mclogit: Conditional Logit Models and Mixed Conditional Logit Models

In mclogit: Multinomial Logit Models, with or without Random Effects or Overdispersion

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.2009.02.002

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)

mclogit documentation built on Oct. 29, 2022, 1:09 a.m.