Baseline-Category Logit Models for Categorical and Multinomial Responses

The function mblogit fits baseline-category logit models for categorical and multinomial count responses with fixed alternatives.

mblogit(
  formula,
  data = parent.frame(),
  random = NULL,
  catCov = c("free", "diagonal", "single"),
  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,
  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.

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.

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 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

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.

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.

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)
#> Loading required package: lattice
#> 
#> Attaching package: ‘memisc’
#> The following object is masked from ‘package:Matrix’:
#> 
#>     as.array
#> The following objects are masked from ‘package:stats’:
#> 
#>     contr.sum, contr.treatment, contrasts
#> The following object is masked from ‘package:base’:
#> 
#>     as.array

(house.mult<- multinom(Sat ~ Infl + Type + Cont, weights = Freq,
                       data = housing))
#> # weights:  24 (14 variable)
#> initial  value 1846.767257 
#> iter  10 value 1747.045232
#> final  value 1735.041933 
#> converged
#> Call:
#> multinom(formula = Sat ~ Infl + Type + Cont, data = housing, 
#>     weights = Freq)
#> 
#> Coefficients:
#>        (Intercept) InflMedium  InflHigh TypeApartment TypeAtrium TypeTerrace
#> Medium  -0.4192316  0.4464003 0.6649367    -0.4356851  0.1313663  -0.6665728
#> High    -0.1387453  0.7348626 1.6126294    -0.7356261 -0.4079808  -1.4123333
#>         ContHigh
#> Medium 0.3608513
#> High   0.4818236
#> 
#> Residual Deviance: 3470.084 
#> AIC: 3498.084 


(house.mblogit <- mblogit(Sat ~ Infl + Type + Cont, weights = Freq,
                         data = housing))
#> 
#> Iteration 1 - deviance = 3493.764 - criterion = 0.9614469
#> Iteration 2 - deviance = 3470.111 - criterion = 0.00681597
#> Iteration 3 - deviance = 3470.084 - criterion = 7.82437e-06
#> Iteration 4 - deviance = 3470.084 - criterion = 7.469596e-11
#> converged
#> 
#> Call: mblogit(formula = Sat ~ Infl + Type + Cont, data = housing, weights = Freq)
#> 
#> Coefficients:
#>             Predictors
#> Logit eqn.    (Intercept)  InflMedium  InflHigh  TypeApartment  TypeAtrium
#>   Medium/Low  -0.4192       0.4464      0.6649   -0.4357         0.1314   
#>   High/Low    -0.1387       0.7349      1.6126   -0.7356        -0.4080   
#>             Predictors
#> Logit eqn.    TypeTerrace  ContHigh
#>   Medium/Low  -0.6666       0.3609 
#>   High/Low    -1.4123       0.4818 
#> 
#> Null Deviance:     3694 
#> Residual Deviance: 3470

summary(house.mult)
#> Call:
#> multinom(formula = Sat ~ Infl + Type + Cont, data = housing, 
#>     weights = Freq)
#> 
#> Coefficients:
#>        (Intercept) InflMedium  InflHigh TypeApartment TypeAtrium TypeTerrace
#> Medium  -0.4192316  0.4464003 0.6649367    -0.4356851  0.1313663  -0.6665728
#> High    -0.1387453  0.7348626 1.6126294    -0.7356261 -0.4079808  -1.4123333
#>         ContHigh
#> Medium 0.3608513
#> High   0.4818236
#> 
#> Std. Errors:
#>        (Intercept) InflMedium  InflHigh TypeApartment TypeAtrium TypeTerrace
#> Medium   0.1729344  0.1415572 0.1863374     0.1725327  0.2231065   0.2062532
#> High     0.1592295  0.1369380 0.1671316     0.1552714  0.2114965   0.2001496
#>         ContHigh
#> Medium 0.1323975
#> High   0.1241371
#> 
#> Residual Deviance: 3470.084 
#> AIC: 3498.084 

summary(house.mblogit)
#> 
#> Call:
#> mblogit(formula = Sat ~ Infl + Type + Cont, data = housing, weights = Freq)
#> 
#> Equation for Medium vs Low:
#>               Estimate Std. Error z value Pr(>|z|)    
#> (Intercept)    -0.4192     0.1729  -2.424 0.015342 *  
#> InflMedium      0.4464     0.1416   3.153 0.001613 ** 
#> InflHigh        0.6649     0.1863   3.568 0.000359 ***
#> TypeApartment  -0.4357     0.1725  -2.525 0.011562 *  
#> TypeAtrium      0.1314     0.2231   0.589 0.555980    
#> TypeTerrace    -0.6666     0.2063  -3.232 0.001230 ** 
#> ContHigh        0.3609     0.1324   2.726 0.006420 ** 
#> 
#> Equation for High vs Low:
#>               Estimate Std. Error z value Pr(>|z|)    
#> (Intercept)    -0.1387     0.1592  -0.871 0.383570    
#> InflMedium      0.7349     0.1369   5.366 8.03e-08 ***
#> InflHigh        1.6126     0.1671   9.649  < 2e-16 ***
#> TypeApartment  -0.7356     0.1553  -4.738 2.16e-06 ***
#> TypeAtrium     -0.4080     0.2115  -1.929 0.053730 .  
#> TypeTerrace    -1.4123     0.2001  -7.056 1.71e-12 ***
#> ContHigh        0.4818     0.1241   3.881 0.000104 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Approximate residual Deviance: 3470 
#> Number of Fisher scoring iterations:  4 
#> Number of observations:  1681 
#> 

mtable(house.mblogit)
#> 
#> Calls:
#> house.mblogit: mblogit(formula = Sat ~ Infl + Type + Cont, data = housing, weights = Freq)
#> 
#> ================================================
#>                          Medium/Low  High/Low   
#> ------------------------------------------------
#>   (Intercept)              -0.419*   -0.139     
#>                            (0.173)   (0.159)    
#>   Infl: Medium/Low          0.446**   0.735***  
#>                            (0.142)   (0.137)    
#>   Infl: High/Low            0.665***  1.613***  
#>                            (0.186)   (0.167)    
#>   Type: Apartment/Tower    -0.436*   -0.736***  
#>                            (0.173)   (0.155)    
#>   Type: Atrium/Tower        0.131    -0.408     
#>                            (0.223)   (0.211)    
#>   Type: Terrace/Tower      -0.667**  -1.412***  
#>                            (0.206)   (0.200)    
#>   Cont: High/Low            0.361**   0.482***  
#>                            (0.132)   (0.124)    
#> ------------------------------------------------
#>   Deviance               3470.1                 
#>   N                      1681                   
#> ================================================
#>   Significance: *** = p < 0.001;   
#>                 ** = p < 0.01; * = p < 0.05