ex1.sim{bivpois} |
R Documentation |
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
data(ex1.sim)
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 |
This data is used as
example one in Karlis and Ntzoufras (2004).
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.
pbivpois
, simple.bp
, lm.bp
, lm.dibp , ex2.sim , ex3.health , ex4.ita91 .
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