ex4.ita91{bivpois} |
R Documentation |
Italian Serie A
football scores for season 1991-92.
data(ex4.ita91)
Dataframe with four variables
of length 306.
No |
Name |
Description |
1 |
g1 |
Goals scored by the home team |
2 |
g1 |
Goals scored by the away team |
3 |
team1 |
Categorical variable indicating the home team. (1): Ascoli, (2):Atalanta, (3):Bari, (4):Cagliari, (5):Cremonese,
(6):Fiorentina, (7):Foggia, (8):Genoa, (9):Inter, (10):Juventus, (11):Lazio,
(12):Milan, (13):Napoli, (14):Parma, (15): Roma, (16):Sampdoria, (17):Torino,
(18):Verona |
4 |
team2 |
Categorical variable indicating the away team. Level codes are defined
as in team1. |
Data were originally
used in Karlis and Ntzoufras (2003). The data consist of pairs of counts indicating
the number of goals scored by each of the two competing teams. As covariates we
have used dummy variables to model the team strength. In modelling outcomes of
football games, it has been observed an excess of draws and small
over-dispersion. Introducing diagonal inflated models we correct for both the
over-dispersion and the excess of draws.
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 , ex1.sim , ex2.sim , ex3health .
library(bivpois) # loading of bivpois library
data(ex4.ita91) # loading ex4.ita91 data from bivpois library
#
# formula for modeling of lambda1 and lambda2
form1 <- y1y2~noncommon+c(team1,team2)+c(team2,team1)
#
# Model 1: Double Poisson
ex4.m1<-lm.bp( 'g1', 'g2', form1, zeroL3=T, data=ex4.ita91)
#
# Models 2-5: bivariate Poisson models
ex4.m2<-lm.bp('g1','g2', form1, data=ex4.ita91)
ex4.m3<-lm.bp('g1','g2', form1, y3~team1, data=ex4.ita91)
ex4.m4<-lm.bp('g1','g2', form1, y3~team2, data=ex4.ita91)
ex4.m5<-lm.bp('g1','g2', form1, y3~team1+team2, data=ex4.ita91)
#
# Model 6: Zero Inflated Model
ex4.m6 <-lm.dibp('g1','g2', form1, data=ex4.ita91, jmax=0)
#
# Models 7-11: Diagonal Inflated Bivariate Poisson Models
ex4.m7 <-lm.dibp('g1','g2',form1, data=ex4.ita91, distribution='geometric' )
ex4.m8 <-lm.dibp('g1','g2', form1, data=ex4.ita91, jmax=1)
ex4.m9 <-lm.dibp('g1','g2', form1, data=ex4.ita91, jmax=2)
ex4.m10<-lm.dibp('g1','g2', form1, data=ex4.ita91, jmax=3)
ex4.m11<-lm.dibp('g1','g2', form1, data=ex4.ita91, distribution='poisson' )
#
# Models 12: Diagonal Inflated Double Poisson Model
ex4.m12 <- lm.dibp( 'g1', 'g2', form1, data=ex4.ita91, distribution='poisson', zeroL3=T )
# --------------------------------------------------------------------------
# monitoring parameters for model 8: Biv Poisson with Dis(1) diagonal distribution
#
#
ex4.m8$diagonal.distribution # printing details for the diagonal distribution
round(ex4.m8$beta1,2) # model parameters for lambda1
round(ex4.m8$beta2[1],2) # Intercept for lambda2.
round(ex4.m8$beta2[1]-ex4.m8$beta2[2],2)# estimated home effect
#
# estimating the effect for 18th level of attack (team1.team2) [Verona]
round(-sum(ex4.m8$beta[ 2:18]),2)
# estimating the effect for 18th level of defence(team2.team1) [Verona]
round(-sum(ex4.m8$beta[19:35]),2)
#
ex4.m8$beta3 # parameters for lambda3 (here the intercept)
exp(ex4.m8$beta3) # lambda3 (here constant)
ex4.m8$p # mixing proportion
ex4.m8$theta # printing theta parameters