# ztp.glm: GLM for a zero truncated Poisson variable In CopulaRegression: Bivariate Copula Based Regression Models

## Description

Zero truncated generalized linear model.

## Usage

 1 ztp.glm(y, S, exposure = rep(1, length(y)),sd.error=FALSE) 

## Arguments

 y vector of response values S design matrix exposure exposure time for the zero-truncated Poisson model, all entries of the vector have to be >0. Default is a constant vector of 1. sd.error logical. Should the standard errors of the regression coefficients be returned? Default is FALSE.

## Details

We consider positive count variables Y_i. We model Y_i in terms of a covariate vector s_i. The generalized linear model is specified via

Y_i\sim ZTP(λ_{i})

with \ln(λ_{i})=\ln(e_i)+{s_i}^\top β. Here e_i denotes the exposure time.

## Value

 coefficients estimated regression coefficients sd estimated standard error, if sd.error=TRUE

## Author(s)

Nicole Kraemer

mle_marginal, mle_joint
  1 2 3 4 5 6 7 8 9 10 11 12 13 n<-200 # number of examples R<-S<-cbind(rep(1,n),rnorm(n)) # design matrices with intercept alpha<-beta<-c(1,-1) # regression coefficients exposure<-rep(1,n) # constant exposure delta<-0.5 # dispersion parameter tau<-0.3 # Kendall's tau family=3 # Clayton copula # simulate data my.data<-simulate_regression_data(n,alpha,beta,R,S,delta,tau,family,TRUE,exposure) x<-my.data[,1] y<-my.data[,2] # fit marginal ZTP-model with standard errors my.model<-ztp.glm(y,S,exposure=exposure,TRUE)