ex1.sim{bivpois}

R Documentation

Bivpois Example 1 Dataset: Simulated Data

Description

The data has one pair (x,y) of bivariate Poisson variables and five variables (z1,…,z5) generated from  N(0, 0.12) distribution. Hence

Xi, Yi ~ BP( λ1i, λ2i, λ3i  )

logλ1i = 1.8 + 2 Z1i + 3 Z3i

logλ2i = 0.7 – Z1i – 3 Z3i + 3 Z5i

logλ3i = 1.7 + Z1i – 2 Z2i + 2 Z3i – 2 Z4i

Usage

data(ex1.sim)

Format

Dataframe with seven variables of length 100.

No

Name

Description

1

x,y

Simulated Bivariate Poisson Variables used as response

2

z1, z2, z3, z4, z5

Simulated N(0,0.12) Explanatory variables used as response

Details

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

 

References

1.      Karlis, D. and Ntzoufras, I. (2004). Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in S. (submitted). Technical Report, Athens University of Economics and Business, Athens, Greece.

2.      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.

See Also

pbivpois,  simple.bp , lm.bp, lm.dibp , ex2.sim , ex3.health , ex4.ita91 .

Examples

library(bivpois)       # load bivpois library
data(ex1.sim)          # load data of example 1
# -------------------------------------------------------------------------------
# Simple Bivariate Poisson Model
ex1.simple<-simple.bp( ex1.sim$x, ex1.sim$y ) # fit simple model of section 4.1.1
names(ex1.simple)      # monitor output variables
ex1.simple$lambda      # view lambda1 
ex1.simple$BIC         # view BIC
ex1.simple             # view all results of the model
#
# plot of loglikelihood vs. iterations
win.graph()
plot( 1:ex1.simple$iterations, ex1.simple$loglikelihood, xlab='Iterations',
ylab='Log-likelihood', type='l' )
 
# -------------------------------------------------------------------------------
# Fit Double and Bivariate Poisson models ()
#
# Model 2: DblPoisson(l1, l2)
ex1.m2<-lm.bp('x','y', y1y2~noncommon, data=ex1.sim, zeroL3=T ) 
# Model 3: BivPoisson(l1, l2, l3); same as simple.bp(ex1.sim$x, ex1.sim$y)
ex1.m3<-lm.bp('x','y', y1y2~noncommon, data=ex1.sim )           
# Model 4: DblPoisson (l1=Full, l2=Full) 
ex1.m4<-lm.bp('x','y', y1y2~., data=ex1.sim, zeroL3=T )
# Model 5: BivPoisson(l1=full, l2=full, l3=constant)
ex1.m5<-lm.bp('x','y', y1y2~., data=ex1.sim)
# Model 6: DblPois(l1,l2)
ex1.m6<-lm.bp('x','y', y1y2~noncommon+z1:noncommon+z3+I(z5*l2), data=ex1.sim, zeroL3=T)
# Model 7: BivPois(l1,l2,l3=constant)
ex1.m7<-lm.bp('x','y', y1y2~noncommon+z1:noncommon+z3+I(z5*l2), data=ex1.sim)          
# Model 8: BivPoisson(l1=full, l2=full, l3=full)
ex1.m8<-lm.bp('x','y', y1y2~., y3~., data=ex1.sim)                                         
# Model 9: BivPoisson(l1=full, l2=full, l3=z1+z2+z3+z4)
ex1.m9<-lm.bp('x','y', y1y2~., y3~z1+z2+z3+z4, data=ex1.sim)                          
# Model 10: BivPoisson(l1, l2, l3=full)
ex1.m10<-lm.bp('x','y',y1y2~noncommon+z1:noncommon+z3+I(z5*l2), y3~., data=ex1.sim)   
# Model 11: BivPoisson(l1, l2, l3= z1+z2+z3+z4)
ex1.m11<-lm.bp('x','y',y1y2~noncommon+z1:noncommon+z3+I(z5*l2), y3~z1+z2+z3+z4, data=ex1.sim) 
#
ex1.m11$beta  # monitor all beta parameters of model 11
#
ex1.m11$beta1 # monitor all beta parameters of lambda1 of model 11
ex1.m11$beta2 # monitor all beta parameters of lambda2 of model 11
ex1.m11$beta3 # monitor all beta parameters of lambda3 of model 11
 

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