ordBTL: ordinal Bradley-Terry-Luce model (ordBTL)
In ordBTL: Modelling comparison data with ordinal response
Description
Usage
Arguments
Value
Author(s)
References
See Also
Examples
Description
Fits ordinal regression models to paired comparison data.
Usage
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2
Arguments
formula
a formula describing the model to be fitted.
data
a data frame containing the design matrix for the model
(See also design to generate such an design matrix).
family
a character specifying which ordinal BTL model should be fitted.
Can be either "cumulative" for the cumulative link model or "acat" for the adjacent categories model.
family.control
a list with arguments passed to the corresponding family,
either cumulative for the cumulative link model or acat for the adjacent categories model.
restrict
(optional) a character vector specifying the covariates from formula that should be fitted with a symmetry constraint (can be used to fit threshold covariates).
...
further arguments for fitting function (see vglm).
Value
An object of class vglm.
Author(s)
Giuseppe Casalicchio
References
Dittrich R, Hatzinger R and Katzenbeisser W (2001).
"Corrigendum: Modelling the effect of subject-specific covariates
in paired comparison studies with an application to university rankings."
Journal of the Royal Statistical Society: Series C (Applied Statistics),
*50*(2), pp. 247-249.
Agresti A (1992). "Analysis of ordinal paired comparison data."
Applied Statistics, pp. 287-297. Table 1.
See Also
Examples
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############################################################
## ##
## Example 1: Adjacent categories logit model for CEMS ##
## ##
############################################################
############################################################
# Reproduce results from Table 3 of Dittrich et al. (2001)
############################################################
# Get the CEMS data and generate design matrix
example(wide2long, package="ordBTL", echo=FALSE)
des1 <- design(CEMSlong, var1="object1", var2="object2",
use.vars="Y", reference="Stockholm")
# Fit the adjacent categories model, which corresponds to
# the log-linear BTL model (see Agresti, 1992)
mod1 <- ordBTL(Y~., data=des1, family="acat",
family.control=list(reverse=TRUE))
# We get the same results from Table 3 of Dittrich et al (2001).
# Since Stockholm is the reference university, its estimate
# is set to zero (due to identifiability)
getRank(mod1)
############################################################
# Reproduce results from Table 6 of Dittrich et al. (2001)
############################################################
# Generate design matrix and specify model formula
des2 <- design(CEMSlong, var1="object1", var2="object2",
use.vars="ALL", reference="Stockholm")
form2 <- Y~GAMMA.London + GAMMA.Paris + GAMMA.Milano +
GAMMA.StGallen + GAMMA.Barcelona + WOR +
SEX + WOR:GAMMA.Paris + WOR:GAMMA.Milano +
WOR:GAMMA.Barcelona + DEG:GAMMA.StGallen +
STUD:GAMMA.Paris + STUD:GAMMA.StGallen +
ENG:GAMMA.StGallen + FRA:GAMMA.London +
FRA:GAMMA.Paris + SPA:GAMMA.Barcelona +
ITA:GAMMA.London + ITA:GAMMA.Milano +
SEX:GAMMA.Milano
# Fit the adjacent categories model with symmetric
# constraint for covariable WOR and SEX
mod2 <- ordBTL(form2, data=des2, family="acat",
family.control=list(reverse=TRUE),
restrict=c("WOR", "SEX"))
# We get the same results from Table 6 of Dittrich et al. (2001)
getRank(mod2)
# Notice that the change in sign for (Intercept), WOR and SEX
# is because we use here a different "coding".
############################################################
## ##
## Example 2: Fitting models from Agresti (1992) ##
## ##
############################################################
# Data from Table 1 of Agresti (1992)
data(ribbon)
# design matrix
des3 <- design(ribbon, var1="obj1", var2="obj2", use.vars="ALL")
# Note that Agresti (1992) used the constraint that the object
# parameters sum up to 1. To get the same results, we use the model
form3 <- cbind(V1,V2,V3,V4,V5,V6,V7)~I(GAMMA.1-GAMMA.5)+
I(GAMMA.2-GAMMA.5)+I(GAMMA.3-GAMMA.5)+I(GAMMA.4-GAMMA.5)
# Fit the adjacent categories logit model
ac <- ordBTL(form3, data=des3, family="acat",
family.control=list(reverse=TRUE))
# Fit the cumulative logit model
clm.logit <- ordBTL(form3, data=des3)
# Fit the cumulative probit model
clm.probit <- ordBTL(form3, data=des3,
family.control=list(link="probit"))
# Parameter estimates
coefs <- t(rbind("Adjacent categories logit"=coefficients(ac),
"Cumulative probit"=coefficients(clm.probit),
"Cumulative logit"=coefficients(clm.logit)))
coefs <- rbind(coefs, "GAMMA.5"=0-colSums(coefs[4:7,]))
coefs
############################################################
## ##
## Example 3: Fitting models for Bundesliga 2005/2006 ##
## ##
############################################################
# real ranking can be obtained from:
# http://fussballdaten.sport.de/bundesliga/2006
# load data
example(design, package="ordBTL", echo=FALSE)
# Model without home advantage
des.nohome <- design(buli0506, var1="Heim", var2="Gast",
use.vars="Y3", home.advantage="no",
reference="GAMMA.MSV.Duisburg")
mod.nohome <- ordBTL(Y3~., data=des.nohome)
# team 'abilities' (should be approximately the ranking of the final standings)
getRank(mod.nohome, prefix="GAMMA", reference="GAMMA.MSV.Duisburg")
# Model with home advantage
des.onehome <- design(buli0506, var1="Heim", var2="Gast",
use.vars="Y3", home.advantage="yes",
reference="GAMMA.MSV.Duisburg")
mod.onehome <- ordBTL(Y3~., data=des.onehome)
# team 'abilities'
getRank(mod.onehome, prefix="GAMMA", reference="GAMMA.MSV.Duisburg")
# home advantage
getRank(mod.onehome, prefix="ALPHA")
# Model with team-specific home advantage
des.teamhome <- design(buli0506, var1="Heim", var2="Gast",
use.vars="Y3", home.advantage="specific",
reference="GAMMA.MSV.Duisburg")
mod.teamhome <- ordBTL(Y3~., data=des.teamhome)
# team 'abilities' (should be approximately the ranking for the away table)
getRank(mod.teamhome, prefix="GAMMA", reference="GAMMA.MSV.Duisburg")
# team-specific home advantages
getRank(mod.teamhome, prefix="ALPHA")
Example output
Loading required package: caret
Loading required package: lattice
Loading required package: ggplot2
Loading required package: VGAM
Loading required package: stats4
Loading required package: splines
Attaching package: 'VGAM'
The following object is masked from 'package:caret':
predictors
Loading required package: wikibooks
Loading required package: gtools
Attaching package: 'gtools'
The following object is masked from 'package:VGAM':
logit
Warning messages:
1: In eval(slot(family, "initialize")) :
response should be ordinal---see ordered()
2: In vglm.fitter(x = x, y = y, w = w, offset = offset, Xm2 = Xm2, :
iterations terminated because half-step sizes are very small
3: In vglm.fitter(x = x, y = y, w = w, offset = offset, Xm2 = Xm2, :
some quantities such as z, residuals, SEs may be inaccurate due to convergence at a half-step
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.3171797 0.04850831 27.153690 2.290333e-162
GAMMA.London 0.9114010 0.04157245 21.923199 1.560935e-106
GAMMA.Paris 0.5162669 0.03878553 13.310814 2.002882e-40
GAMMA.Barcelona 0.3064662 0.03758382 8.154207 3.514783e-16
GAMMA.StGallen 0.2991610 0.03757425 7.961864 1.694665e-15
GAMMA.Milano 0.2209861 0.03800946 5.813975 6.100654e-09
Warning message:
In eval(slot(family, "initialize")) :
response should be ordinal---see ordered()
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.4101679 0.07407699 19.036517 8.499457e-81
GAMMA.London 1.2796797 0.09977634 12.825482 1.180494e-37
GAMMA.Milano 1.1237633 0.09498545 11.830900 2.702301e-32
GAMMA.Barcelona 1.0514442 0.09658294 10.886439 1.337696e-27
GAMMA.Paris:WOR 0.6942689 0.17117497 4.055902 4.994120e-05
GAMMA.Paris 0.6412652 0.05532038 11.591844 4.532696e-31
WOR 0.6406664 0.30350233 2.110911 3.477996e-02
GAMMA.Barcelona:WOR 0.5406832 0.15452633 3.498971 4.670571e-04
GAMMA.Milano:WOR 0.5345675 0.15466490 3.456295 5.476562e-04
GAMMA.Paris:STUD 0.4233486 0.06993863 6.053144 1.420454e-09
GAMMA.StGallen:DEG 0.2759380 0.06471569 4.263850 2.009341e-05
GAMMA.StGallen 0.2503909 0.05324186 4.702896 2.564968e-06
GAMMA.StGallen:ENG 0.1469205 0.06811840 2.156840 3.101814e-02
GAMMA.London:FRA -0.1564219 0.07123406 -2.195887 2.810006e-02
GAMMA.Milano:SEX -0.1841493 0.06439549 -2.859661 4.240935e-03
GAMMA.StGallen:STUD -0.1993143 0.06672730 -2.986997 2.817325e-03
GAMMA.London:ITA -0.2943846 0.09774864 -3.011649 2.598327e-03
SEX -0.3396928 0.09740395 -3.487464 4.876244e-04
GAMMA.Paris:FRA -0.7214285 0.06744770 -10.696116 1.061337e-26
GAMMA.Barcelona:SPA -0.8526536 0.09783728 -8.715018 2.907133e-18
GAMMA.Milano:ITA -0.9642430 0.09812584 -9.826596 8.649266e-23
Adjacent categories logit Cumulative probit
(Intercept):1 -0.85198602 -1.37896215
(Intercept):2 0.83260807 -0.48950762
(Intercept):3 -0.54437393 -0.21894776
I(GAMMA.1 - GAMMA.5) 0.04216091 0.05779022
I(GAMMA.2 - GAMMA.5) -0.05032611 -0.08807263
I(GAMMA.3 - GAMMA.5) 0.27003510 0.49396332
I(GAMMA.4 - GAMMA.5) -0.33952267 -0.60710964
GAMMA.5 0.07765277 0.14342873
Cumulative logit
(Intercept):1 -2.3998818
(Intercept):2 -0.8295968
(Intercept):3 -0.3711039
I(GAMMA.1 - GAMMA.5) 0.1168923
I(GAMMA.2 - GAMMA.5) -0.1960107
I(GAMMA.3 - GAMMA.5) 0.8873016
I(GAMMA.4 - GAMMA.5) -1.0476375
GAMMA.5 0.2394542
'data.frame': 306 obs. of 11 variables:
$ Saison : Factor w/ 44 levels "1963/1964","1964/1965",..: 43 43 43 43 43 43 43 43 43 43 ...
$ Spieltag : int 1 1 1 1 1 1 1 1 1 2 ...
$ Datum : Date, format: "2005-08-05" "2005-08-06" ...
$ Anpfiff : Factor w/ 31 levels "14:00","14:15",..: 28 6 6 6 6 6 6 15 15 6 ...
$ Heim : Factor w/ 50 levels "1. FC Kaiserslautern",..: 18 2 31 24 49 40 25 20 16 8 ...
$ Gast : Factor w/ 50 levels "1. FC Kaiserslautern",..: 11 5 47 3 10 7 27 1 8 18 ...
$ Tore.Heim : int 3 1 1 3 2 5 2 2 1 2 ...
$ Tore.Gast : int 0 0 1 0 2 2 2 1 4 5 ...
$ Tore.Heim.Halbzeit: int 1 0 1 2 1 3 0 0 1 1 ...
$ Tore.Gast.Halbzeit: int 0 0 1 0 0 2 0 1 1 3 ...
$ Y3 : Ord.factor w/ 3 levels "1"<"2"<"3": 1 1 2 1 2 1 2 1 3 3 ...
'data.frame': 306 obs. of 18 variables:
$ GAMMA.1.FC.Kaiserslautern : num 0 0 0 0 0 0 0 -1 0 0 ...
$ GAMMA.1.FC.Koeln : num 0 1 0 0 0 0 0 0 0 0 ...
$ GAMMA.1.FC.Nuernberg : num 0 0 0 -1 0 0 0 0 0 0 ...
$ GAMMA.1.FSV.Mainz.05 : num 0 -1 0 0 0 0 0 0 0 0 ...
$ GAMMA.Arminia.Bielefeld : num 0 0 0 0 0 -1 0 0 0 0 ...
$ GAMMA.Bayer.Leverkusen : num 0 0 0 0 0 0 0 0 -1 1 ...
$ GAMMA.Borussia.Dortmund : num 0 0 0 0 -1 0 0 0 0 0 ...
$ GAMMA.Borussia.Moenchengladbach: num -1 0 0 0 0 0 0 0 0 0 ...
$ GAMMA.Eintracht.Frankfurt : num 0 0 0 0 0 0 0 0 1 0 ...
$ GAMMA.FC.Bayern.Muenchen : num 1 0 0 0 0 0 0 0 0 -1 ...
$ GAMMA.FC.Schalke.04 : num 0 0 0 0 0 0 0 1 0 0 ...
$ GAMMA.Hamburger.SV : num 0 0 0 1 0 0 0 0 0 0 ...
$ GAMMA.Hannover.96 : num 0 0 0 0 0 0 1 0 0 0 ...
$ GAMMA.Hertha.BSC.Berlin : num 0 0 0 0 0 0 -1 0 0 0 ...
$ GAMMA.MSV.Duisburg : num 0 0 1 0 0 0 0 0 0 0 ...
$ GAMMA.SV.Werder.Bremen : num 0 0 0 0 0 1 0 0 0 0 ...
$ GAMMA.VfB.Stuttgart : num 0 0 -1 0 0 0 0 0 0 0 ...
$ GAMMA.VfL.Wolfsburg : num 0 0 0 0 1 0 0 0 0 0 ...
'data.frame': 306 obs. of 19 variables:
$ GAMMA.1.FC.Kaiserslautern : num 0 0 0 0 0 0 0 -1 0 0 ...
$ GAMMA.1.FC.Koeln : num 0 1 0 0 0 0 0 0 0 0 ...
$ GAMMA.1.FC.Nuernberg : num 0 0 0 -1 0 0 0 0 0 0 ...
$ GAMMA.1.FSV.Mainz.05 : num 0 -1 0 0 0 0 0 0 0 0 ...
$ GAMMA.Arminia.Bielefeld : num 0 0 0 0 0 -1 0 0 0 0 ...
$ GAMMA.Bayer.Leverkusen : num 0 0 0 0 0 0 0 0 -1 1 ...
$ GAMMA.Borussia.Dortmund : num 0 0 0 0 -1 0 0 0 0 0 ...
$ GAMMA.Borussia.Moenchengladbach: num -1 0 0 0 0 0 0 0 0 0 ...
$ GAMMA.Eintracht.Frankfurt : num 0 0 0 0 0 0 0 0 1 0 ...
$ GAMMA.FC.Bayern.Muenchen : num 1 0 0 0 0 0 0 0 0 -1 ...
$ GAMMA.FC.Schalke.04 : num 0 0 0 0 0 0 0 1 0 0 ...
$ GAMMA.Hamburger.SV : num 0 0 0 1 0 0 0 0 0 0 ...
$ GAMMA.Hannover.96 : num 0 0 0 0 0 0 1 0 0 0 ...
$ GAMMA.Hertha.BSC.Berlin : num 0 0 0 0 0 0 -1 0 0 0 ...
$ GAMMA.MSV.Duisburg : num 0 0 1 0 0 0 0 0 0 0 ...
$ GAMMA.SV.Werder.Bremen : num 0 0 0 0 0 1 0 0 0 0 ...
$ GAMMA.VfB.Stuttgart : num 0 0 -1 0 0 0 0 0 0 0 ...
$ GAMMA.VfL.Wolfsburg : num 0 0 0 0 1 0 0 0 0 0 ...
$ ALPHA : num 1 1 1 1 1 1 1 1 1 1 ...
'data.frame': 306 obs. of 36 variables:
$ GAMMA.1.FC.Kaiserslautern : num 0 0 0 0 0 0 0 -1 0 0 ...
$ GAMMA.1.FC.Koeln : num 0 1 0 0 0 0 0 0 0 0 ...
$ GAMMA.1.FC.Nuernberg : num 0 0 0 -1 0 0 0 0 0 0 ...
$ GAMMA.1.FSV.Mainz.05 : num 0 -1 0 0 0 0 0 0 0 0 ...
$ GAMMA.Arminia.Bielefeld : num 0 0 0 0 0 -1 0 0 0 0 ...
$ GAMMA.Bayer.Leverkusen : num 0 0 0 0 0 0 0 0 -1 1 ...
$ GAMMA.Borussia.Dortmund : num 0 0 0 0 -1 0 0 0 0 0 ...
$ GAMMA.Borussia.Moenchengladbach: num -1 0 0 0 0 0 0 0 0 0 ...
$ GAMMA.Eintracht.Frankfurt : num 0 0 0 0 0 0 0 0 1 0 ...
$ GAMMA.FC.Bayern.Muenchen : num 1 0 0 0 0 0 0 0 0 -1 ...
$ GAMMA.FC.Schalke.04 : num 0 0 0 0 0 0 0 1 0 0 ...
$ GAMMA.Hamburger.SV : num 0 0 0 1 0 0 0 0 0 0 ...
$ GAMMA.Hannover.96 : num 0 0 0 0 0 0 1 0 0 0 ...
$ GAMMA.Hertha.BSC.Berlin : num 0 0 0 0 0 0 -1 0 0 0 ...
$ GAMMA.MSV.Duisburg : num 0 0 1 0 0 0 0 0 0 0 ...
$ GAMMA.SV.Werder.Bremen : num 0 0 0 0 0 1 0 0 0 0 ...
$ GAMMA.VfB.Stuttgart : num 0 0 -1 0 0 0 0 0 0 0 ...
$ GAMMA.VfL.Wolfsburg : num 0 0 0 0 1 0 0 0 0 0 ...
$ ALPHA.1.FC.Kaiserslautern : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.1.FC.Koeln : num 0 1 0 0 0 0 0 0 0 0 ...
$ ALPHA.1.FC.Nuernberg : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.1.FSV.Mainz.05 : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.Arminia.Bielefeld : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.Bayer.Leverkusen : num 0 0 0 0 0 0 0 0 0 1 ...
$ ALPHA.Borussia.Dortmund : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.Borussia.Moenchengladbach: num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.Eintracht.Frankfurt : num 0 0 0 0 0 0 0 0 1 0 ...
$ ALPHA.FC.Bayern.Muenchen : num 1 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.FC.Schalke.04 : num 0 0 0 0 0 0 0 1 0 0 ...
$ ALPHA.Hamburger.SV : num 0 0 0 1 0 0 0 0 0 0 ...
$ ALPHA.Hannover.96 : num 0 0 0 0 0 0 1 0 0 0 ...
$ ALPHA.Hertha.BSC.Berlin : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.MSV.Duisburg : num 0 0 1 0 0 0 0 0 0 0 ...
$ ALPHA.SV.Werder.Bremen : num 0 0 0 0 0 1 0 0 0 0 ...
$ ALPHA.VfB.Stuttgart : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.VfL.Wolfsburg : num 0 0 0 0 1 0 0 0 0 0 ...
'data.frame': 306 obs. of 19 variables:
$ GAMMA.1.FC.Kaiserslautern : num 0 0 0 0 0 0 0 -1 0 0 ...
$ GAMMA.1.FC.Koeln : num 0 1 0 0 0 0 0 0 0 0 ...
$ GAMMA.1.FC.Nuernberg : num 0 0 0 -1 0 0 0 0 0 0 ...
$ GAMMA.1.FSV.Mainz.05 : num 0 -1 0 0 0 0 0 0 0 0 ...
$ GAMMA.Arminia.Bielefeld : num 0 0 0 0 0 -1 0 0 0 0 ...
$ GAMMA.Bayer.Leverkusen : num 0 0 0 0 0 0 0 0 -1 1 ...
$ GAMMA.Borussia.Dortmund : num 0 0 0 0 -1 0 0 0 0 0 ...
$ GAMMA.Borussia.Moenchengladbach: num -1 0 0 0 0 0 0 0 0 0 ...
$ GAMMA.Eintracht.Frankfurt : num 0 0 0 0 0 0 0 0 1 0 ...
$ GAMMA.FC.Bayern.Muenchen : num 1 0 0 0 0 0 0 0 0 -1 ...
$ GAMMA.FC.Schalke.04 : num 0 0 0 0 0 0 0 1 0 0 ...
$ GAMMA.Hamburger.SV : num 0 0 0 1 0 0 0 0 0 0 ...
$ GAMMA.Hannover.96 : num 0 0 0 0 0 0 1 0 0 0 ...
$ GAMMA.Hertha.BSC.Berlin : num 0 0 0 0 0 0 -1 0 0 0 ...
$ GAMMA.MSV.Duisburg : num 0 0 1 0 0 0 0 0 0 0 ...
$ GAMMA.SV.Werder.Bremen : num 0 0 0 0 0 1 0 0 0 0 ...
$ GAMMA.VfB.Stuttgart : num 0 0 -1 0 0 0 0 0 0 0 ...
$ GAMMA.VfL.Wolfsburg : num 0 0 0 0 1 0 0 0 0 0 ...
$ Spieltag : int 1 1 1 1 1 1 1 1 1 2 ...
Estimate Std. Error z value Pr(>|z|)
GAMMA.FC.Bayern.Muenchen 2.15183470 0.4894014 4.3968712 1.098225e-05
GAMMA.SV.Werder.Bremen 1.97066756 0.4805982 4.1004475 4.123520e-05
GAMMA.Hamburger.SV 1.85128996 0.4755611 3.8928539 9.907181e-05
GAMMA.FC.Schalke.04 1.53694777 0.4650047 3.3052306 9.489829e-04
GAMMA.Bayer.Leverkusen 1.11218303 0.4562407 2.4377114 1.478057e-02
GAMMA.Hertha.BSC.Berlin 0.96890640 0.4545961 2.1313565 3.305978e-02
GAMMA.Borussia.Dortmund 0.88674951 0.4539380 1.9534594 5.076519e-02
GAMMA.VfB.Stuttgart 0.84283463 0.4536699 1.8578147 6.319534e-02
GAMMA.Borussia.Moenchengladbach 0.73609299 0.4532612 1.6239928 1.043773e-01
GAMMA.1.FC.Nuernberg 0.69608421 0.4531961 1.5359449 1.245519e-01
GAMMA.Hannover.96 0.67862317 0.4531825 1.4974611 1.342733e-01
GAMMA.1.FSV.Mainz.05 0.46470092 0.4537577 1.0241170 3.057800e-01
GAMMA.VfL.Wolfsburg 0.37696046 0.4543918 0.8295935 4.067687e-01
GAMMA.Eintracht.Frankfurt 0.33368265 0.4547928 0.7337027 4.631300e-01
GAMMA.Arminia.Bielefeld 0.29518165 0.4551965 0.6484708 5.166805e-01
GAMMA.1.FC.Kaiserslautern 0.17249245 0.4567996 0.3776108 7.057198e-01
GAMMA.1.FC.Koeln 0.06391278 0.4586289 0.1393562 8.891687e-01
GAMMA.MSV.Duisburg 0.00000000 NA NA 0.000000e+00
Warning message:
In rbind(coefs, c(0, NA, NA)) :
number of columns of result is not a multiple of vector length (arg 2)
Estimate Std. Error z value Pr(>|z|)
GAMMA.FC.Bayern.Muenchen 2.3235491 0.5014555 4.6336096 3.593443e-06
GAMMA.SV.Werder.Bremen 2.0997972 0.4905261 4.2807044 1.863027e-05
GAMMA.Hamburger.SV 2.0047016 0.4864772 4.1208543 3.774701e-05
GAMMA.FC.Schalke.04 1.6475512 0.4741837 3.4745000 5.118064e-04
GAMMA.Bayer.Leverkusen 1.1758857 0.4642465 2.5328907 1.131262e-02
GAMMA.Hertha.BSC.Berlin 1.0625127 0.4628525 2.2955754 2.170017e-02
GAMMA.Borussia.Dortmund 0.9907894 0.4621643 2.1438033 3.204865e-02
GAMMA.VfB.Stuttgart 0.9464535 0.4618139 2.0494261 4.042046e-02
GAMMA.1.FC.Nuernberg 0.8013961 0.4610664 1.7381360 8.218686e-02
GAMMA.Borussia.Moenchengladbach 0.7895854 0.4610324 1.7126460 8.677768e-02
GAMMA.Hannover.96 0.7479451 0.4609455 1.6226326 1.046680e-01
GAMMA.1.FSV.Mainz.05 0.5139848 0.4614065 1.1139522 2.652997e-01
GAMMA.Arminia.Bielefeld 0.3932144 0.4622875 0.8505840 3.950005e-01
GAMMA.VfL.Wolfsburg 0.3810249 0.4624011 0.8240139 4.099317e-01
GAMMA.Eintracht.Frankfurt 0.3726626 0.4624820 0.8057884 4.203649e-01
GAMMA.1.FC.Kaiserslautern 0.2277652 0.4642310 0.4906291 6.236888e-01
GAMMA.1.FC.Koeln 0.1154838 0.4660537 0.2477907 8.042964e-01
GAMMA.MSV.Duisburg 0.0000000 NA NA 0.000000e+00
Warning message:
In rbind(coefs, c(0, NA, NA)) :
number of columns of result is not a multiple of vector length (arg 2)
Estimate Std. Error z value Pr(>|z|)
ALPHA 0.4783205 0.1138493 4.201349 2.653296e-05
Estimate Std. Error z value Pr(>|z|)
GAMMA.Hamburger.SV 3.1099530 0.7517584 4.1369049 3.520219e-05
GAMMA.FC.Bayern.Muenchen 2.3908022 0.7174690 3.3322725 8.613985e-04
GAMMA.SV.Werder.Bremen 2.3366551 0.7170423 3.2587407 1.119079e-03
GAMMA.FC.Schalke.04 1.9493387 0.7098522 2.7461191 6.030487e-03
GAMMA.Bayer.Leverkusen 1.8480170 0.7092524 2.6055846 9.171763e-03
GAMMA.VfB.Stuttgart 1.6529623 0.7081540 2.3341849 1.958604e-02
GAMMA.Borussia.Dortmund 1.3997838 0.7083819 1.9760299 4.815139e-02
GAMMA.Hertha.BSC.Berlin 1.3556703 0.7085335 1.9133469 5.570366e-02
GAMMA.Hannover.96 1.3194838 0.7091386 1.8606853 6.278864e-02
GAMMA.Eintracht.Frankfurt 0.9328451 0.7149118 1.3048394 1.919475e-01
GAMMA.1.FC.Nuernberg 0.7365706 0.7181336 1.0256735 3.050455e-01
GAMMA.1.FSV.Mainz.05 0.5230322 0.7262813 0.7201510 4.714320e-01
GAMMA.1.FC.Kaiserslautern 0.5050734 0.7279605 0.6938198 4.877952e-01
GAMMA.1.FC.Koeln 0.4907825 0.7287591 0.6734496 5.006613e-01
GAMMA.Arminia.Bielefeld 0.4166108 0.7308322 0.5700499 5.686438e-01
GAMMA.Borussia.Moenchengladbach 0.4145654 0.7280079 0.5694517 5.690496e-01
GAMMA.VfL.Wolfsburg 0.3465493 0.7342260 0.4719927 6.369320e-01
GAMMA.MSV.Duisburg 0.0000000 NA NA 0.000000e+00
Warning message:
In rbind(coefs, c(0, NA, NA)) :
number of columns of result is not a multiple of vector length (arg 2)
Estimate Std. Error z value Pr(>|z|)
ALPHA.Borussia.Moenchengladbach 1.77652713 0.7056276 2.51765544 0.01181388
ALPHA.1.FC.Nuernberg 1.19589778 0.6864074 1.74225655 0.08146356
ALPHA.FC.Bayern.Muenchen 1.19167218 0.8052264 1.47992187 0.13889410
ALPHA.VfL.Wolfsburg 1.01149055 0.6942559 1.45694202 0.14513239
ALPHA.Arminia.Bielefeld 1.00667937 0.6910826 1.45667009 0.14520747
ALPHA.1.FSV.Mainz.05 0.97400086 0.6868702 1.41802755 0.15618272
ALPHA.MSV.Duisburg 0.93190263 0.7180099 1.29789664 0.19432285
ALPHA.SV.Werder.Bremen 0.69264920 0.7413129 0.93435469 0.35012096
ALPHA.FC.Schalke.04 0.53237551 0.6959067 0.76500989 0.44426566
ALPHA.1.FC.Kaiserslautern 0.50884370 0.6874515 0.74018853 0.45918561
ALPHA.Hertha.BSC.Berlin 0.42616963 0.6704364 0.63566002 0.52499804
ALPHA.1.FC.Koeln 0.34717866 0.6899041 0.50322743 0.61480438
ALPHA.Borussia.Dortmund 0.28596554 0.6681120 0.42802037 0.66863629
ALPHA.Eintracht.Frankfurt -0.06144533 0.6741292 -0.09114771 0.92737522
ALPHA.Hannover.96 -0.12600926 0.6648810 -0.18952152 0.84968409
ALPHA.Bayer.Leverkusen -0.19364804 0.6664336 -0.29057362 0.77137744
ALPHA.VfB.Stuttgart -0.40821401 0.6625411 -0.61613387 0.53780617
ALPHA.Hamburger.SV -1.17494354 0.7110832 -1.65232917 0.09846747
Warning message:
system call failed: Cannot allocate memory
ordBTL documentation built on May 2, 2019, 7:59 a.m.
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Description Usage Arguments Value Author(s) References See Also Examples
Description
Fits ordinal regression models to paired comparison data.
Usage
1 2 |
Arguments
formula |
a formula describing the model to be fitted. |
data |
a data frame containing the design matrix for the model
(See also |
family |
a character specifying which ordinal BTL model should be fitted.
Can be either |
family.control |
a list with arguments passed to the corresponding |
restrict |
(optional) a character vector specifying the covariates from |
... |
further arguments for fitting function (see |
Value
An object of class vglm.
Author(s)
Giuseppe Casalicchio
References
Dittrich R, Hatzinger R and Katzenbeisser W (2001). "Corrigendum: Modelling the effect of subject-specific covariates in paired comparison studies with an application to university rankings." Journal of the Royal Statistical Society: Series C (Applied Statistics), *50*(2), pp. 247-249.
Agresti A (1992). "Analysis of ordinal paired comparison data." Applied Statistics, pp. 287-297. Table 1.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 | ############################################################
## ##
## Example 1: Adjacent categories logit model for CEMS ##
## ##
############################################################
############################################################
# Reproduce results from Table 3 of Dittrich et al. (2001)
############################################################
# Get the CEMS data and generate design matrix
example(wide2long, package="ordBTL", echo=FALSE)
des1 <- design(CEMSlong, var1="object1", var2="object2",
use.vars="Y", reference="Stockholm")
# Fit the adjacent categories model, which corresponds to
# the log-linear BTL model (see Agresti, 1992)
mod1 <- ordBTL(Y~., data=des1, family="acat",
family.control=list(reverse=TRUE))
# We get the same results from Table 3 of Dittrich et al (2001).
# Since Stockholm is the reference university, its estimate
# is set to zero (due to identifiability)
getRank(mod1)
############################################################
# Reproduce results from Table 6 of Dittrich et al. (2001)
############################################################
# Generate design matrix and specify model formula
des2 <- design(CEMSlong, var1="object1", var2="object2",
use.vars="ALL", reference="Stockholm")
form2 <- Y~GAMMA.London + GAMMA.Paris + GAMMA.Milano +
GAMMA.StGallen + GAMMA.Barcelona + WOR +
SEX + WOR:GAMMA.Paris + WOR:GAMMA.Milano +
WOR:GAMMA.Barcelona + DEG:GAMMA.StGallen +
STUD:GAMMA.Paris + STUD:GAMMA.StGallen +
ENG:GAMMA.StGallen + FRA:GAMMA.London +
FRA:GAMMA.Paris + SPA:GAMMA.Barcelona +
ITA:GAMMA.London + ITA:GAMMA.Milano +
SEX:GAMMA.Milano
# Fit the adjacent categories model with symmetric
# constraint for covariable WOR and SEX
mod2 <- ordBTL(form2, data=des2, family="acat",
family.control=list(reverse=TRUE),
restrict=c("WOR", "SEX"))
# We get the same results from Table 6 of Dittrich et al. (2001)
getRank(mod2)
# Notice that the change in sign for (Intercept), WOR and SEX
# is because we use here a different "coding".
############################################################
## ##
## Example 2: Fitting models from Agresti (1992) ##
## ##
############################################################
# Data from Table 1 of Agresti (1992)
data(ribbon)
# design matrix
des3 <- design(ribbon, var1="obj1", var2="obj2", use.vars="ALL")
# Note that Agresti (1992) used the constraint that the object
# parameters sum up to 1. To get the same results, we use the model
form3 <- cbind(V1,V2,V3,V4,V5,V6,V7)~I(GAMMA.1-GAMMA.5)+
I(GAMMA.2-GAMMA.5)+I(GAMMA.3-GAMMA.5)+I(GAMMA.4-GAMMA.5)
# Fit the adjacent categories logit model
ac <- ordBTL(form3, data=des3, family="acat",
family.control=list(reverse=TRUE))
# Fit the cumulative logit model
clm.logit <- ordBTL(form3, data=des3)
# Fit the cumulative probit model
clm.probit <- ordBTL(form3, data=des3,
family.control=list(link="probit"))
# Parameter estimates
coefs <- t(rbind("Adjacent categories logit"=coefficients(ac),
"Cumulative probit"=coefficients(clm.probit),
"Cumulative logit"=coefficients(clm.logit)))
coefs <- rbind(coefs, "GAMMA.5"=0-colSums(coefs[4:7,]))
coefs
############################################################
## ##
## Example 3: Fitting models for Bundesliga 2005/2006 ##
## ##
############################################################
# real ranking can be obtained from:
# http://fussballdaten.sport.de/bundesliga/2006
# load data
example(design, package="ordBTL", echo=FALSE)
# Model without home advantage
des.nohome <- design(buli0506, var1="Heim", var2="Gast",
use.vars="Y3", home.advantage="no",
reference="GAMMA.MSV.Duisburg")
mod.nohome <- ordBTL(Y3~., data=des.nohome)
# team 'abilities' (should be approximately the ranking of the final standings)
getRank(mod.nohome, prefix="GAMMA", reference="GAMMA.MSV.Duisburg")
# Model with home advantage
des.onehome <- design(buli0506, var1="Heim", var2="Gast",
use.vars="Y3", home.advantage="yes",
reference="GAMMA.MSV.Duisburg")
mod.onehome <- ordBTL(Y3~., data=des.onehome)
# team 'abilities'
getRank(mod.onehome, prefix="GAMMA", reference="GAMMA.MSV.Duisburg")
# home advantage
getRank(mod.onehome, prefix="ALPHA")
# Model with team-specific home advantage
des.teamhome <- design(buli0506, var1="Heim", var2="Gast",
use.vars="Y3", home.advantage="specific",
reference="GAMMA.MSV.Duisburg")
mod.teamhome <- ordBTL(Y3~., data=des.teamhome)
# team 'abilities' (should be approximately the ranking for the away table)
getRank(mod.teamhome, prefix="GAMMA", reference="GAMMA.MSV.Duisburg")
# team-specific home advantages
getRank(mod.teamhome, prefix="ALPHA")
|
Example output
Loading required package: caret
Loading required package: lattice
Loading required package: ggplot2
Loading required package: VGAM
Loading required package: stats4
Loading required package: splines
Attaching package: 'VGAM'
The following object is masked from 'package:caret':
predictors
Loading required package: wikibooks
Loading required package: gtools
Attaching package: 'gtools'
The following object is masked from 'package:VGAM':
logit
Warning messages:
1: In eval(slot(family, "initialize")) :
response should be ordinal---see ordered()
2: In vglm.fitter(x = x, y = y, w = w, offset = offset, Xm2 = Xm2, :
iterations terminated because half-step sizes are very small
3: In vglm.fitter(x = x, y = y, w = w, offset = offset, Xm2 = Xm2, :
some quantities such as z, residuals, SEs may be inaccurate due to convergence at a half-step
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.3171797 0.04850831 27.153690 2.290333e-162
GAMMA.London 0.9114010 0.04157245 21.923199 1.560935e-106
GAMMA.Paris 0.5162669 0.03878553 13.310814 2.002882e-40
GAMMA.Barcelona 0.3064662 0.03758382 8.154207 3.514783e-16
GAMMA.StGallen 0.2991610 0.03757425 7.961864 1.694665e-15
GAMMA.Milano 0.2209861 0.03800946 5.813975 6.100654e-09
Warning message:
In eval(slot(family, "initialize")) :
response should be ordinal---see ordered()
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.4101679 0.07407699 19.036517 8.499457e-81
GAMMA.London 1.2796797 0.09977634 12.825482 1.180494e-37
GAMMA.Milano 1.1237633 0.09498545 11.830900 2.702301e-32
GAMMA.Barcelona 1.0514442 0.09658294 10.886439 1.337696e-27
GAMMA.Paris:WOR 0.6942689 0.17117497 4.055902 4.994120e-05
GAMMA.Paris 0.6412652 0.05532038 11.591844 4.532696e-31
WOR 0.6406664 0.30350233 2.110911 3.477996e-02
GAMMA.Barcelona:WOR 0.5406832 0.15452633 3.498971 4.670571e-04
GAMMA.Milano:WOR 0.5345675 0.15466490 3.456295 5.476562e-04
GAMMA.Paris:STUD 0.4233486 0.06993863 6.053144 1.420454e-09
GAMMA.StGallen:DEG 0.2759380 0.06471569 4.263850 2.009341e-05
GAMMA.StGallen 0.2503909 0.05324186 4.702896 2.564968e-06
GAMMA.StGallen:ENG 0.1469205 0.06811840 2.156840 3.101814e-02
GAMMA.London:FRA -0.1564219 0.07123406 -2.195887 2.810006e-02
GAMMA.Milano:SEX -0.1841493 0.06439549 -2.859661 4.240935e-03
GAMMA.StGallen:STUD -0.1993143 0.06672730 -2.986997 2.817325e-03
GAMMA.London:ITA -0.2943846 0.09774864 -3.011649 2.598327e-03
SEX -0.3396928 0.09740395 -3.487464 4.876244e-04
GAMMA.Paris:FRA -0.7214285 0.06744770 -10.696116 1.061337e-26
GAMMA.Barcelona:SPA -0.8526536 0.09783728 -8.715018 2.907133e-18
GAMMA.Milano:ITA -0.9642430 0.09812584 -9.826596 8.649266e-23
Adjacent categories logit Cumulative probit
(Intercept):1 -0.85198602 -1.37896215
(Intercept):2 0.83260807 -0.48950762
(Intercept):3 -0.54437393 -0.21894776
I(GAMMA.1 - GAMMA.5) 0.04216091 0.05779022
I(GAMMA.2 - GAMMA.5) -0.05032611 -0.08807263
I(GAMMA.3 - GAMMA.5) 0.27003510 0.49396332
I(GAMMA.4 - GAMMA.5) -0.33952267 -0.60710964
GAMMA.5 0.07765277 0.14342873
Cumulative logit
(Intercept):1 -2.3998818
(Intercept):2 -0.8295968
(Intercept):3 -0.3711039
I(GAMMA.1 - GAMMA.5) 0.1168923
I(GAMMA.2 - GAMMA.5) -0.1960107
I(GAMMA.3 - GAMMA.5) 0.8873016
I(GAMMA.4 - GAMMA.5) -1.0476375
GAMMA.5 0.2394542
'data.frame': 306 obs. of 11 variables:
$ Saison : Factor w/ 44 levels "1963/1964","1964/1965",..: 43 43 43 43 43 43 43 43 43 43 ...
$ Spieltag : int 1 1 1 1 1 1 1 1 1 2 ...
$ Datum : Date, format: "2005-08-05" "2005-08-06" ...
$ Anpfiff : Factor w/ 31 levels "14:00","14:15",..: 28 6 6 6 6 6 6 15 15 6 ...
$ Heim : Factor w/ 50 levels "1. FC Kaiserslautern",..: 18 2 31 24 49 40 25 20 16 8 ...
$ Gast : Factor w/ 50 levels "1. FC Kaiserslautern",..: 11 5 47 3 10 7 27 1 8 18 ...
$ Tore.Heim : int 3 1 1 3 2 5 2 2 1 2 ...
$ Tore.Gast : int 0 0 1 0 2 2 2 1 4 5 ...
$ Tore.Heim.Halbzeit: int 1 0 1 2 1 3 0 0 1 1 ...
$ Tore.Gast.Halbzeit: int 0 0 1 0 0 2 0 1 1 3 ...
$ Y3 : Ord.factor w/ 3 levels "1"<"2"<"3": 1 1 2 1 2 1 2 1 3 3 ...
'data.frame': 306 obs. of 18 variables:
$ GAMMA.1.FC.Kaiserslautern : num 0 0 0 0 0 0 0 -1 0 0 ...
$ GAMMA.1.FC.Koeln : num 0 1 0 0 0 0 0 0 0 0 ...
$ GAMMA.1.FC.Nuernberg : num 0 0 0 -1 0 0 0 0 0 0 ...
$ GAMMA.1.FSV.Mainz.05 : num 0 -1 0 0 0 0 0 0 0 0 ...
$ GAMMA.Arminia.Bielefeld : num 0 0 0 0 0 -1 0 0 0 0 ...
$ GAMMA.Bayer.Leverkusen : num 0 0 0 0 0 0 0 0 -1 1 ...
$ GAMMA.Borussia.Dortmund : num 0 0 0 0 -1 0 0 0 0 0 ...
$ GAMMA.Borussia.Moenchengladbach: num -1 0 0 0 0 0 0 0 0 0 ...
$ GAMMA.Eintracht.Frankfurt : num 0 0 0 0 0 0 0 0 1 0 ...
$ GAMMA.FC.Bayern.Muenchen : num 1 0 0 0 0 0 0 0 0 -1 ...
$ GAMMA.FC.Schalke.04 : num 0 0 0 0 0 0 0 1 0 0 ...
$ GAMMA.Hamburger.SV : num 0 0 0 1 0 0 0 0 0 0 ...
$ GAMMA.Hannover.96 : num 0 0 0 0 0 0 1 0 0 0 ...
$ GAMMA.Hertha.BSC.Berlin : num 0 0 0 0 0 0 -1 0 0 0 ...
$ GAMMA.MSV.Duisburg : num 0 0 1 0 0 0 0 0 0 0 ...
$ GAMMA.SV.Werder.Bremen : num 0 0 0 0 0 1 0 0 0 0 ...
$ GAMMA.VfB.Stuttgart : num 0 0 -1 0 0 0 0 0 0 0 ...
$ GAMMA.VfL.Wolfsburg : num 0 0 0 0 1 0 0 0 0 0 ...
'data.frame': 306 obs. of 19 variables:
$ GAMMA.1.FC.Kaiserslautern : num 0 0 0 0 0 0 0 -1 0 0 ...
$ GAMMA.1.FC.Koeln : num 0 1 0 0 0 0 0 0 0 0 ...
$ GAMMA.1.FC.Nuernberg : num 0 0 0 -1 0 0 0 0 0 0 ...
$ GAMMA.1.FSV.Mainz.05 : num 0 -1 0 0 0 0 0 0 0 0 ...
$ GAMMA.Arminia.Bielefeld : num 0 0 0 0 0 -1 0 0 0 0 ...
$ GAMMA.Bayer.Leverkusen : num 0 0 0 0 0 0 0 0 -1 1 ...
$ GAMMA.Borussia.Dortmund : num 0 0 0 0 -1 0 0 0 0 0 ...
$ GAMMA.Borussia.Moenchengladbach: num -1 0 0 0 0 0 0 0 0 0 ...
$ GAMMA.Eintracht.Frankfurt : num 0 0 0 0 0 0 0 0 1 0 ...
$ GAMMA.FC.Bayern.Muenchen : num 1 0 0 0 0 0 0 0 0 -1 ...
$ GAMMA.FC.Schalke.04 : num 0 0 0 0 0 0 0 1 0 0 ...
$ GAMMA.Hamburger.SV : num 0 0 0 1 0 0 0 0 0 0 ...
$ GAMMA.Hannover.96 : num 0 0 0 0 0 0 1 0 0 0 ...
$ GAMMA.Hertha.BSC.Berlin : num 0 0 0 0 0 0 -1 0 0 0 ...
$ GAMMA.MSV.Duisburg : num 0 0 1 0 0 0 0 0 0 0 ...
$ GAMMA.SV.Werder.Bremen : num 0 0 0 0 0 1 0 0 0 0 ...
$ GAMMA.VfB.Stuttgart : num 0 0 -1 0 0 0 0 0 0 0 ...
$ GAMMA.VfL.Wolfsburg : num 0 0 0 0 1 0 0 0 0 0 ...
$ ALPHA : num 1 1 1 1 1 1 1 1 1 1 ...
'data.frame': 306 obs. of 36 variables:
$ GAMMA.1.FC.Kaiserslautern : num 0 0 0 0 0 0 0 -1 0 0 ...
$ GAMMA.1.FC.Koeln : num 0 1 0 0 0 0 0 0 0 0 ...
$ GAMMA.1.FC.Nuernberg : num 0 0 0 -1 0 0 0 0 0 0 ...
$ GAMMA.1.FSV.Mainz.05 : num 0 -1 0 0 0 0 0 0 0 0 ...
$ GAMMA.Arminia.Bielefeld : num 0 0 0 0 0 -1 0 0 0 0 ...
$ GAMMA.Bayer.Leverkusen : num 0 0 0 0 0 0 0 0 -1 1 ...
$ GAMMA.Borussia.Dortmund : num 0 0 0 0 -1 0 0 0 0 0 ...
$ GAMMA.Borussia.Moenchengladbach: num -1 0 0 0 0 0 0 0 0 0 ...
$ GAMMA.Eintracht.Frankfurt : num 0 0 0 0 0 0 0 0 1 0 ...
$ GAMMA.FC.Bayern.Muenchen : num 1 0 0 0 0 0 0 0 0 -1 ...
$ GAMMA.FC.Schalke.04 : num 0 0 0 0 0 0 0 1 0 0 ...
$ GAMMA.Hamburger.SV : num 0 0 0 1 0 0 0 0 0 0 ...
$ GAMMA.Hannover.96 : num 0 0 0 0 0 0 1 0 0 0 ...
$ GAMMA.Hertha.BSC.Berlin : num 0 0 0 0 0 0 -1 0 0 0 ...
$ GAMMA.MSV.Duisburg : num 0 0 1 0 0 0 0 0 0 0 ...
$ GAMMA.SV.Werder.Bremen : num 0 0 0 0 0 1 0 0 0 0 ...
$ GAMMA.VfB.Stuttgart : num 0 0 -1 0 0 0 0 0 0 0 ...
$ GAMMA.VfL.Wolfsburg : num 0 0 0 0 1 0 0 0 0 0 ...
$ ALPHA.1.FC.Kaiserslautern : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.1.FC.Koeln : num 0 1 0 0 0 0 0 0 0 0 ...
$ ALPHA.1.FC.Nuernberg : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.1.FSV.Mainz.05 : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.Arminia.Bielefeld : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.Bayer.Leverkusen : num 0 0 0 0 0 0 0 0 0 1 ...
$ ALPHA.Borussia.Dortmund : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.Borussia.Moenchengladbach: num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.Eintracht.Frankfurt : num 0 0 0 0 0 0 0 0 1 0 ...
$ ALPHA.FC.Bayern.Muenchen : num 1 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.FC.Schalke.04 : num 0 0 0 0 0 0 0 1 0 0 ...
$ ALPHA.Hamburger.SV : num 0 0 0 1 0 0 0 0 0 0 ...
$ ALPHA.Hannover.96 : num 0 0 0 0 0 0 1 0 0 0 ...
$ ALPHA.Hertha.BSC.Berlin : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.MSV.Duisburg : num 0 0 1 0 0 0 0 0 0 0 ...
$ ALPHA.SV.Werder.Bremen : num 0 0 0 0 0 1 0 0 0 0 ...
$ ALPHA.VfB.Stuttgart : num 0 0 0 0 0 0 0 0 0 0 ...
$ ALPHA.VfL.Wolfsburg : num 0 0 0 0 1 0 0 0 0 0 ...
'data.frame': 306 obs. of 19 variables:
$ GAMMA.1.FC.Kaiserslautern : num 0 0 0 0 0 0 0 -1 0 0 ...
$ GAMMA.1.FC.Koeln : num 0 1 0 0 0 0 0 0 0 0 ...
$ GAMMA.1.FC.Nuernberg : num 0 0 0 -1 0 0 0 0 0 0 ...
$ GAMMA.1.FSV.Mainz.05 : num 0 -1 0 0 0 0 0 0 0 0 ...
$ GAMMA.Arminia.Bielefeld : num 0 0 0 0 0 -1 0 0 0 0 ...
$ GAMMA.Bayer.Leverkusen : num 0 0 0 0 0 0 0 0 -1 1 ...
$ GAMMA.Borussia.Dortmund : num 0 0 0 0 -1 0 0 0 0 0 ...
$ GAMMA.Borussia.Moenchengladbach: num -1 0 0 0 0 0 0 0 0 0 ...
$ GAMMA.Eintracht.Frankfurt : num 0 0 0 0 0 0 0 0 1 0 ...
$ GAMMA.FC.Bayern.Muenchen : num 1 0 0 0 0 0 0 0 0 -1 ...
$ GAMMA.FC.Schalke.04 : num 0 0 0 0 0 0 0 1 0 0 ...
$ GAMMA.Hamburger.SV : num 0 0 0 1 0 0 0 0 0 0 ...
$ GAMMA.Hannover.96 : num 0 0 0 0 0 0 1 0 0 0 ...
$ GAMMA.Hertha.BSC.Berlin : num 0 0 0 0 0 0 -1 0 0 0 ...
$ GAMMA.MSV.Duisburg : num 0 0 1 0 0 0 0 0 0 0 ...
$ GAMMA.SV.Werder.Bremen : num 0 0 0 0 0 1 0 0 0 0 ...
$ GAMMA.VfB.Stuttgart : num 0 0 -1 0 0 0 0 0 0 0 ...
$ GAMMA.VfL.Wolfsburg : num 0 0 0 0 1 0 0 0 0 0 ...
$ Spieltag : int 1 1 1 1 1 1 1 1 1 2 ...
Estimate Std. Error z value Pr(>|z|)
GAMMA.FC.Bayern.Muenchen 2.15183470 0.4894014 4.3968712 1.098225e-05
GAMMA.SV.Werder.Bremen 1.97066756 0.4805982 4.1004475 4.123520e-05
GAMMA.Hamburger.SV 1.85128996 0.4755611 3.8928539 9.907181e-05
GAMMA.FC.Schalke.04 1.53694777 0.4650047 3.3052306 9.489829e-04
GAMMA.Bayer.Leverkusen 1.11218303 0.4562407 2.4377114 1.478057e-02
GAMMA.Hertha.BSC.Berlin 0.96890640 0.4545961 2.1313565 3.305978e-02
GAMMA.Borussia.Dortmund 0.88674951 0.4539380 1.9534594 5.076519e-02
GAMMA.VfB.Stuttgart 0.84283463 0.4536699 1.8578147 6.319534e-02
GAMMA.Borussia.Moenchengladbach 0.73609299 0.4532612 1.6239928 1.043773e-01
GAMMA.1.FC.Nuernberg 0.69608421 0.4531961 1.5359449 1.245519e-01
GAMMA.Hannover.96 0.67862317 0.4531825 1.4974611 1.342733e-01
GAMMA.1.FSV.Mainz.05 0.46470092 0.4537577 1.0241170 3.057800e-01
GAMMA.VfL.Wolfsburg 0.37696046 0.4543918 0.8295935 4.067687e-01
GAMMA.Eintracht.Frankfurt 0.33368265 0.4547928 0.7337027 4.631300e-01
GAMMA.Arminia.Bielefeld 0.29518165 0.4551965 0.6484708 5.166805e-01
GAMMA.1.FC.Kaiserslautern 0.17249245 0.4567996 0.3776108 7.057198e-01
GAMMA.1.FC.Koeln 0.06391278 0.4586289 0.1393562 8.891687e-01
GAMMA.MSV.Duisburg 0.00000000 NA NA 0.000000e+00
Warning message:
In rbind(coefs, c(0, NA, NA)) :
number of columns of result is not a multiple of vector length (arg 2)
Estimate Std. Error z value Pr(>|z|)
GAMMA.FC.Bayern.Muenchen 2.3235491 0.5014555 4.6336096 3.593443e-06
GAMMA.SV.Werder.Bremen 2.0997972 0.4905261 4.2807044 1.863027e-05
GAMMA.Hamburger.SV 2.0047016 0.4864772 4.1208543 3.774701e-05
GAMMA.FC.Schalke.04 1.6475512 0.4741837 3.4745000 5.118064e-04
GAMMA.Bayer.Leverkusen 1.1758857 0.4642465 2.5328907 1.131262e-02
GAMMA.Hertha.BSC.Berlin 1.0625127 0.4628525 2.2955754 2.170017e-02
GAMMA.Borussia.Dortmund 0.9907894 0.4621643 2.1438033 3.204865e-02
GAMMA.VfB.Stuttgart 0.9464535 0.4618139 2.0494261 4.042046e-02
GAMMA.1.FC.Nuernberg 0.8013961 0.4610664 1.7381360 8.218686e-02
GAMMA.Borussia.Moenchengladbach 0.7895854 0.4610324 1.7126460 8.677768e-02
GAMMA.Hannover.96 0.7479451 0.4609455 1.6226326 1.046680e-01
GAMMA.1.FSV.Mainz.05 0.5139848 0.4614065 1.1139522 2.652997e-01
GAMMA.Arminia.Bielefeld 0.3932144 0.4622875 0.8505840 3.950005e-01
GAMMA.VfL.Wolfsburg 0.3810249 0.4624011 0.8240139 4.099317e-01
GAMMA.Eintracht.Frankfurt 0.3726626 0.4624820 0.8057884 4.203649e-01
GAMMA.1.FC.Kaiserslautern 0.2277652 0.4642310 0.4906291 6.236888e-01
GAMMA.1.FC.Koeln 0.1154838 0.4660537 0.2477907 8.042964e-01
GAMMA.MSV.Duisburg 0.0000000 NA NA 0.000000e+00
Warning message:
In rbind(coefs, c(0, NA, NA)) :
number of columns of result is not a multiple of vector length (arg 2)
Estimate Std. Error z value Pr(>|z|)
ALPHA 0.4783205 0.1138493 4.201349 2.653296e-05
Estimate Std. Error z value Pr(>|z|)
GAMMA.Hamburger.SV 3.1099530 0.7517584 4.1369049 3.520219e-05
GAMMA.FC.Bayern.Muenchen 2.3908022 0.7174690 3.3322725 8.613985e-04
GAMMA.SV.Werder.Bremen 2.3366551 0.7170423 3.2587407 1.119079e-03
GAMMA.FC.Schalke.04 1.9493387 0.7098522 2.7461191 6.030487e-03
GAMMA.Bayer.Leverkusen 1.8480170 0.7092524 2.6055846 9.171763e-03
GAMMA.VfB.Stuttgart 1.6529623 0.7081540 2.3341849 1.958604e-02
GAMMA.Borussia.Dortmund 1.3997838 0.7083819 1.9760299 4.815139e-02
GAMMA.Hertha.BSC.Berlin 1.3556703 0.7085335 1.9133469 5.570366e-02
GAMMA.Hannover.96 1.3194838 0.7091386 1.8606853 6.278864e-02
GAMMA.Eintracht.Frankfurt 0.9328451 0.7149118 1.3048394 1.919475e-01
GAMMA.1.FC.Nuernberg 0.7365706 0.7181336 1.0256735 3.050455e-01
GAMMA.1.FSV.Mainz.05 0.5230322 0.7262813 0.7201510 4.714320e-01
GAMMA.1.FC.Kaiserslautern 0.5050734 0.7279605 0.6938198 4.877952e-01
GAMMA.1.FC.Koeln 0.4907825 0.7287591 0.6734496 5.006613e-01
GAMMA.Arminia.Bielefeld 0.4166108 0.7308322 0.5700499 5.686438e-01
GAMMA.Borussia.Moenchengladbach 0.4145654 0.7280079 0.5694517 5.690496e-01
GAMMA.VfL.Wolfsburg 0.3465493 0.7342260 0.4719927 6.369320e-01
GAMMA.MSV.Duisburg 0.0000000 NA NA 0.000000e+00
Warning message:
In rbind(coefs, c(0, NA, NA)) :
number of columns of result is not a multiple of vector length (arg 2)
Estimate Std. Error z value Pr(>|z|)
ALPHA.Borussia.Moenchengladbach 1.77652713 0.7056276 2.51765544 0.01181388
ALPHA.1.FC.Nuernberg 1.19589778 0.6864074 1.74225655 0.08146356
ALPHA.FC.Bayern.Muenchen 1.19167218 0.8052264 1.47992187 0.13889410
ALPHA.VfL.Wolfsburg 1.01149055 0.6942559 1.45694202 0.14513239
ALPHA.Arminia.Bielefeld 1.00667937 0.6910826 1.45667009 0.14520747
ALPHA.1.FSV.Mainz.05 0.97400086 0.6868702 1.41802755 0.15618272
ALPHA.MSV.Duisburg 0.93190263 0.7180099 1.29789664 0.19432285
ALPHA.SV.Werder.Bremen 0.69264920 0.7413129 0.93435469 0.35012096
ALPHA.FC.Schalke.04 0.53237551 0.6959067 0.76500989 0.44426566
ALPHA.1.FC.Kaiserslautern 0.50884370 0.6874515 0.74018853 0.45918561
ALPHA.Hertha.BSC.Berlin 0.42616963 0.6704364 0.63566002 0.52499804
ALPHA.1.FC.Koeln 0.34717866 0.6899041 0.50322743 0.61480438
ALPHA.Borussia.Dortmund 0.28596554 0.6681120 0.42802037 0.66863629
ALPHA.Eintracht.Frankfurt -0.06144533 0.6741292 -0.09114771 0.92737522
ALPHA.Hannover.96 -0.12600926 0.6648810 -0.18952152 0.84968409
ALPHA.Bayer.Leverkusen -0.19364804 0.6664336 -0.29057362 0.77137744
ALPHA.VfB.Stuttgart -0.40821401 0.6625411 -0.61613387 0.53780617
ALPHA.Hamburger.SV -1.17494354 0.7110832 -1.65232917 0.09846747
Warning message:
system call failed: Cannot allocate memory
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