ex2.sim {bivpois}R Documentation

Bivpois Example 2 Dataset: Simulated Data

Description

The data has one pair $(x,y)$ of diagonal inflated bivariate Poisson variables and five variables $(z_1,...,z_5)$ generated from $N(0, 0.12)$ distribution. Hence

hspace{1cm} $X_i, Y_i sim DIBP( λ_{1i}, λ_{2i}, λ_{3i} , p=0.30, Poisson(2) ) $ with

hspace{2cm} $logλ_{1i} = 1.8 + 2 Z_{1i} + 3 Z_{3i}$

hspace{2cm} $logλ_{2i} = 0.7 - Z_{1i} - 3 Z_{3i} + 3 Z_{5i}$

hspace{2cm} $logλ_{3i} = 1.7 + Z_{1i} - 2 Z_{2i} + 2 Z_{3i} - 2 Z_{4i}.$

Usage

data(ex2.sim)

Format

A data frame with 100 observations on the following 7 variables.

x,y
Simulated Bivariate Poisson Variables used as response
z1,z2,z3,z4,z5
Simulated N(0,0.01) explanatory variables

Details

This data is used as example one in Karlis and Ntzoufras (2004).

Source

1. Karlis, D. and Ntzoufras, I. (2005). Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R. Journal of Statistical Software (to appear).

References

Karlis, D. and Ntzoufras, I. (2003). Analysis of Sports Data Using Bivariate Poisson Models. Journal of the Royal Statistical Society, D, (Statistician), 52, 381 - 393.

Examples

#  Models of example 2 can be fitted using the command
#  demo(ex2, package='bivpois')
#
#  Here we present the same commands but iterations of the EM were restricted to 2 to save time

library(bivpois) # load bivpois library
data(ex2.sim)    # load ex2.sim data from bivpois library
#
# Model 1: BivPois
ex2.m1<-lm.bp( x~z1 , y~z1+z5, l1l2=~z3, l3=~.-z5, data=ex2.sim, maxit=2 )
# Model 2: Zero Inflated BivPois 
ex2.m2<-lm.dibp( x~z1 , y~z1+z5, l1l2=~z3, l3=~.-z5, data=ex2.sim , jmax=0, maxit=2 )
# Model 3: Diagonal Inflated BivPois with DISCRETE(1) diagonal  distribution
ex2.m3<-lm.dibp( x~z1 , y~z1+z5, l1l2=~z3, l3=~.-z5, data=ex2.sim , jmax=1, maxit=2 )
# Model 4: Diagonal Inflated BivPois with DISCRETE(2) diagonal  distribution
ex2.m4<-lm.dibp( x~z1 , y~z1+z5, l1l2=~z3, l3=~.-z5, data=ex2.sim , jmax=2, maxit=2 )
# Model 5: Diagonal Inflated BivPois with DISCRETE(3) diagonal  distribution
ex2.m5<-lm.dibp( x~z1 , y~z1+z5, l1l2=~z3, l3=~.-z5, data=ex2.sim , jmax=3, maxit=2 )
# Model 6: Diagonal Inflated BivPois with DISCRETE(4) diagonal  distribution
ex2.m6<-lm.dibp( x~z1 , y~z1+z5, l1l2=~z3, l3=~.-z5, data=ex2.sim , jmax=4, maxit=2 )
# Model 7: Diagonal Inflated BivPois with DISCRETE(5) diagonal  distribution
ex2.m7<-lm.dibp( x~z1 , y~z1+z5, l1l2=~z3, l3=~.-z5, data=ex2.sim , jmax=5, maxit=2 )
# Model 8: Diagonal Inflated BivPois with DISCRETE(6) diagonal  distribution
ex2.m8<-lm.dibp( x~z1 , y~z1+z5, l1l2=~z3, l3=~.-z5, data=ex2.sim , jmax=6, maxit=2 )
# Model 9: Diagonal Inflated BivPois with POISSON diagonal distribution
ex2.m9<-lm.dibp( x~z1 , y~z1+z5, l1l2=~z3, l3=~.-z5, data=ex2.sim , 
                 distribution="poisson", maxit=2 )
# Model 10: Diagonal Inflated BivPois with GEOMETRIC diagonal distribution
ex2.m10<-lm.dibp( x~z1 , y~z1+z5, l1l2=~z3, l3=~.-z5, data=ex2.sim , 
                  distribution="geometric", maxit=2 )
#
# printing parameters of model 7
ex2.m7$beta1
ex2.m7$beta2
ex2.m7$beta3
ex2.m7$p
ex2.m7$theta
#
# printing parameters of model 9
ex2.m9$beta1
ex2.m9$beta2
ex2.m9$beta3
ex2.m9$p
ex2.m9$theta

[Package bivpois version 0.50-3 Index]