Conditional Logit Models and Mixed Conditional Logit Models

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,
        groups = 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.

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.

offset

an optional model offset.

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.

groups

an optional formula that specifies groups of observations relevant for the estimation of overdispersion. Covariates should be constant within groups, otherwise a warning is generated since the overdispersion estimate may be imprecise.

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.

From version 0.9.7 it is possible to choose the optimization technique used for the inner iterations of the PQL/MQL: either nlminb (the default), nlm, or any of the algorithms (other than "Brent" supported by optim). To choose the optimizer, use the appropriate argument for mmclogit.control .

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

Examples

data(Transport)

summary(mclogit(
  cbind(resp,suburb)~distance+cost,
  data=Transport
  ))
#> 
#> Iteration 1 - deviance = 39.74973 - criterion = 0.8590917
#> Iteration 2 - deviance = 10.50328 - criterion = 2.758244
#> Iteration 3 - deviance = 9.231325 - criterion = 0.1363107
#> Iteration 4 - deviance = 9.227742 - criterion = 0.0003840654
#> Iteration 5 - deviance = 9.227742 - criterion = 3.446459e-09
#> converged
#> 
#> Call:
#> mclogit(formula = cbind(resp, suburb) ~ distance + cost, data = Transport)
#> 
#>          Estimate Std. Error z value Pr(>|z|)    
#> distance -1.43940    0.05318  -27.07   <2e-16 ***
#> cost     -0.97753    0.03987  -24.52   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Null Deviance:     2734 
#> Residual Deviance: 9.228 
#> Number of Fisher Scoring iterations:  5 
#> Number of observations:  1994 
#> 
#> 
# New syntactic sugar:
summary(mclogit(
  resp|suburb~distance+cost,
  data=Transport
  ))
#> 
#> Iteration 1 - deviance = 39.74973 - criterion = 0.8590917
#> Iteration 2 - deviance = 10.50328 - criterion = 2.758244
#> Iteration 3 - deviance = 9.231325 - criterion = 0.1363107
#> Iteration 4 - deviance = 9.227742 - criterion = 0.0003840654
#> Iteration 5 - deviance = 9.227742 - criterion = 3.446459e-09
#> converged
#> 
#> Call:
#> mclogit(formula = resp | suburb ~ distance + cost, data = Transport)
#> 
#>          Estimate Std. Error z value Pr(>|z|)    
#> distance -1.43940    0.05318  -27.07   <2e-16 ***
#> cost     -0.97753    0.03987  -24.52   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Null Deviance:     2734 
#> Residual Deviance: 9.228 
#> Number of Fisher Scoring iterations:  5 
#> Number of observations:  1994 
#> 
#> 


if (FALSE)  # 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))
#> 
#> Warning: Possible non-convergence of inner iterations - nlminb message: singular convergence (7)
#> 
#> Iteration 1 - deviance = 495.6469 - criterion = 0.1640698
#> Iteration 2 - deviance = 379.0387 - criterion = 0.02944294
#> Iteration 3 - deviance = 363.3644 - criterion = 0.006445485
#> Iteration 4 - deviance = 362.7738 - criterion = 0.0003382211
#> Iteration 5 - deviance = 362.7685 - criterion = 6.930447e-07
#> Iteration 6 - deviance = 362.7684 - criterion = 2.672458e-12
#> converged
#> 
#> Call:
#> mclogit(formula = Freq | time.class ~ econ.left/class + welfare/class + 
#>     auth/class, data = electors, random = ~1 | party/time)
#> 
#> Coefficents:
#>                           Estimate Std. Error z value Pr(>|z|)    
#> econ.left                 -0.04035    0.73004  -0.055   0.9559    
#> welfare                    1.95936    1.16585   1.681   0.0928 .  
#> auth                       0.16811    0.62795   0.268   0.7889    
#> econ.left:classnew.middle -2.04700    0.11816 -17.324   <2e-16 ***
#> econ.left:classold.middle -3.39457    0.17416 -19.491   <2e-16 ***
#> classnew.middle:welfare   -0.75181    0.07501 -10.023   <2e-16 ***
#> classold.middle:welfare   -1.27119    0.14517  -8.757   <2e-16 ***
#> classnew.middle:auth      -1.49715    0.05188 -28.855   <2e-16 ***
#> classold.middle:auth       1.40982    0.05997  23.510   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> (Co-)Variances:
#> Grouping level: party 
#>          Estimate   Std.Err.
#>          (Const.)   (Const.)
#> (Const.)  2.002      2.143  
#> 
#> Grouping level: party:time 
#>          Estimate    Std.Err.
#>          (Const.)    (Const.)
#> (Const.) 2.372e-08   1.09e-24
#> 
#> Approximate residual deviance: 362.8 
#> Number of Fisher scoring iterations:  6
#> Number of observations
#>   Groups by party: 6
#>   Groups by party:time: 150
#>   Individual observations:  37500
#> 

# 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))
#> 
#> Iteration 1 - deviance = 495.6162 - criterion = 0.1640703
#> Iteration 2 - deviance = 378.9601 - criterion = 0.02945638
#> Iteration 3 - deviance = 363.1957 - criterion = 0.006453598
#> Iteration 4 - deviance = 362.5831 - criterion = 0.0003390481
#> Iteration 5 - deviance = 362.5743 - criterion = 6.961201e-07
#> Iteration 6 - deviance = 362.574 - criterion = 2.692818e-12
#> converged
#> 
#> Call:
#> mclogit(formula = Freq | time.class ~ econ.left/class + welfare/class + 
#>     auth/class, data = electors, random = list(~1 | party, ~econ.left + 
#>     0 | time))
#> 
#> Coefficents:
#>                           Estimate Std. Error z value Pr(>|z|)    
#> econ.left                 -0.04034    0.73006  -0.055   0.9559    
#> welfare                    1.95937    1.16587   1.681   0.0928 .  
#> auth                       0.16811    0.62797   0.268   0.7889    
#> econ.left:classnew.middle -2.04703    0.11816 -17.324   <2e-16 ***
#> econ.left:classold.middle -3.39462    0.17416 -19.492   <2e-16 ***
#> classnew.middle:welfare   -0.75181    0.07501 -10.023   <2e-16 ***
#> classold.middle:welfare   -1.27119    0.14517  -8.757   <2e-16 ***
#> classnew.middle:auth      -1.49715    0.05188 -28.855   <2e-16 ***
#> classold.middle:auth       1.40982    0.05997  23.510   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> (Co-)Variances:
#> Grouping level: party 
#>          Estimate   Std.Err.
#>          (Const.)   (Const.)
#> (Const.)  2.002      2.143  
#> 
#> Grouping level: time 
#>           Estimate    Std.Err. 
#>           econ.left   econ.left
#> econ.left 0.0002345   2.579e-12
#> 
#> Approximate residual deviance: 362.6 
#> Number of Fisher scoring iterations:  6
#> Number of observations
#>   Groups by party: 6
#>   Groups by time: 25
#>   Individual observations:  37500
#> 
 # \dontrun{}