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, 0.01) distribution. Hence Xi, Yi ~ BP( lambda_1i, lambda_2i, lambda_3i ) log(lambda_1i) = 1.8 + 2 Z1i + 3 Z3i log(lambda_2i) = 0.7 – Z1i – 3 Z3i + 3 Z5i log(lambda_3i) = 1.7 + Z1i – 2 Z2i + 2 Z3i – 2 Z4i
data(ex1.sim)
A data frame with 100 observations on the following 7 variables.
This data is used as example one in Karlis and Ntzoufras (2004).
Karlis, D. and Ntzoufras, I. (2004). Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in S. (submitted). Technical Report, Department of Statistics, Athens University of Economics and Business, Athens, Greece.
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.
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=TRUE ) # 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=TRUE ) # 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=TRUE) # 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