dispersion mclogit 0.8.5.1

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, ...)
## S4 method for signature '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.

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)
Iteration 1 - Deviance = 3493.764
Iteration 2 - Deviance = 3470.111
Iteration 3 - Deviance = 3470.084
Iteration 4 - Deviance = 3470.084
converged
dispersion(house.mblogit,method="Afroz")
[1] 20.45129
dispersion(house.mblogit,method="Deviance")
[1] 26.69295
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

Null Deviance:     3694
Residual Deviance: 3470
Number of Fisher Scoring iterations:  4
Number of observations:  1681
phi.Afroz <- dispersion(house.mblogit,method="Afroz")
summary(house.mblogit, dispersion=phi.Afroz)
Call:
mblogit(formula = Sat ~ Infl + Type + Cont, data = housing, weights = Freq)

Equation for Medium vs Low:
              Estimate Std. Error t value Pr(>|t|)
(Intercept)    -0.4192     0.7821  -0.536    0.593
InflMedium      0.4464     0.6402   0.697    0.487
InflHigh        0.6649     0.8427   0.789    0.432
TypeApartment  -0.4357     0.7802  -0.558    0.578
TypeAtrium      0.1314     1.0090   0.130    0.897
TypeTerrace    -0.6666     0.9327  -0.715    0.476
ContHigh        0.3609     0.5987   0.603    0.548

Equation for High vs Low:
              Estimate Std. Error t value Pr(>|t|)
(Intercept)    -0.1387     0.7201  -0.193   0.8475
InflMedium      0.7349     0.6193   1.187   0.2375
InflHigh        1.6126     0.7558   2.134   0.0348 *
TypeApartment  -0.7356     0.7022  -1.048   0.2968
TypeAtrium     -0.4080     0.9565  -0.427   0.6704
TypeTerrace    -1.4123     0.9051  -1.560   0.1211
ContHigh        0.4818     0.5614   0.858   0.3923
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Dispersion:  20.45129  on  130  degrees of freedom
Null Deviance:     3694
Residual Deviance: 3470
Number of Fisher Scoring iterations:  4
Number of observations:  1681
summary(update(house.mblogit, dispersion="Afroz"))
Call:
mblogit(formula = Sat ~ Infl + Type + Cont, data = housing, weights = Freq)

Equation for Medium vs Low:
              Estimate Std. Error t value Pr(>|t|)
(Intercept)    -0.4192     0.7821  -0.536    0.593
InflMedium      0.4464     0.6402   0.697    0.487
InflHigh        0.6649     0.8427   0.789    0.432
TypeApartment  -0.4357     0.7802  -0.558    0.578
TypeAtrium      0.1314     1.0090   0.130    0.897
TypeTerrace    -0.6666     0.9327  -0.715    0.476
ContHigh        0.3609     0.5987   0.603    0.548

Equation for High vs Low:
              Estimate Std. Error t value Pr(>|t|)
(Intercept)    -0.1387     0.7201  -0.193   0.8475
InflMedium      0.7349     0.6193   1.187   0.2375
InflHigh        1.6126     0.7558   2.134   0.0348 *
TypeApartment  -0.7356     0.7022  -1.048   0.2968
TypeAtrium     -0.4080     0.9565  -0.427   0.6704
TypeTerrace    -1.4123     0.9051  -1.560   0.1211
ContHigh        0.4818     0.5614   0.858   0.3923
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Dispersion:  20.45129  on  130  degrees of freedom
Null Deviance:     3694
Residual Deviance: 3470
Number of Fisher Scoring iterations:  4
Number of observations:  1681
# 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")
Iteration 1 - Deviance = 38.84842
Iteration 2 - Deviance = 38.66222
Iteration 3 - Deviance = 38.6622
Iteration 4 - Deviance = 38.6622
converged
# Now the estimated dispersion parameter is no longer larger than 20,
# but just bit over 1.0.
summary(house.mblogit.corrected)
Call:
mblogit(formula = Sat ~ Infl + Type + Cont, data = housing, weights = Freq,
    dispersion = "Afroz", from.table = TRUE)

Equation for Medium vs Low:
              Estimate Std. Error t value Pr(>|t|)
(Intercept)    -0.4192     0.1832  -2.289  0.02842 *
InflMedium      0.4464     0.1499   2.977  0.00533 **
InflHigh        0.6649     0.1974   3.369  0.00189 **
TypeApartment  -0.4357     0.1827  -2.384  0.02284 *
TypeAtrium      0.1314     0.2363   0.556  0.58189
TypeTerrace    -0.6666     0.2184  -3.051  0.00440 **
ContHigh        0.3609     0.1402   2.573  0.01461 *

Equation for High vs Low:
              Estimate Std. Error t value Pr(>|t|)
(Intercept)    -0.1387     0.1686  -0.823 0.416418
InflMedium      0.7349     0.1450   5.067 1.41e-05 ***
InflHigh        1.6126     0.1770   9.110 1.20e-10 ***
TypeApartment  -0.7356     0.1645  -4.473 8.19e-05 ***
TypeAtrium     -0.4080     0.2240  -1.821 0.077370 .
TypeTerrace    -1.4123     0.2120  -6.662 1.20e-07 ***
ContHigh        0.4818     0.1315   3.665 0.000837 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Dispersion:  1.121765  on  34  degrees of freedom
Null Deviance:     262.1
Residual Deviance: 38.66
Number of Fisher Scoring iterations:  4
Number of observations:  1681