x, ...) prpar(x, ...) drpar(x, ...) ## S3 method for class 'rpar' qrpar(x, norm = NULL, ...) ## S3 method for class 'rpar' prpar(x, norm = NULL, ...) ## S3 method for class 'rpar' drpar(x, norm = NULL, ...) ## S3 method for class 'mlogit' qrpar(x, par = 1, y = NULL, norm = NULL, ...) ## S3 method for class 'mlogit' prpar(x, par = 1, y = NULL, norm = NULL, ...) ## S3 method for class 'mlogit' drpar(x, par = 1, y = NULL, norm = NULL, ...)stdev(x, ...) rg(x, ...) med(x, ...) ## S3 method for class 'rpar' mean(x, norm = NULL, ...) ## S3 method for class 'rpar' med(x, norm = NULL, ...) ## S3 method for class 'rpar' stdev(x, norm = NULL, ...) ## S3 method for class 'rpar' rg(x, norm = NULL, ...) ## S3 method for class 'mlogit' mean(x, par = NULL, norm = NULL, ...) ## S3 method for class 'mlogit' med(x, par = NULL, norm = NULL, ...) ## S3 method for class 'mlogit' stdev(x, par = NULL, norm = NULL, ...) ## S3 method for class 'mlogit' rg(x, par = NULL, norm = NULL, ...) qrpar(x, ...) prpar(x, ...) drpar(x, ...) ## S3 method for class 'rpar' qrpar(x, norm = NULL, ...) ## S3 method for class 'rpar' prpar(x, norm = NULL, ...) ## S3 method for class 'rpar' drpar(x, norm = NULL, ...) ## S3 method for class 'mlogit' qrpar(x, par = 1, y = NULL, norm = NULL, ...) ## S3 method for class 'mlogit' prpar(x, par = 1, y = NULL, norm = NULL, ...) ## S3 method for class 'mlogit' drpar(x, par = 1, y = NULL, norm = NULL, ...)
x |
a |
... |
further arguments. |
norm |
the variable used for normalization if any : for the
|
par |
the required parameter(s) for the |
y |
values for which the function has to be evaluated, |
rpar objects contain all the relevant information about
the distribution of random parameters. These functions enables
to obtain easily descriptive statistics, density, probability
and quantiles of the distribution.
mean, med, stdev and rg compute respectively the mean, the
median, the standard deviation and the range of the random
parameter. qrpar, prpar, drpar return functions that compute
the quantiles, the probability and the density of the random
parameters (note that sd and range are not generic function in
R and that median is, but without ...).
a numeric vector for qrpar, drpar and prpar, a
numeric vector for mean, stdev and med and a numeric
matrix for rg.
Yves Croissant
mlogit() for the estimation of random parameters logit
models and rpar() for the description of rpar objects.
The effects method for mlogit objects computes the marginal
effects of the selected covariate on the probabilities of choosing the
alternatives
## S3 method for class 'mlogit' effects( object, covariate = NULL, type = c("aa", "ar", "rr", "ra"), data = NULL, ... )## S3 method for class 'mlogit' effects( object, covariate = NULL, type = c("aa", "ar", "rr", "ra"), data = NULL, ... )
object |
a |
covariate |
the name of the covariate for which the effect should be computed, |
type |
the effect is a ratio of two marginal variations of the
probability and of the covariate ; these variations can be absolute
|
data |
a data.frame containing the values for which the effects should be calculated. The number of lines of this data.frame should be equal to the number of alternatives, |
... |
further arguments. |
If the covariate is alternative specific, a matrix is
returned, being the number of alternatives. Each line contains the
marginal effects of the covariate of one alternative on the probability to
choose any alternative. If the covariate is individual specific, a vector of
length is returned.
Yves Croissant
mlogit() for the estimation of multinomial logit
models.
data("Fishing", package = "mlogit") library("zoo") Fish <- mlogit.data(Fishing, varying = c(2:9), shape = "wide", choice = "mode") m <- mlogit(mode ~ price | income | catch, data = Fish) # compute a data.frame containing the mean value of the covariates in # the sample z <- with(Fish, data.frame(price = tapply(price, index(m)$alt, mean), catch = tapply(catch, index(m)$alt, mean), income = mean(income))) # compute the marginal effects (the second one is an elasticity ## IGNORE_RDIFF_BEGIN effects(m, covariate = "income", data = z) ## IGNORE_RDIFF_END effects(m, covariate = "price", type = "rr", data = z) effects(m, covariate = "catch", type = "ar", data = z)data("Fishing", package = "mlogit") library("zoo") Fish <- mlogit.data(Fishing, varying = c(2:9), shape = "wide", choice = "mode") m <- mlogit(mode ~ price | income | catch, data = Fish) # compute a data.frame containing the mean value of the covariates in # the sample z <- with(Fish, data.frame(price = tapply(price, index(m)$alt, mean), catch = tapply(catch, index(m)$alt, mean), income = mean(income))) # compute the marginal effects (the second one is an elasticity ## IGNORE_RDIFF_BEGIN effects(m, covariate = "income", data = z) ## IGNORE_RDIFF_END effects(m, covariate = "price", type = "rr", data = z) effects(m, covariate = "catch", type = "ar", data = z)
A sample of 2308 households in the United States
A dataframe containing :
choice: the choice of the individual, one of 1, 2, 3, 4,
id: the individual index,
pfi: fixed price at a stated cents per kWh, with the price varying over suppliers and experiments, for scenario i=(1, 2, 3, 4),
cli: the length of contract that the supplier offered, in years (such as 1 year or 5 years.) During this contract period, the supplier guaranteed the prices and the buyer would have to pay a penalty if he/she switched to another supplier. The supplier could offer no contract in which case either side could stop the agreement at any time. This is recorded as a contract length of 0,
loci: is the supplier a local company,
wki: is the supplier a well-known company,
todi: a time-of-day rate under which the price is 11 cents per kWh from 8am to 8pm and 5 cents per kWh from 8pm to 8am. These TOD prices did not vary over suppliers or experiments: whenever the supplier was said to offer TOD, the prices were stated as above.
seasi: a seasonal rate under which the price is 10 cents per kWh in the summer, 8 cents per kWh in the winter, and 6 cents per kWh in the spring and fall. Like TOD rates, these prices did not vary. Note that the price is for the electricity only, not transmission and distribution, which is supplied by the local regulated utility.
Huber J, Train K (2000). “On the Similarity of Classical and Bayesian Estimates of Individual Mean Partworths.” Marketing Letters, 12, 259–269.
Revelt D, Train K (2001). “Customer-Specific Taste Parameters and Mixed Logit: Households' Choice of Electricity Supplier.” Econometrics 0012001, University Library of Munich, Germany. https://ideas.repec.org/p/wpa/wuwpem/0012001.html.
A sample of 1182 individuals in the United-States for the choice of 4 alternative fishing modes.
A dataframe containing :
mode: recreation mode choice, one of : beach, pier, boat and charter,
price.beach: price for beach mode
price.pier: price for pier mode,
price.boat: price for private boat mode,
price.charter: price for charter boat mode,
catch.beach: catch rate for beach mode,
catch.pier: catch rate for pier mode,
catch.boat: catch rate for private boat mode,
catch.charter: catch rate for charter boat mode,
income: monthly income,
Cameron A, Trivedi P (2005). Microeconometrics. Cambridge University Press. https://EconPapers.repec.org/RePEc:cup:cbooks:9780521848053.
Herriges JA, Kling CL (1999). “Nonlinear Income Effects in Random Utility Models.” The Review of Economics and Statistics, 81(1), 62-72. doi:10.1162/003465399767923827, https://doi.org/10.1162/003465399767923827, https://doi.org/10.1162/003465399767923827.
A sample of 91 Dutch individuals
A dataframe containing :
ch.Platform: where platform is one of Xbox,
PlayStation, PSPortable, GameCube,
GameBoy and PC. This variables contain the ranking of
the platforms from 1 to 6,
own.Platform: these 6 variables are dummies which indicate whether the given plaform is already owned by the respondent,
age: the age of the respondent,
hours: hours per week spent on gaming.,
The data are also provided in long format (use in this case
data(Game2). In this case, the alternative and the choice
situation are respectively indicated in the platform and
chid variables.
Journal of Applied Econometrics data archive.
Fok D, Paap R, Van Dijk B (2012). “A Rank-Ordered Logit Model With Unobserved Heterogeneity In Ranking Capatibilities.” Journal of Applied Econometrics, 27(5), 831-846. doi:10.1002/jae.1223, https://onlinelibrary.wiley.com/doi/pdf/10.1002/jae.1223, https://onlinelibrary.wiley.com/doi/abs/10.1002/jae.1223.
A sample of 250 Californian households
A dataframe containing :
depvar: heating system, one of gcc (gas central heat with
cooling), ecc (electric central resistence heat with cooling), erc
(electric room resistence heat with cooling), hpc (electric heat
pump which provides cooling also), gc (gas central heat without
cooling), ec (electric central resistence heat without cooling), er
(electric room resistence heat without cooling),
ich.z: installation cost of the heating portion of the system,
icca: installation cost for cooling,
och.z: operating cost for the heating portion of the system,
occa: operating cost for cooling,
income: annual income of the household.
A sample of 900 Californian households#'
A dataframe containing:
idcase: id,
depvar: heating system, one of gc (gas central), gr (gas room), ec (electric central), er (electric room), hp (heat pump),
ic.z: installation cost for heating system z (defined for the 5 heating systems),
oc.z: annual operating cost for heating system z (defined for the 5 heating systems),
pb.z: ratio oc.z/ic.z ,
income: annual income of the household,
agehed: age of the household head
rooms: numbers of rooms in the house,
Test the IIA hypothesis (independence of irrelevant alternatives) for a multinomial logit model.
hmftest(x, ...) ## S3 method for class 'formula' hmftest(x, alt.subset, ...) ## S3 method for class 'mlogit' hmftest(x, z, ...)hmftest(x, ...) ## S3 method for class 'formula' hmftest(x, alt.subset, ...) ## S3 method for class 'mlogit' hmftest(x, z, ...)
x |
an object of class |
... |
further arguments passed to |
alt.subset |
a subset of alternatives, |
z |
an object of class |
This is an implementation of the Hausman's consistency test for
multinomial logit models. If the independance of irrelevant
alternatives applies, the probability ratio of every two
alternatives depends only on the characteristics of these
alternatives. Consequentely, the results obtained on the estimation
with all the alternatives or only on a subset of them are
consistent, but more efficient in the first case. On the contrary,
only the results obtained from the estimation on a relevant subset
are consistent. To compute this test, one needs a model estimated
with all the alternatives and one model estimated on a subset of
alternatives. This can be done by providing two objects of class
mlogit, one object of class mlogit and a character vector
indicating the subset of alternatives, or a formula and a subset of
alternatives.
an object of class "htest".
Yves Croissant
Hausman, J.A. and D. McFadden (1984), A Specification Test for the Multinomial Logit Model, Econometrica, 52, pp.1219–1240.
## from Greene's Econometric Analysis p. 731 data("TravelMode",package="AER") TravelMode <- mlogit.data(TravelMode,choice="choice",shape="long", alt.var="mode",chid.var="individual") ## Create a variable of income only for the air mode TravelMode$avinc <- with(TravelMode,(mode=='air')*income) ## Estimate the model on all alternatives, with car as the base level ## like in Greene's book. #x <- mlogit(choice~wait+gcost+avinc,TravelMode,reflevel="car") x <- mlogit(choice~wait+gcost+avinc,TravelMode) ## Estimate the same model for ground modes only (the variable avinc ## must be dropped because it is 0 for every observation g <- mlogit(choice~wait+gcost,TravelMode,reflevel="car", alt.subset=c("car","bus","train")) ## Compute the test hmftest(x,g)## from Greene's Econometric Analysis p. 731 data("TravelMode",package="AER") TravelMode <- mlogit.data(TravelMode,choice="choice",shape="long", alt.var="mode",chid.var="individual") ## Create a variable of income only for the air mode TravelMode$avinc <- with(TravelMode,(mode=='air')*income) ## Estimate the model on all alternatives, with car as the base level ## like in Greene's book. #x <- mlogit(choice~wait+gcost+avinc,TravelMode,reflevel="car") x <- mlogit(choice~wait+gcost+avinc,TravelMode) ## Estimate the same model for ground modes only (the variable avinc ## must be dropped because it is 0 for every observation g <- mlogit(choice~wait+gcost,TravelMode,reflevel="car", alt.subset=c("car","bus","train")) ## Compute the test hmftest(x,g)
A sample of 452 Japanese production units in Europe #'
A dataframe containing :
firm: the investment id,
country: the country,
region: the region (nuts1 nomenclature),
choice: a dummy indicating the chosen region ,
choice.c: the chosen country,
wage: wage rate in the region,
unemp: unemployment rate in the region,
elig: is the country eligible to european subsidies,
area: the area of the region,
scrate: social charge rate (country level),
ctaxrate: corporate tax rate (country level),
gdp: regional gdp,
harris: harris' market potential,
krugman: krugman's market potential,
domind: domestic industry count,
japind: japan industry count,
network: network count.
kindly provided by Thierry Mayer
Head K, Mayer T (2004). “Market Potential and the Location of Japanese Investment in the European Union.” The Review of Economics and Statistics, 86(4), 959-972. doi:10.1162/0034653043125257, https://doi.org/10.1162/0034653043125257, https://doi.org/10.1162/0034653043125257.
The logsum function computes the inclusive value, or inclusive
utility, which is used to compute the surplus and to estimate the two steps
nested logit model.
logsum( coef, X = NULL, formula = NULL, data = NULL, type = NULL, output = c("chid", "obs") )logsum( coef, X = NULL, formula = NULL, data = NULL, type = NULL, output = c("chid", "obs") )
coef |
a numerical vector or a |
X |
a matrix or a |
formula |
a formula or a |
data |
a |
type |
either |
output |
the shape of the results: if |
The inclusive value, or inclusive utility, or log-sum is the log of the
denominator of the probabilities of the multinomial logit model. If a
"group" variable is provided in the "mlogit.data" function,
the denominator can either be the one of the multinomial model or those of
the lower model of the nested logit model.
If only one argument (coef) is provided, it should a mlogit
object and in this case, the coefficients and the model.matrix
are extracted from this model.
In order to provide a different model.matrix, further arguments could
be used. X is a matrix or a mlogit from which the
model.matrix is extracted. The formula-data interface
can also be used to construct the relevant model.matrix.
either a vector or a matrix.
Yves Croissant
mlogit() for the estimation of a multinomial logit
model.
Two kinds of variables are used in logit models: alternative specific and
individual specific variables. mFormula provides a relevant class to
deal with this specificity and suitable methods to extract the elements of
the model.
mFormula(object) ## S3 method for class 'formula' mFormula(object) is.mFormula(object) ## S3 method for class 'mFormula' model.frame( formula, data, ..., lhs = NULL, rhs = NULL, alt.subset = NULL, reflevel = NULL ) ## S3 method for class 'mFormula' model.matrix(object, data, ...)mFormula(object) ## S3 method for class 'formula' mFormula(object) is.mFormula(object) ## S3 method for class 'mFormula' model.frame( formula, data, ..., lhs = NULL, rhs = NULL, alt.subset = NULL, reflevel = NULL ) ## S3 method for class 'mFormula' model.matrix(object, data, ...)
object |
for the |
formula |
a |
data |
a |
... |
further arguments. |
lhs |
see |
rhs |
see |
alt.subset |
a vector of subset of alternatives one want to select, |
reflevel |
the alternative selected to be the reference alternative, |
Let J being the number of alternatives. The formula may
include alternative-specific and individual specific
variables. For the latter, J - 1 coefficients are estimated for
each variable. For the former, only one (generic) coefficient
or J different coefficient may be estimated.
A mFormula is a formula for which the right hand side may contain
three parts: the first one contains the alternative specific
variables with generic coefficient, i.e. a unique coefficient for
all the alternatives ; the second one contains the individual
specific variables for which one coefficient is estimated for all
the alternatives except one of them ; the third one contains the
alternative specific variables with alternative specific
coefficients. The different parts are separeted by a | sign. If
a standard formula is writen, it is assumed that there are only
alternative specific variables with generic coefficients.
The intercept is necessarely alternative specific (a generic
intercept is not identified because only utility differences are
relevant). Therefore, it deals with the second part of the
formula. As it is usual in R, the default behaviour is to include
an intercept. A model without an intercept may be specified by
including + 0 or - 1 in the second right-hand side part of the
formula. + 0 or - 1 in the first and in the third part of the
formula are simply ignored.
Specific methods are provided to build correctly the model matrix
and to update the formula. The mFormula function is not intended
to be use directly. While using the mlogit() function, the first
argument is automaticaly coerced to a mFormula object.
an object of class mFormula.
Yves Croissant
data("Fishing", package = "mlogit") Fish <- mlogit.data(Fishing, varying = c(2:9), shape = "wide", choice = "mode") # a formula with to alternative specific variables (price and # catch) and an intercept f1 <- mFormula(mode ~ price + catch) head(model.matrix(f1, Fish), 2) # same, with an individual specific variable (income) f2 <- mFormula(mode ~ price + catch | income) head(model.matrix(f2, Fish), 2) # same, without an intercept f3 <- mFormula(mode ~ price + catch | income + 0) head(model.matrix(f3, Fish), 2) # same as f2, but now, coefficients of catch are alternative # specific f4 <- mFormula(mode ~ price | income | catch) head(model.matrix(f4, Fish), 2)data("Fishing", package = "mlogit") Fish <- mlogit.data(Fishing, varying = c(2:9), shape = "wide", choice = "mode") # a formula with to alternative specific variables (price and # catch) and an intercept f1 <- mFormula(mode ~ price + catch) head(model.matrix(f1, Fish), 2) # same, with an individual specific variable (income) f2 <- mFormula(mode ~ price + catch | income) head(model.matrix(f2, Fish), 2) # same, without an intercept f3 <- mFormula(mode ~ price + catch | income + 0) head(model.matrix(f3, Fish), 2) # same as f2, but now, coefficients of catch are alternative # specific f4 <- mFormula(mode ~ price | income | catch) head(model.matrix(f4, Fish), 2)
Miscellaneous methods for mlogit objects.
## S3 method for class 'mlogit' residuals(object, outcome = TRUE, ...) ## S3 method for class 'mlogit' df.residual(object, ...) ## S3 method for class 'mlogit' terms(x, ...) ## S3 method for class 'mlogit' model.matrix(object, ...) model.response.mlogit(object, ...) ## S3 method for class 'mlogit' update(object, new, ...) ## 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' summary(object, ..., type = c("chol", "cov", "cor")) ## S3 method for class 'summary.mlogit' print( x, digits = max(3, getOption("digits") - 2), width = getOption("width"), ... ) ## S3 method for class 'mlogit' index(x, ...) ## S3 method for class 'mlogit' predict(object, newdata = NULL, returnData = FALSE, ...) ## S3 method for class 'mlogit' fitted( object, type = c("outcome", "probabilities", "linpred", "parameters"), outcome = NULL, ... ) ## S3 method for class 'mlogit' coef( object, subset = c("all", "iv", "sig", "sd", "sp", "chol"), fixed = FALSE, ... ) ## S3 method for class 'summary.mlogit' coef(object, ...)## S3 method for class 'mlogit' residuals(object, outcome = TRUE, ...) ## S3 method for class 'mlogit' df.residual(object, ...) ## S3 method for class 'mlogit' terms(x, ...) ## S3 method for class 'mlogit' model.matrix(object, ...) model.response.mlogit(object, ...) ## S3 method for class 'mlogit' update(object, new, ...) ## 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' summary(object, ..., type = c("chol", "cov", "cor")) ## S3 method for class 'summary.mlogit' print( x, digits = max(3, getOption("digits") - 2), width = getOption("width"), ... ) ## S3 method for class 'mlogit' index(x, ...) ## S3 method for class 'mlogit' predict(object, newdata = NULL, returnData = FALSE, ...) ## S3 method for class 'mlogit' fitted( object, type = c("outcome", "probabilities", "linpred", "parameters"), outcome = NULL, ... ) ## S3 method for class 'mlogit' coef( object, subset = c("all", "iv", "sig", "sd", "sp", "chol"), fixed = FALSE, ... ) ## S3 method for class 'summary.mlogit' coef(object, ...)
outcome |
a boolean which indicates, for the |
... |
further arguments. |
x, object
|
an object of class |
new |
an updated formula for the |
digits |
the number of digits, |
width |
the width of the printing, |
type |
one of |
newdata |
a |
returnData |
for the |
subset |
an optional vector of coefficients to extract for the
|
fixed |
if |
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, ... )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 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 mFormula 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, http://www.sciencedirect.com/science/article/pii/0047272774900036.
Adummy A (2024). “Not avalable.” Failed to insert reference with key = TRAI:09 from package = 'mlogit'. Possible cause — missing or misspelled key.
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 <- 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")## 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")
shape a data.frame in a suitable form for the use of the
mlogit function.
mlogit.data( data, choice = NULL, shape = c("long", "wide"), varying = NULL, sep = ".", alt.var = NULL, chid.var = NULL, alt.levels = NULL, id.var = NULL, group.var = NULL, opposite = NULL, drop.index = FALSE, ranked = FALSE, subset = NULL, ... ) ## S3 method for class 'mlogit.data' print(x, ...) ## S3 method for class 'mlogit.data' index(x, ...) ## S3 method for class 'mlogit.data' x[i, j, drop = TRUE] ## S3 method for class 'mlogit.data' x[[y]] ## S3 method for class 'mlogit.data' x$y ## S3 replacement method for class 'mlogit.data' object$y <- value ## S3 replacement method for class 'mlogit.data' object[[y]] <- value ## S3 method for class 'mlogit.data' mean(x, ...)mlogit.data( data, choice = NULL, shape = c("long", "wide"), varying = NULL, sep = ".", alt.var = NULL, chid.var = NULL, alt.levels = NULL, id.var = NULL, group.var = NULL, opposite = NULL, drop.index = FALSE, ranked = FALSE, subset = NULL, ... ) ## S3 method for class 'mlogit.data' print(x, ...) ## S3 method for class 'mlogit.data' index(x, ...) ## S3 method for class 'mlogit.data' x[i, j, drop = TRUE] ## S3 method for class 'mlogit.data' x[[y]] ## S3 method for class 'mlogit.data' x$y ## S3 replacement method for class 'mlogit.data' object$y <- value ## S3 replacement method for class 'mlogit.data' object[[y]] <- value ## S3 method for class 'mlogit.data' mean(x, ...)
data |
a |
choice |
the variable indicating the choice made: it can be either a logical vector, a numerical vector with 0 where the alternative is not chosen, a factor with level 'yes' when the alternative is chosen |
shape |
the shape of the |
varying |
the indexes of the variables that are alternative specific, |
sep |
the seperator of the variable name and the alternative
name (only relevant for a |
alt.var |
the name of the variable that contains the
alternative index (for a |
chid.var |
the name of the variable that contains the choice index or the name under which the choice index will be stored, |
alt.levels |
the name of the alternatives: if null, for a
|
id.var |
the name of the variable that contains the individual index if any, |
group.var |
the name of the variable that contains the group index if any, |
opposite |
returns the opposite of the specified variables, |
drop.index |
should the index variables be dropped from the
|
ranked |
a logical value which is true if the response is a rank, |
subset |
a logical expression which defines the subset of observations to be selected, |
... |
further arguments passed to |
x, object
|
a |
i |
the rows to extract, |
j |
the columns to extract, |
drop |
a boolean, equal to |
y |
the column of the |
value |
the replacement value, |
A mlogit.data object, which is a data.frame in long
format, i.e. one line for each alternative. It has a index
attribute, which is a data.frame that contains the index of
the choice made (chid), the index of the alternative (alt)
and, if any, the index of the individual (id) and of the
alternative groups (group). The choice variable is a boolean
which indicates the choice made. This function use
stats::reshape() if the data.frame is in wide format.
Yves Croissant
# ModeChoice is a long data.frame data("TravelMode", package = "AER") TM <- mlogit.data(TravelMode, choice = "choice", shape = "long", alt.levels = c("air", "train", "bus", "car")) # Same but the alt variable called mode is provided TM <- mlogit.data(TravelMode ,choice = "choice", shape = "long", alt.var = "mode") # Same but the chid variable called individual is provided TM <- mlogit.data(TravelMode, choice = "choice", shape = "long", id.var = "individual", alt.levels = c("air", "train", "bus", "car")) # Same but with two own provided variables TM <- mlogit.data(TravelMode, choice = "choice", shape = "long", id.var = "individual", alt.var = "mode") # Same but with two own provided variables which are deleted from the # data.frame TM <- mlogit.data(TravelMode, choice = "choice", shape = "long", id.var = "individual", alt.var = "mode", drop.index = TRUE) # Train is a wide data.frame with columns 'choiceid' is the choice # index, the alternatives are named "ch1" and "ch2", the opposite of # the variables is returned data("Train", package = "mlogit") Train <- mlogit.data(Train, choice = "choice", shape = "wide", varying = 4:11, alt.levels = c("A", "B"), sep = "_", opposite = c("price", "time", "change", "comfort")) data("HC", package = "mlogit") HC <- mlogit.data(HC, choice = "depvar", varying=c(2:8, 10:16), shape="wide") # Game is a data.frame in wide format for which the response is a # ranking variable data("Game", package = "mlogit") G <- mlogit.data(Game, shape="wide", varying = 1:12, alt.var = 'platform', drop.index = TRUE, choice="ch", ranked =TRUE) # Game2 contains the same data, but in long format data("Game2", package = "mlogit") G2 <- mlogit.data(Game2, shape='long', choice="ch", alt.var = 'platform', ranked = TRUE)# ModeChoice is a long data.frame data("TravelMode", package = "AER") TM <- mlogit.data(TravelMode, choice = "choice", shape = "long", alt.levels = c("air", "train", "bus", "car")) # Same but the alt variable called mode is provided TM <- mlogit.data(TravelMode ,choice = "choice", shape = "long", alt.var = "mode") # Same but the chid variable called individual is provided TM <- mlogit.data(TravelMode, choice = "choice", shape = "long", id.var = "individual", alt.levels = c("air", "train", "bus", "car")) # Same but with two own provided variables TM <- mlogit.data(TravelMode, choice = "choice", shape = "long", id.var = "individual", alt.var = "mode") # Same but with two own provided variables which are deleted from the # data.frame TM <- mlogit.data(TravelMode, choice = "choice", shape = "long", id.var = "individual", alt.var = "mode", drop.index = TRUE) # Train is a wide data.frame with columns 'choiceid' is the choice # index, the alternatives are named "ch1" and "ch2", the opposite of # the variables is returned data("Train", package = "mlogit") Train <- mlogit.data(Train, choice = "choice", shape = "wide", varying = 4:11, alt.levels = c("A", "B"), sep = "_", opposite = c("price", "time", "change", "comfort")) data("HC", package = "mlogit") HC <- mlogit.data(HC, choice = "depvar", varying=c(2:8, 10:16), shape="wide") # Game is a data.frame in wide format for which the response is a # ranking variable data("Game", package = "mlogit") G <- mlogit.data(Game, shape="wide", varying = 1:12, alt.var = 'platform', drop.index = TRUE, choice="ch", ranked =TRUE) # Game2 contains the same data, but in long format data("Game2", package = "mlogit") G2 <- mlogit.data(Game2, shape='long', choice="ch", alt.var = 'platform', ranked = TRUE)
This function performs efficiently the optimization of the likelihood functions for multinomial logit models
mlogit.optim( logLik, start, method = c("bfgs", "nr", "bhhh"), iterlim = 2000, tol = 1e-06, ftol = 1e-08, steptol = 1e-10, print.level = 0, constPar = NULL, ... )mlogit.optim( logLik, start, method = c("bfgs", "nr", "bhhh"), iterlim = 2000, tol = 1e-06, ftol = 1e-08, steptol = 1e-10, print.level = 0, constPar = NULL, ... )
logLik |
the likelihood function to be maximized, |
start |
the initial value of the vector of coefficients, |
method |
the method used, one of |
iterlim |
the maximum number of iterations, |
tol |
the value of the criteria for the gradient, |
ftol |
the value of the criteria for the function, |
steptol |
the value of the criteria for the step, |
print.level |
one of (0, 1, 2), the details of the printing
messages. If |
constPar |
a numeric or a character vector which indicates that some parameters should be treated as constant, |
... |
further arguments passed to |
The optimization is performed by updating, at each iteration, the vector of parameters by the amount step * direction, where step is a positive scalar and direction = H^-1 * g, where g is the gradient and H^-1 is an estimation of the inverse of the hessian. The choice of H^-1 depends on the method chosen :
if method = 'nr', H is the hessian (i.e. is the second
derivates matrix of the likelihood function),
if method = 'bhhh', H is the outer-product of the individual
contributions of each individual to the gradient,
if method = 'bfgs', H^-1 is updated at each iteration using a
formula that uses the variations of the vector of parameters and
the gradient. The initial value of the matrix is the inverse of the
outer-product of the gradient (i.e. the bhhh estimator of the
hessian).
The initial step is 1 and, if the new value of the function is less than the previous value, it is divided by two, until a higher value is obtained.
The routine stops when the gradient is sufficiently close to 0. The
criteria is g * H^-1 * g which is compared to the tol
argument. It also may stops if the number of iterations equals
iterlim.
The function f has a initial.value argument which is the
initial value of the likelihood. The function is then evaluated a
first time with a step equals to one. If the value is lower than
the initial value, the step is divided by two until the likelihood
increases. The gradient is then computed and the function returns
as attributes the gradient is the step. This method is more
efficient than other functions available for R:
For the optim and the maxLik functions, the function and the
gradient should be provided as separate functions. But, for
multinomial logit models, both depends on the probabilities which
are the most time-consuming elements of the model to compute.
For the nlm function, the fonction returns the gradient as an
attribute. The gradient is therefore computed at each iteration,
even when the function is computed with a step that is unable to
increase the value of the likelihood.
Previous versions of mlogit depended on the 'maxLik' package.
We kept the same interface, namely the start, method,
iterlim, tol, print.level and constPar arguments.
The default method is 'bfgs', which is known to perform well,
even if the likelihood function is not well behaved and the default
value for print.level = 1, which means moderate printing.
A special default behavior is performed if a simple multinomial
logit model is estimated. Indeed, for this model, the likelihood
function is concave, the analytical hessian is simple to write and
the optimization is straightforward. Therefore, in this case, the
default method is 'nr' and print.level = 0.
a list that contains the followings elements :
optimum: the value of the function at the optimum, with
attributes: gradi a matrix that contains the contribution of each
individual to the gradient, gradient the gradient and, if method = 'nr', hessian' the hessian,
coefficients: the vector of the parameters at the optimum,
est.stat: a list that contains some information about the
optimization : 'nb.iter' the number of iterations, 'eps' the
value of the stoping criteria, 'method' the method of
optimization method used, ''message'
Yves Croissant
A sample of 453 individuals for 4 transport modes.
A dataframe containing :
choice: one of car, carpool, bus or rail,
cost.z: cost of mode z,
time.z: time of mode z.
A sample of 3880 travellers for the Montreal-Toronto corridor
A dataframe containing
case: the individual index,
alt: the alternative, one of train, car, bus and air,
choice: one if the mode is chosen, zero otherwise,
cost: monetary cost,
ivt: in vehicule time,
ovt: out vehicule time,
frequency: frequency,
income: income,
urban: urban,
noalt: the number of alternatives available.
kindly provided by S. Koppelman
Bhat CR (1995). “A heteroscedastic extreme value model of intercity travel mode choice.” Transportation Research Part B: Methodological, 29(6), 471 - 483. ISSN 0191-2615, http://www.sciencedirect.com/science/article/pii/0191261595000156.
Koppelman FS, Wen C (2000). “The paired combinatorial logit model: properties, estimation and application.” Transportation Research Part B: Methodological, 34(2), 75 - 89. ISSN 0191-2615, http://www.sciencedirect.com/science/article/pii/S0191261599000120.
Wen C, Koppelman FS (2001). “The generalized nested logit model.” Transportation Research Part B: Methodological, 35(7), 627 - 641. ISSN 0191-2615, http://www.sciencedirect.com/science/article/pii/S019126150000045X.
data("ModeCanada", package = "mlogit") bususers <- with(ModeCanada, case[choice == 1 & alt == "bus"]) ModeCanada <- subset(ModeCanada, ! case %in% bususers) ModeCanada <- subset(ModeCanada, noalt == 4) ModeCanada <- subset(ModeCanada, alt != "bus") ModeCanada$alt <- ModeCanada$alt[drop = TRUE] KoppWen00 <- mlogit.data(ModeCanada, shape='long', chid.var = 'case', alt.var = 'alt', choice='choice', drop.index=TRUE) pcl <- mlogit(choice~freq+cost+ivt+ovt, KoppWen00, reflevel='car', nests='pcl', constPar=c('iv:train.air'))data("ModeCanada", package = "mlogit") bususers <- with(ModeCanada, case[choice == 1 & alt == "bus"]) ModeCanada <- subset(ModeCanada, ! case %in% bususers) ModeCanada <- subset(ModeCanada, noalt == 4) ModeCanada <- subset(ModeCanada, alt != "bus") ModeCanada$alt <- ModeCanada$alt[drop = TRUE] KoppWen00 <- mlogit.data(ModeCanada, shape='long', chid.var = 'case', alt.var = 'alt', choice='choice', drop.index=TRUE) pcl <- mlogit(choice~freq+cost+ivt+ovt, KoppWen00, reflevel='car', nests='pcl', constPar=c('iv:train.air'))
A sample of 632 American production units
A dataframe containing:
chid: the plant id,
alt: the alternative,
id: the owner id,
choice: the chosen alternative,
available: a dummy indicating that the alternative is available,
env: the regulatory environment, one of 'regulated',
'deregulated' and 'public',
post: dummy for post-combustion polution control technology,
cm: dummy for combustion modification technology,
lnb: dummy for low NOx burners technology,
age: age of the plant (in deviation from the mean age).,
vcost: variable cost,
kcost: capital cost.
American Economic Association data archive.
Fowlie M (2010). “Emissions Trading, Electricity Restructuring, and Investment in Pollution Abatement.” American Economic Review, 100(3), 837-69. doi:10.1257/aer.100.3.837, http://www.aeaweb.org/articles?id=10.1257/aer.100.3.837.
Methods for rpar and mlogit objects which provide a plot of the
distribution of one or all of the estimated random parameters
## S3 method for class 'mlogit' plot(x, par = NULL, norm = NULL, type = c("density", "probability"), ...) ## S3 method for class 'rpar' plot(x, norm = NULL, type = c("density", "probability"), ...)## S3 method for class 'mlogit' plot(x, par = NULL, norm = NULL, type = c("density", "probability"), ...) ## S3 method for class 'rpar' plot(x, norm = NULL, type = c("density", "probability"), ...)
x |
a |
par |
a subset of the random parameters ; if |
norm |
the coefficient's name for the |
type |
the function to be plotted, whether the density or the probability density function, |
... |
further arguments, passed to |
For the rpar method, one plot is drawn. For the mlogit method,
one plot for each selected random parameter is drawn.
Yves Croissant
mlogit() the estimation of random parameters logit
models and rpar() for the description of rpar objects and
distribution for functions which return informations about
the distribution of random parameters.
1793 choices by 561 individuals of a transport mode at Freetwon airport
A dataframe containing:
id: individual id,
choice: 1 for the chosen mode,
mode: one of Helicopter,WaterTaxi, Ferry, and Hovercraft',
cost: the generalised cost of the transport mode,
risk: the fatality rate, numbers of death per 100,000 trips,
weight: weights,
seats: ,
noise: ,
crowdness: ,
convloc: ,
clientele: ,
chid: choice situation id,
african: yes if born in Africa, no otherwise,
lifeExp: declared life expectancy,
dwage: declared hourly wage,
iwage: imputed hourly wage,
educ: level of education, one of low and high,
fatalism: self-ranking of the degree of fatalism,
gender: gender, one of female and male,
age: age,
haveChildren: yes if the traveler has children,
no otherwise,
swim: yes if the traveler knows how to swim, 'no,
otherwise.
American Economic Association data archive.
León G, Miguel E (2017). “Risky Transportation Choices and the Value of a Statistical Life.” American Economic Journal: Applied Economics, 9(1), 202-28. doi:10.1257/app.20160140, http://www.aeaweb.org/articles?id=10.1257/app.20160140.
rpar objects contain the relevant information about estimated
random parameters. The homonymous function extract on rpar object
from a mlogit object.
rpar(x, par = NULL, norm = NULL, ...) ## S3 method for class 'rpar' print( x, digits = max(3, getOption("digits") - 2), width = getOption("width"), ... ) ## S3 method for class 'rpar' summary(object, ...)rpar(x, par = NULL, norm = NULL, ...) ## S3 method for class 'rpar' print( x, digits = max(3, getOption("digits") - 2), width = getOption("width"), ... ) ## S3 method for class 'rpar' summary(object, ...)
x, object
|
a |
par |
the name or the index of the parameters to be extracted
; if |
norm |
the coefficient used for normalization if any, |
... |
further arguments. |
digits |
the number of digits |
width |
the width of the printed output |
mlogit objects contain an element called rpar which contain a
list of rpar objects, one for each estimated random
parameter. The print method prints the name of the distribution
and the parameter, the summary behave like the one for numeric
vectors.
a rpar object, which contains:
dist: the name of the distribution,
mean: the first parameter of the distribution,
sigma: the second parameter of the distribution,
name: the name of the parameter.
Yves Croissant
mlogit() for the estimation of a random parameters logit
model.
Three tests for mlogit models: specific methods for the Wald test and the likelihood ration test and a new function for the score test
scoretest(object, ...) ## S3 method for class 'mlogit' scoretest(object, ...) ## Default S3 method: scoretest(object, ...) ## S3 method for class 'mlogit' waldtest(object, ...) ## S3 method for class 'mlogit' lrtest(object, ...)scoretest(object, ...) ## S3 method for class 'mlogit' scoretest(object, ...) ## Default S3 method: scoretest(object, ...) ## S3 method for class 'mlogit' waldtest(object, ...) ## S3 method for class 'mlogit' lrtest(object, ...)
object |
an object of class |
... |
two kinds of arguments can be used. If |
The scoretest function and mlogit method for
waldtest and lrtest from the lmtest package provides the
infrastructure to compute the three tests of hypothesis for
mlogit objects.
The first argument must be a mlogit object. If the second one is a
fitted model or a formula, the behaviour of the three functions is the one
of the default methods of waldtest and lrtest: the two
models provided should be nested and the hypothesis tested is that the
constrained model is the ‘right’ model.
If no second model is provided and if the model provided is the
constrained model, some specific arguments of mlogit should be
provided to descibe how the initial model should be updated. If the
first model is the unconstrained model, it is tested versus the
‘natural’ constrained model; for example, if the model is a
heteroscedastic logit model, the constrained one is the multinomial
logit model.
an object of class htest.
Yves Croissant
library("mlogit") library("lmtest") data("TravelMode", package = "AER") ml <- mlogit(choice ~ wait + travel + vcost, TravelMode, shape = "long", chid.var = "individual", alt.var = "mode") hl <- mlogit(choice ~ wait + travel + vcost, TravelMode, shape = "long", chid.var = "individual", alt.var = "mode", method = "bfgs", heterosc = TRUE) lrtest(ml, hl) waldtest(hl) scoretest(ml, heterosc = TRUE)library("mlogit") library("lmtest") data("TravelMode", package = "AER") ml <- mlogit(choice ~ wait + travel + vcost, TravelMode, shape = "long", chid.var = "individual", alt.var = "mode") hl <- mlogit(choice ~ wait + travel + vcost, TravelMode, shape = "long", chid.var = "individual", alt.var = "mode", method = "bfgs", heterosc = TRUE) lrtest(ml, hl) waldtest(hl) scoretest(ml, heterosc = TRUE)
A sample of 235 Dutch individuals facing 2929 choice situations
A dataframe containing:
id: individual identifient,
choiceid: choice identifient,
choice: one of 'A' or 'B',
price_z: price of proposition z (z = 'A', 'B') in cents of guilders,
time_z: travel time of proposition z (z = 'A', 'B') in minutes,
comfort_z: comfort of proposition z (z = 'A', 'B'), 0, 1 or 2 in decreasing comfort order,
change_z: number of changes for proposition z (z = 'A', 'B').
Journal of Applied Econometrics data archive.
Ben-Akiva M, Bolduc D, Bradley M (1993). “Estimation of Travel Choice Models with Randomly Distributed Values of Time.” Papers 9303, Laval - Recherche en Energie. https://ideas.repec.org/p/fth/lavaen/9303.html.
Meijer E, Rouwendal J (2006). “Measuring welfare effects in models with random coefficients.” Journal of Applied Econometrics, 21(2), 227-244. doi:10.1002/jae.841, https://onlinelibrary.wiley.com/doi/pdf/10.1002/jae.841, https://onlinelibrary.wiley.com/doi/abs/10.1002/jae.841.
The vcov method for mlogit objects extract the covariance
matrix of the coefficients, the errors or the random parameters.
## S3 method for class 'mlogit' vcov( object, what = c("coefficient", "errors", "rpar"), subset = c("all", "iv", "sig", "sd", "sp", "chol"), type = c("cov", "cor", "sd"), reflevel = NULL, ... ) ## S3 method for class 'vcov.mlogit' print(x, ...) ## S3 method for class 'vcov.mlogit' summary(object, ...) ## S3 method for class 'summary.vcov.mlogit' print( x, digits = max(3, getOption("digits") - 2), width = getOption("width"), ... )## S3 method for class 'mlogit' vcov( object, what = c("coefficient", "errors", "rpar"), subset = c("all", "iv", "sig", "sd", "sp", "chol"), type = c("cov", "cor", "sd"), reflevel = NULL, ... ) ## S3 method for class 'vcov.mlogit' print(x, ...) ## S3 method for class 'vcov.mlogit' summary(object, ...) ## S3 method for class 'summary.vcov.mlogit' print( x, digits = max(3, getOption("digits") - 2), width = getOption("width"), ... )
object |
a |
what |
indicates which covariance matrix has to be extracted : the
default value is |
subset |
the subset of the coefficients that have to be extracted (only
relevant if |
type |
with this argument, the covariance matrix may be returned (the default) ; the correlation matrix with the standard deviation on the diagonal may also be extracted, |
reflevel |
relevent for the extraction of the errors of a multinomial probit model ; in this case the covariance matrix is of error differences is returned and, with this argument, the alternative used for differentiation is indicated, |
... |
further arguments. |
x |
a |
digits |
the number of digits, |
width |
the width of the printing, |
This new interface replaces the cor.mlogit and cov.mlogit
functions which are deprecated.
Yves Croissant
mlogit() for the estimation of multinomial logit
models.