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# nbinomial.r msme package
# Joseph M Hilbe and Andrew P Robinson
# Methods of Statistical Model Estimation
# Chapman & Hall/CRC 2013
# Examples of use for the nbinomial.r function for maximum likelihood
# NB2 and heterogeneous NB2 regression. The default "family" is
# "nb2", which estimates parameters and the dispersion parameter using
# a direct relationship between the dispersion and Poisson variance.
# The default NB variance is mu + alpha*mu^2. Use the "negBinomial" family
# to produce the inverted dispersion, which is given by R's glm.nb function
library(msme)
# library(msme, lib.loc="lib")
data(medpar)
# TRADITIONAL NB REGRESSION WITH ALPHA
mynb1 <- nbinomial(los ~ hmo + white, data=medpar)
summary(mynb1)
# DISPERSION STATISTIC A
mynb1$dispersion
# INCIDENCE RATE RATIOS
exp(mynb1$coefficients)
# IRR SEs USING DELTA METHOD
exp(mynb1$coefficients)*mynb1$se.beta.hat
#IRR CONFIDENCE INTERVALS
mynb1$coefficients - 1.96*mynb1$se.beta.hat
mynb1$coefficients + 1.96*mynb1$se.beta.hat
# TRADITIONAL NB -- SUMMARY INCLUDED IN FUNCTION CALL
summary(mynb1_5 <- nbinomial(los ~ hmo + white, data=medpar))
# TRADITIONAL NB -- SHOWING ALL OPTIONS
mynb2 <- nbinomial(los ~ hmo + white,
formula2 = ~ 1,
data = medpar,
family = "nb2",
mean.link = "log",
scale.link = "inverse_s")
summary(mynb2)
# R GLM.NB - LIKE INVERTED DISPERSION BASED M
mynb3 <- nbinomial(los ~ hmo + white,
formula2 = ~ 1,
data = medpar,
family = "negBinomial",
mean.link = "log",
scale.link = "inverse_s")
summary(mynb3)
# R GLM.NB-TYPE INVERTED DISPERSON --THETA ; WITH DEFAULTS
mynb4 <- nbinomial(los ~ hmo + white, family="negBinomial", data =medpar)
summary(mynb4)
# HETEROGENEOUS NB; DISPERSION PARAMETERIZED
mynb5 <- nbinomial(los ~ hmo + white,
formula2 = ~ hmo + white,
data = medpar,
family = "negBinomial",
mean.link = "log",
scale.link = "log_s")
summary(mynb5)
# SAVED STATISTICS FROM NBINOMIAL2.R
# USE OF "nbh" for glm.nb-like dipersion
# nbinomial now has "negBinomial" as the family for glm.nb
# TRADITIONAL NB2 REGRESSION. USING DEFAULT OPTIONS
tnb1 <- nbinomial(los ~ hmo + white, data=medpar)
summary(tnb1)
# TRADITIONAL NB2 REGRESSION. PROVIDING EXPLICIT OPTIONS
tnb2 <- nbinomial(los ~ hmo + white,
formula2 = ~ 1,
data = medpar,
family = "nb2",
mean.link = "log",
scale.link = "inverse_s")
summary(tnb2)
# PEARSON CHI2 STATISTIC
tnb1$pearson
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