| wald.test {ZIGP} | R Documentation |
'wald.test' is used to fit ZIGP(mu(i), phi(i), omega(i)) - Regression Models.
wald.test(Yin, Xin, Win=NULL, Zin=NULL, Offset = rep(1, length(Yin)), init = T)
Yin |
response vector of length n. |
Xin |
design matrix of dim (n x p) for mean modelling. |
Win |
design matrix of dim (n x r) for overdispersion modelling. |
Zin |
design matrix of dim (n x q) for zero inflation modelling. |
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'. |
In order to include an intercept in a design matrix, one has to add a vector of ones to the design matrix: 'Intercept <- rep(1,n)'. Overall overdispersion and/or zero-inflation can be modelled using an Intercept design. Setting W to NULL corresponds to modelling a ZIP model. Setting Z to NULL corresponds to modelling a GP model. Setting W and Z to NULL corresponds to modelling a Poisson GLM.
If the output should have variable names additionally to parameter tokens (such as 'b0', 'a0' or 'g0'), create the design matrix by 'W <- cbind(Intercept, gender, height)'.
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.
# 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)
Intercept <- rep(1,length(damage))
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)
brand2 <- ifelse(brand==2,1,0)
brand3 <- ifelse(brand==3,1,0)
# 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
X <- cbind(Intercept, drivers.age)
W <- cbind(brand2,brand3)
Z <- cbind(abroad) # so name will be printed
wald.test(Yin=Y, Xin=X, Win=W, Zin=Z, Offset = insurance.year, init = FALSE)
#1 Estimate Std. Error z value Pr(>|z|)
#2 MU REGRESSION
#3 b0 Intercept 1.47148 1.07377 1.37038 0.17057
#4 b1 drivers.age -0.05075 0.03907 -1.29897 0.19395
#5 PHI REGRESSION
#6 a0 brand2 -8.64637 2132.15915 -0.00406 0.99676
#7 a1 brand3 0.17339 1.50296 0.11536 0.90816
#8 OMEGA REGRESSION
#9 g0 abroad -1.10339 2.46771 -0.44713 0.65478
#10
#
#11 Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
#12 Iterations 43
#13 Log Likelihood -23.4
#14 Pearson Chi Squared 15.1
#15 AIC 57
#16 Range Mu 0.23 2.45
#17 Range Phi 1.00 2.19
#18 Range Omega 0.25 0.50
# approximate equivalence of Poisson-glm and ZIGP-package results
# glm uses IWLS, ZIGP uses numerical maximization of the log-likelihood
# (time series character of the data is neglected)
data(Seatbelts)
DriversKilled <- as.vector(Seatbelts[,1]) # will be response
kms <- as.vector(Seatbelts[,5]) # will be exposure
PetrolPrice <- as.vector(Seatbelts[,6]) # will be covariate 1
law <- as.vector(Seatbelts[,8]) # will be covariate 2
fmla <- DriversKilled ~ PetrolPrice + law
out.glm <- glm(fmla, family=poisson, offset=log(kms))
summary(out.glm)
X <- cbind(rep(1,length(DriversKilled)),PetrolPrice,law)
wald.test(DriversKilled, X, NULL, NULL, Offset = kms)
# GP with constant overdispersion
X <- cbind(rep(1,length(DriversKilled)),PetrolPrice,law)
W <- rep(1,length(DriversKilled))
wald.test(DriversKilled, X, W, NULL, Offset = kms)
# ZIGP with constant overdispersion and constant zero-inflation
X <- cbind(rep(1,length(DriversKilled)),PetrolPrice,law)
W <- rep(1,length(DriversKilled))
Z <- cbind(rep(1,length(DriversKilled)))
wald.test(DriversKilled, X, W, Z, Offset = kms)
# no significant zero-inflation according to the Wald test