mclogit (version 0.9.15)

dispersion: 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 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. tools:::Rd_expr_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")

# 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 'aggregate=TRUE' or 
# by requesting the dispersion in advance.
house.mblogit.agg <- mblogit(Sat ~ Infl + Type + Cont, 
                             weights = Freq,
                             data = housing, 
                             aggregate = TRUE)
# Now the estimated dispersion parameter is no longer larger than 20,
# but just bit over 1.0.
dispersion(house.mblogit.agg, method = "Afroz")
dispersion(house.mblogit.agg, method = "Deviance")

# It is possible to obtain the dispersion after estimating the coefficients:
phi.Afroz <- dispersion(house.mblogit.agg, method = "Afroz")
summary(house.mblogit.agg, dispersion = phi.Afroz)

summary(update(house.mblogit.agg, dispersion = "Afroz"))

# If an estimate of the (over-)dispersion is requested, 'aggregate' is set to
# TRUE by default:
house.mblogit.odsp <- mblogit(Sat ~ Infl + Type + Cont, 
                              weights = Freq,
                              data = housing, 
                              dispersion = "Afroz")
summary(house.mblogit.odsp)
dispersion(house.mblogit.odsp, method = "Deviance")

# Note that aggregation (either implicitly or explicitly required) affects
# the reported deviance in surprising ways:
house.mblogit.o.00 <- mblogit(Sat ~ Infl, 
                              weights = Freq,
                              data = housing, 
                              dispersion = TRUE)
deviance(house.mblogit.o.00)
dispersion(house.mblogit.o.00)
# The deviance is (almost) zero, because aggregation leads to a two-way
# table and a single-predictor model is already saturated.

# In order to make models comparable, one will need to set the groups:
house.mblogit.o.0 <- mblogit(Sat ~ Infl, 
                             weights = Freq,
                             data = housing, 
                             groups = ~ Infl + Type + Cont,
                             dispersion = TRUE)
deviance(house.mblogit.o.0)
dispersion(house.mblogit.o.0)

anova(house.mblogit.o.0,
      house.mblogit.odsp)

# These complications with the deviances do not arise if no aggregation is 
# requested:
house.mblogit.0 <- mblogit(Sat ~ Infl, 
                           weights = Freq,
                           data = housing)
anova(house.mblogit.0,
      house.mblogit)


# Using frequences on the left-hand side is perhaps the safest option:
housing.wide <- memisc::Aggregate(table(Sat) ~ Infl + Type + Cont,
                                  data = housing) # Note that 'Aggegate' uses
                                                # variable 'Freq' for weighting.
house.mblogit.wide <- mblogit(cbind(Low,Medium,High) ~ Infl + Type + Cont, 
                              data = housing.wide)
summary(house.mblogit.wide)
dispersion(house.mblogit.wide, method = "Afroz")

house.mblogit.wide.0 <- mblogit(cbind(Low,Medium,High) ~ Infl, 
                                data = housing.wide)
summary(house.mblogit.wide.0)
dispersion(house.mblogit.wide.0, method="Afroz")

anova(house.mblogit.wide.0,
      house.mblogit.wide)