Choice of Means of Transport
Description
This is an artificial data set on choice of means of transport based on cost and walking distance.
Usage
data(Transport)Format
A data frame containing the following variables:
- transport
means of transportation that can be chosen.
- suburb
identifying number for each suburb
- distance
walking distance to bus or train station
- cost
cost of each means of transportation
- working
size of working population of each suburb
- prop.true
true choice probabilities
- resp
choice frequencies of means of transportation
Overdispersion in Multinomial Logit Models
Description
The function dispersion() extracts the dispersion parameter
from a multinomial logit model or computes a dispersion parameter
estimate based on a given method. This dispersion parameter can
be attached to a model using update(). It can also given as an
argument to summary().
Usage
dispersion(object,method, ...)
## S3 method for class 'mclogit'
dispersion(object,method=NULL, ...)
Arguments
object
an object that inherits class "mclogit".
When passed to dispersion(), it
should be the result of a call of mclogit() of
mblogit(), without random effects.
method
a character string, either "Afroz",
"Fletcher", "Pearson", or "Deviance", that
specifies the estimator of the dispersion; or
NULL, in which case the default estimator, "Afroz"
is used. The estimators are discussed in Afroz et al. (2019).
...
other arguments, ignored or passed to other methods.
References
Afroz, Farzana, Matt Parry, and David Fletcher. (2020). "Estimating Overdispersion in Sparse Multinomial Data." Biometrics 76(3): 834-842. doi:10.1111/biom.13194.
Examples
library(MASS) # For 'housing' data
# Note that with a factor response and frequency weighted data,
# Overdispersion will be overestimated:
house.mblogit <- mblogit(Sat ~ Infl + Type + Cont, weights = Freq,
data = housing)
dispersion(house.mblogit,method="Afroz")
dispersion(house.mblogit,method="Deviance")
summary(house.mblogit)
phi.Afroz <- dispersion(house.mblogit,method="Afroz")
summary(house.mblogit, dispersion=phi.Afroz)
summary(update(house.mblogit, dispersion="Afroz"))
# In order to be able to estimate overdispersion accurately,
# data like the above (which usually comes from applying
# 'as.data.frame' to a contingency table) the model has to be
# fitted with the optional argument 'from.table=TRUE':
house.mblogit.corrected <- mblogit(Sat ~ Infl + Type + Cont, weights = Freq,
data = housing, from.table=TRUE,
dispersion="Afroz")
# Now the estimated dispersion parameter is no longer larger than 20,
# but just bit over 1.0.
summary(house.mblogit.corrected)
Class, Party Position, and Electoral Choice
Description
This is an artificial data set on electoral choice as influenced by class and party positions.
Usage
data(electors)Format
A data frame containing the following variables:
- class
class position of voters
- party
party that runs for election
- Freq
freqency by which each party list is chosen by members of each class
- time
time variable, runs from zero to one
- econ.left
economic-policy "leftness" of each party
- welfare
emphasis of welfare expansion of each party
- auth
position on authoritarian issues
Examples
data(electors)
summary(mclogit(
cbind(Freq,interaction(time,class))~econ.left+welfare+auth,
data=electors))
summary(mclogit(
cbind(Freq,interaction(time,class))~econ.left/class+welfare/class+auth/class,
data=electors))
## Not run: # This takes a bit longer.
summary(mclogit(
cbind(Freq,interaction(time,class))~econ.left/class+welfare/class+auth/class,
random=~1|party.time,
data=within(electors,party.time<-interaction(party,time))))
summary(mclogit(
cbind(Freq,interaction(time,class))~econ.left/(class*time)+welfare/class+auth/class,
random=~1|party.time,
data=within(electors,{
party.time <-interaction(party,time)
econ.left.sq <- (econ.left-mean(econ.left))^2
})))
## End(Not run)
'getSummary' Methods
Description
getSummary methods for use by mtable
Usage
## S3 method for class 'mblogit'
getSummary(obj,
alpha=.05,
...)
## S3 method for class 'mclogit'
getSummary(obj,
alpha=.05,
rearrange=NULL,
...)
## S3 method for class 'mmblogit'
getSummary(obj,
alpha=.05,
...)
## S3 method for class 'mmclogit'
getSummary(obj,
alpha=.05,
rearrange=NULL,
...)
Arguments
alpha
level of the confidence intervals; their coverage should be 1-alpha/2
rearrange
an optional named list of character vectors. Each element of the list designates a column in the table of estimates, and each element of a character vector refers to a coefficient. Names of list elements become column heads and names of the character vector elements become coefficient labels.
...
further arguments; ignored.
Examples
## Not run:
summary(classd.model <- mclogit(cbind(Freq,choice.set)~
(econdim1.sq+nonmatdim1.sq+nonmatdim2.sq)+
(econdim1+nonmatdim1+nonmatdim2)+
(econdim1+nonmatdim1+nonmatdim2):classd,
data=mvoteint.classd,random=~1|mvoteint/eb,
subset=classd!="Farmers"))
myGetSummary.classd <- function(x)getSummary.mclogit(x,rearrange=list(
"Econ. Left/Right"=c(
"Squared effect"="econdim1.sq",
"Linear effect"="econdim1",
" x Intermediate/Manual worker"="econdim1:classdIntermediate",
" x Service class/Manual worker"="econdim1:classdService class",
" x Self-employed/Manual worker"="econdim1:classdSelf-employed"
),
"Lib./Auth."=c(
"Squared effect"="nonmatdim1.sq",
"Linear effect"="nonmatdim1",
" x Intermediate/Manual worker"="nonmatdim1:classdIntermediate",
" x Service class/Manual worker"="nonmatdim1:classdService class",
" x Self-employed/Manual worker"="nonmatdim1:classdSelf-employed"
),
"Mod./Trad."=c(
"Squared effect"="nonmatdim2.sq",
"Linear effect"="nonmatdim2",
" x Intermediate/Manual worker"="nonmatdim2:classdIntermediate",
" x Service class/Manual worker"="nonmatdim2:classdService class",
" x Self-employed/Manual worker"="nonmatdim2:classdSelf-employed"
)
))
library(memisc)
mtable(classd.model,getSummary=myGetSummary.classd)
# Output would look like so:
# ==================================================================================
# Econ. Left/Right Lib./Auth. Mod./Trad.
# ----------------------------------------------------------------------------------
# Squared effect 0.030 0.008 -0.129**
# (0.081) (0.041) (0.047)
# Linear effect -0.583*** -0.038 0.137**
# (0.063) (0.041) (0.045)
# x Intermediate/Manual worker 0.632*** -0.029 -0.015
# (0.026) (0.020) (0.019)
# x Service class/Manual worker 1.158*** 0.084** 0.000
# (0.040) (0.032) (0.030)
# x Self-employed/Manual worker 1.140*** 0.363*** 0.112***
# (0.035) (0.027) (0.026)
# Var(mvoteint) 1.080***
# (0.000)
# Var(mvoteint x eb) 0.118***
# (0.000)
# ----------------------------------------------------------------------------------
# Dispersion 1.561
# Deviance 15007.0
# N 173445
# ==================================================================================
## End(Not run)
Baseline-Category Logit Models for Categorical and Multinomial Responses
Description
The function mblogit fits baseline-category logit models for categorical
and multinomial count responses with fixed alternatives.
Usage
mblogit(
formula,
data = parent.frame(),
random = NULL,
catCov = c("free", "diagonal", "single"),
subset,
weights = NULL,
na.action = getOption("na.action"),
model = TRUE,
x = FALSE,
y = TRUE,
contrasts = NULL,
method = NULL,
estimator = c("ML", "REML"),
dispersion = FALSE,
start = NULL,
from.table = FALSE,
groups = NULL,
control = if (length(random)) mmclogit.control(...) else mclogit.control(...),
...
)
Arguments
formula
the model formula. The response must be a factor or a matrix of counts.
data
an optional data frame, list or environment (or object coercible
by as.data.frame to a data frame) containing the variables
in the model. If not found in data, the variables are taken from
environment(formula), typically the environment from which
glm is called.
random
an optional formula or list of formulas that specify the random-effects structure or NULL.
catCov
a character string that specifies optional restrictions on the covariances of random effects between the logit equations. "free" means no restrictions, "diagonal" means that random effects pertinent to different categories are uncorrelated, while "single" means that the random effect variances pertinent to all categories are identical.
subset
an optional vector specifying a subset of observations to be used in the fitting process.
weights
an optional vector of weights to be used in the fitting
process. Should be NULL or a numeric vector.
na.action
a function which indicates what should happen when the data
contain NAs. The default is set by the na.action setting
of options , and is na.fail if that is unset.
The ‘factory-fresh’ default is na.omit . Another
possible value is NULL, no action. Value na.exclude
can be useful.
model
a logical value indicating whether model frame should be included as a component of the returned value.
x, y
logical values indicating whether the response vector and model matrix used in the fitting process should be returned as components of the returned value.
contrasts
an optional list. See the contrasts.arg of
model.matrix.default.
method
NULL or a character string, either "PQL" or "MQL",
specifies the type of the quasilikelihood approximation to be used if a
random-effects model is to be estimated.
estimator
a character string; either "ML" or "REML", specifies which estimator is to be used/approximated.
dispersion
a logical value or a character string; whether and how a
dispersion parameter should be estimated. For details see
dispersion .
start
an optional matrix of starting values (with as many rows
as logit equations). If the model has random effects, the matrix
should have a "VarCov" attribute wtih starting values for
the random effects (co-)variances. If the random effects model
is estimated with the "PQL" method, the starting values matrix
should also have a "random.effects" attribute, which should have
the same structure as the "random.effects" component of an object
returned by mblogit().
from.table
a logical value; do the data represent a contingency table,
e.g. were created by applying as.data.frame() a the result of
table() or xtabs(). This relevant only if the response is
a factor. This argument should be set to TRUE if the data do come
from a contingency table. Correctly setting from.table=TRUE in
this case, will lead to efficiency gains in computing, but more
importantly overdispersion will correctly be computed if present.
groups
an optional formula that specifies groups of observations relevant for the specification of overdispersed response counts.
control
a list of parameters for the fitting process. See
mclogit.control
...
arguments to be passed to mclogit.control or
mmclogit.control
Details
The function mblogit internally rearranges the data into a
'long' format and uses mclogit.fit to compute
estimates. Nevertheless, the 'user data' are unaffected.
Value
mblogit returns an object of class "mblogit", which has almost
the same structure as an object of class "glm". The
difference are the components coefficients, residuals,
fitted.values, linear.predictors, and y, which are
matrices with number of columns equal to the number of response
categories minus one.
References
Agresti, Alan. 2002. Categorical Data Analysis. 2nd ed, Hoboken, NJ: Wiley. doi:10.1002/0471249688
Breslow, N.E. and D.G. Clayton. 1993. "Approximate Inference in Generalized Linear Mixed Models". Journal of the American Statistical Association 88 (421): 9-25. doi:10.1080/01621459.1993.10594284
See Also
The function multinom in package nnet also
fits multinomial baseline-category logit models, but has a slightly less
convenient output and does not support overdispersion or random
effects. However, it provides some other options. Baseline-category logit
models are also supported by the package VGAM, as well as some
reduced-rank and (semi-parametric) additive generalisations. The package
mnlogit estimates logit models in a way optimized for large numbers
of alternatives.
Examples
library(MASS) # For 'housing' data
library(nnet)
library(memisc)
(house.mult<- multinom(Sat ~ Infl + Type + Cont, weights = Freq,
data = housing))
(house.mblogit <- mblogit(Sat ~ Infl + Type + Cont, weights = Freq,
data = housing))
summary(house.mult)
summary(house.mblogit)
mtable(house.mblogit)
Conditional Logit Models and Mixed Conditional Logit Models
Description
mclogit fits conditional logit models and mixed conditional
logit models to count data and individual choice data,
where the choice set may vary across choice occasions.
Conditional logit models without random effects are fitted by Fisher-scoring/IWLS. Models with random effects (mixed conditional logit models) are estimated via maximum likelihood with a simple Laplace aproximation (aka PQL).
Usage
mclogit(formula, data=parent.frame(), random=NULL,
subset, weights = NULL, offset=NULL, na.action = getOption("na.action"),
model = TRUE, x = FALSE, y = TRUE, contrasts=NULL,
method = NULL, estimator=c("ML","REML"),
dispersion = FALSE,
start=NULL,
control=if(length(random))
mmclogit.control(...)
else mclogit.control(...), ...)
## S3 method for class 'mclogit'
update(object, formula., dispersion, ...)
## S3 method for class 'mclogit'
summary(object, dispersion = NULL, correlation = FALSE,
symbolic.cor = FALSE, ...)
Arguments
formula
a model formula: a symbolic description of the model to be fitted. The left-hand side should result in a two-column matrix. The first column contains the choice counts or choice indicators (alternative is chosen=1, is not chosen=0). The second column contains unique numbers for each choice set.
The left-hand side can either take the form cbind(choice,set)
or (from version 0.9.1) choice|set
If individual-level data is used, choice sets correspond to individuals, if aggregated data with choice counts are used, choice sets usually correspond to covariate classes.
The right-hand of the formula contains choice predictors. It should be noted that constants are deleted from the formula as are predictors that do not vary within choice sets.
data
an optional data frame, list or environment (or object
coercible by as.data.frame to a data frame) containing
the variables in the model. If not found in data, the
variables are taken from environment(formula),
typically the environment from which glm is called.
random
an optional formula or list of formulas that specify the random-effects structure or NULL.
weights
an optional vector of weights to be used in the fitting
process. Should be NULL or a numeric vector.
offset
an optional model offset. Currently only supported for models without random effects.
subset
an optional vector specifying a subset of observations to be used in the fitting process.
na.action
a function which indicates what should happen
when the data contain NAs. The default is set by
the na.action setting of options , and is
na.fail if that is unset. The ‘factory-fresh’
default is na.omit . Another possible value is
NULL, no action. Value na.exclude can be useful.
start
an optional numerical vector of starting values for the
conditional logit parameters. If the model has random effects, the
vector should have a "VarCov" attribute wtih starting values for the
random effects (co-)variances. If the random effects model is
estimated with the "PQL" method, the starting values matrix should
also have a "random.effects" attribute, which should have the same
structure as the "random.effects" component of an object returned by
mblogit().
model
a logical value indicating whether model frame should be included as a component of the returned value.
x, y
logical values indicating whether the response vector and model matrix used in the fitting process should be returned as components of the returned value.
contrasts
an optional list. See the contrasts.arg
of model.matrix.default.
method
NULL or a character string, either "PQL" or "MQL", specifies
the type of the quasilikelihood approximation to be used if
a random-effects model is to be estimated.
estimator
a character string; either "ML" or "REML", specifies which estimator is to be used/approximated.
dispersion
a real number used as dispersion parameter;
a character vector that specifies the method to compute the dispersion;
a logical value – if TRUE the default method
("Afroz") is used, if FALSE, the dispersion parameter
is set to 1, that is, no dispersion. For details see dispersion .
control
a list of parameters for the fitting process.
See mclogit.control
...
arguments to be passed to mclogit.control or mmclogit.control
object
an object that inherits class "mclogit".
When passed to dispersion(), it
should be the result of a call of mclogit() of
mblogit(), without random effects.
formula.
a changes to the model formula,
see update.default and
update.formula .
correlation
logical; see summary.lm .
symbolic.cor
logical; see summary.lm .
Value
mclogit returns an object of class "mclogit", which has almost the
same structure as an object of class "glm".
Note
Covariates that are constant within choice sets are automatically
dropped from the model formula specified by the formula
argument of mclogit.
If the model contains random effects, these should
either vary within choice sets (e.g. the levels of a factor that defines the choice sets should not be nested within the levels of factor)
or be random coefficients of covariates that vary within choice sets.
In earlier versions of the package (prior to 0.6) it will lead to a
failure of the model fitting algorithm if these conditions are not
satisfied. Since version 0.6 of the package, the function
mclogit will complain about such model a misspecification
explicitely.
References
Agresti, Alan (2002). Categorical Data Analysis. 2nd ed, Hoboken, NJ: Wiley. doi:10.1002/0471249688
Breslow, N.E. and D.G. Clayton (1993). "Approximate Inference in Generalized Linear Mixed Models". Journal of the American Statistical Association 88 (421): 9-25. doi:10.1080/01621459.1993.10594284
Elff, Martin (2009). "Social Divisions, Party Positions, and Electoral Behaviour". Electoral Studies 28(2): 297-308. doi:10.1016/j.electstud.200902002
McFadden, D. (1973). "Conditionial Logit Analysis of Qualitative Choice Behavior". Pp. 105-135 in P. Zarembka (ed.). Frontiers in Econometrics. New York: Wiley. https://eml.berkeley.edu/reprints/mcfadden/zarembka.pdf
See Also
Conditional logit models are also supported by gmnl, mlogit, and survival. survival supports conditional logit models for binary panel data and case-control studies. mlogit and gmnl treat conditional logit models from an econometric perspective. Unlike the present package, they focus on the random utility interpretation of discrete choice models and support generalisations of conditional logit models, such as nested logit models, that are intended to overcome the IIA (indipendence from irrelevant alterantives) assumption. Mixed multinomial models are also supported and estimated using simulation-based techniques. Unlike the present package, mixed or random-effects extensions are mainly intended to fit repeated choices of the same individuals and not aggregated choices of many individuals facing identical alternatives.
Examples
data(Transport)
summary(mclogit(
cbind(resp,suburb)~distance+cost,
data=Transport
))
# New syntactic sugar:
summary(mclogit(
resp|suburb~distance+cost,
data=Transport
))
## Not run: # This takes a bit longer.
data(electors)
electors <- within(electors,{
party.time <-interaction(party,time)
time.class <- interaction(time,class)
})
# Time points nested within parties
summary(mclogit(
Freq|time.class~econ.left/class+welfare/class+auth/class,
random=~1|party/time,
data=electors))
# Party-level random intercepts and random slopes varying over time points
summary(mclogit(
Freq|time.class~econ.left/class+welfare/class+auth/class,
random=list(~1|party,~econ.left+0|time),
data=electors))
## End(Not run)
Control Parameters for the Fitting Process
Description
mclogit.control returns a list of default parameters
that control the fitting process of mclogit.
Usage
mclogit.control(epsilon = 1e-08,
maxit = 25, trace=TRUE)
mmclogit.control(epsilon = 1e-08,
maxit = 25, trace=TRUE,
trace.inner=FALSE,
avoid.increase = FALSE,
break.on.increase = FALSE,
break.on.infinite = FALSE,
break.on.negative = FALSE)
Arguments
epsilon
positive convergence tolerance \epsilon;
the iterations converge when
|dev - dev_{old}|/(|dev| + 0.1) < \epsilon.
maxit
integer giving the maximal number of IWLS or PQL iterations.
trace
logical indicating if output should be produced for each iteration.
trace.inner
logical; indicating if output should be produced for each inner iteration of the PQL method.
avoid.increase
logical; should an increase of the deviance be avoided by step truncation?
break.on.increase
logical; should an increase of the deviance be avoided by stopping the algorithm?
break.on.infinite
logical; should an infinite deviance stop the algorithm instead of leading to step truncation?
break.on.negative
logical; should a negative deviance stop the algorithm?
Value
A list.
Internal functions used for model fit.
Description
These functions are exported and documented for use by other packages. They are not intended for end users.
Usage
mclogit.fit(y, s, w, X,
dispersion=FALSE,
start = NULL, offset = NULL,
control = mclogit.control())
mmclogit.fitPQLMQL(y, s, w, X, Z, d,
start = NULL,
start.Phi = NULL,
start.b = NULL,
offset = NULL, method=c("PQL","MQL"),
estimator = c("ML","REML"),
control = mmclogit.control())
Arguments
y
a response vector. Should be binary.
s
a vector identifying individuals or covariate strata
w
a vector with observation weights.
X
a model matrix; required.
dispersion
a logical value or a character string; whether and how
a dispersion parameter should be estimated. For details see dispersion .
Z
the random effects design matrix.
d
dimension of random effects. Typically $d=1$ for random intercepts only, $d>1$ for models with random intercepts.
start
an optional numerical vector of starting values for the coefficients.
offset
an optional model offset. Currently only supported for models without random effects.
start.Phi
an optional matrix of strarting values for the (co-)variance parameters.
start.b
an optional list of vectors with starting values for the random effects.
method
a character string, either "PQL" or "MQL", specifies the type of the quasilikelihood approximation.
estimator
a character string; either "ML" or "REML", specifies which estimator is to be used/approximated.
control
a list of parameters for the fitting process.
See mclogit.control
Value
A list with components describing the fitted model.
Predicting responses or linear parts of the baseline-category and conditional logit models
Description
The predict() methods allow to obtain within-sample and
out-of-sample predictions from models
fitted with mclogit() and mblogit().
For models with random effecs fitted using the PQL-method, it is possible to obtain responses that are conditional on the reconstructed random effects.
Usage
## S3 method for class 'mblogit'
predict(object, newdata=NULL,type=c("link","response"),se.fit=FALSE, ...)
## S3 method for class 'mclogit'
predict(object, newdata=NULL,type=c("link","response"),se.fit=FALSE, ...)
## S3 method for class 'mmblogit'
predict(object, newdata=NULL,type=c("link","response"),se.fit=FALSE,
conditional=TRUE, ...)
## S3 method for class 'mmclogit'
predict(object, newdata=NULL,type=c("link","response"),se.fit=FALSE,
conditional=TRUE, ...)
Arguments
object
an object in class "mblogit", "mmblogit", "mclogit", or "mmclogit"
newdata
an optional data frame with new data
type
a character string specifying the kind of prediction
se.fit
a logical value; whether predictions should be accompanied with standard errors
conditional
a logical value; whether predictions should be made
conditional on the random effects (or whether they are set to zero,
i.e. their expectation). This argument is consequential only if
the "mmblogit" or "mmclogit" object was created with method="PQL".
...
other arguments, ignored.
Value
The predict methods return either a matrix (unless called with
se.fit=TRUE) or a list with two matrix-valued elements
"fit" and "se.fit".
Examples
library(MASS)
(house.mblogit <- mblogit(Sat ~ Infl + Type + Cont,
data = housing,
weights=Freq))
head(pred.house.mblogit <- predict(house.mblogit))
str(pred.house.mblogit <- predict(house.mblogit,se=TRUE))
head(pred.house.mblogit <- predict(house.mblogit,
type="response"))
str(pred.house.mblogit <- predict(house.mblogit,se=TRUE,
type="response"))
# This takes a bit longer.
data(electors)
(mcre <- mclogit(
cbind(Freq,interaction(time,class))~econ.left/class+welfare/class+auth/class,
random=~1|party.time,
data=within(electors,party.time<-interaction(party,time))))
str(predict(mcre))
str(predict(mcre,type="response"))
str(predict(mcre,se.fit=TRUE))
str(predict(mcre,type="response",se.fit=TRUE))
Simulating responses from baseline-category and conditional logit models
Description
The simulate() methods allow to simulate responses from models
fitted with mclogit() and mblogit(). Currently only
models without random effects are supported for this.
Usage
## S3 method for class 'mblogit'
simulate(object, nsim = 1, seed = NULL, ...)
## S3 method for class 'mclogit'
simulate(object, nsim = 1, seed = NULL, ...)
# These methods are currently just 'stubs', causing an error
# message stating that simulation from models with random
# effects are not supported yet
## S3 method for class 'mmblogit'
simulate(object, nsim = 1, seed = NULL, ...)
## S3 method for class 'mmclogit'
simulate(object, nsim = 1, seed = NULL, ...)
Arguments
object
an object from the relevant class
nsim
a number, specifying the number of simulated responses for each observation.
seed
an object specifying if and how the random number
generator should be initialized ('seeded'). The interpetation of
this argument follows the default method, see link[stats]{simulate}
...
other arguments, ignored.
Value
The result of the simulate method for objects
created by mclogit is a data frame with one variable for
each requested simulation run (their number is given by the
nsim= argument). The contents of the columns are counts (or
zero-one values), with group-wise multinomial distribution (within
choice sets) just like it is assumed for the original response.
The shape of the result of the simulate method
for objects created by mblogit is also a data frame.
The variables within the data frame have a mode or shape that
corresponds to the response to which the model was fitted. If the
response is a matrix of counts, then the variables in the data frame
are also matrices of counts. If the response is a factor and
mblogit was called with an argument
from.table=FALSE, the variables in the data frame are factors
with the same factor levels as the response to which the model was
fitted. If instead the function was called with
from.table=TRUE, the variables in the data frame are counts,
which represent frequency weights that would result from applying
as.data.frame to a contingency table of simulated
frequency counts.
Examples
library(MASS)
(house.mblogit <- mblogit(Sat ~ Infl + Type + Cont,
data = housing,
weights=Freq,
from.table=TRUE))
sm <- simulate(house.mblogit,nsim=7)
housing.long <- housing[rep(seq.int(nrow(housing)),housing$Freq),]
(housel.mblogit <- mblogit(Sat ~ Infl + Type + Cont,
data=housing.long))
sml <- simulate(housel.mblogit,nsim=7)
housing.table <- xtabs(Freq~.,data=housing)
housing.mat <- memisc::to.data.frame(housing.table)
head(housing.mat)
(housem.mblogit <- mblogit(cbind(Low,Medium,High) ~
Infl + Type + Cont,
data=housing.mat))
smm <- simulate(housem.mblogit,nsim=7)
str(sm)
str(sml)
str(smm)
head(smm[[1]])