mle.zigp {ZIGP}R Documentation

Maximum Likelihood Estimates

Description

'mle.zigp' is used to calculate the MLEs of the regression parameters for mean, overdispersion and zero-inflation.

Usage

mle.zigp(Yin, fm.X, fm.W=NULL, fm.Z=NULL, 
         Offset = rep(1, length(Yin)),init = TRUE)

Arguments

Yin response vector of length n.
fm.X formula for mean design.
fm.W formula for overdispersion design (optional).
fm.Z formula for zero inflation design (optional).
Offset exposure for individual observation lengths. Defaults to a vector of 1. The offset MUST NOT be in 'log' scale.
init a logical value indicating whether initial optimization values for dispersion are set to -2.5 and values for zero inflation regression parameters are set to -1 (init = F) or are estimated by a ZIGP(mu(i), phi, omega)-model (init = T). Defaults to 'T'.

Details

Constant overdispersion and/or zero-inflation can be modelled using an Intercept design on the corresponding level. Setting fm.W to NULL corresponds to modelling a ZIP model. Setting fm.Z to NULL corresponds to modelling a GP model. Setting fm.W and fm.Z to NULL corresponds to modelling a Poisson GLM.

For numerical stability it may be very useful to center and standardize all non-categorical covariates, i.e. use 'x <- (x-mean(x))/sd(x)'.

References

Czado, C., Erhardt, V., Min, A., Wagner, S. (2007) Zero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent outsourcing rates. Statistical Modelling 7 (2), 125-153.

Examples

# Number of damages in car insurance.
# (not a good fit, just to illustrate how the software is used)
     
damage <- c(0,1,0,0,0,4,2,0,1,0,1,1,0,2,0,0,1,0,0,1,0,0,0)
insurance.year <- c(1,1.2,0.8,1,2,1,1.1,1,1,1.1,1.2,1.3,0.9,1.4,1,1,1,
1.2,1,1,1,1,1)
drivers.age <- c(25,19,30,48,30,18,19,29,24,54,56,20,38,18,23,58,
47,36,25,28,38,39,42)
# for overdispersion: car brand dummy in {1,2,3}, brand = 1 is reference
brand <- c(1,2,1,3,3,2,2,1,1,3,2,2,1,3,1,3,2,2,1,1,3,3,2)
# abroad: driver has been abroad for longer time (=1)
abroad <- c(0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,1,1,1,1)
Y <- damage
fm.X <- ~ drivers.age
fm.W <- ~ 0 + factor(brand)
fm.Z <- ~ abroad

mle.zigp(Yin=Y, fm.X=fm.X, fm.W=fm.W, fm.Z=fm.Z, Offset = insurance.year, 
         init = FALSE)


[Package ZIGP version 3.3 Index]