CEMS: Dittrich, Hatzinger and Katzenbeisser (1998, 2001) Data on...
In BradleyTerry2: Bradley-Terry Models

Description Usage Format Details Author(s) Source References Examples

Community of European management schools (CEMS) data as used in the paper by Dittrich et al. (1998, 2001), re-formatted for use with BTm()

CEMS

A list containing three data frames, CEMS$preferences, CEMS$students and CEMS$schools.

The CEMS$preferences data frame has 303 * 15 = 4505 observations (15 possible comparisons, for each of 303 students) on the following 8 variables:

student: a factor with levels 1:303
school1: a factor with levels c("Barcelona", "London", "Milano", "Paris", "St.Gallen", "Stockholm"); the first management school in a comparison
school2: a factor with the same levels as school1; the second management school in a comparison
win1: integer (value 0 or 1) indicating whether school1 was preferred to school2
win2: integer (value 0 or 1) indicating whether school2 was preferred to school1
tied: integer (value 0 or 1) indicating whether no preference was expressed
win1.adj: numeric, equal to win1 + tied/2
win2.adj: numeric, equal to win2 + tied/2

The CEMS$students data frame has 303 observations (one for each student) on the following 8 variables:

STUD: a factor with levels c("other", "commerce"), the student's main discipline of study
ENG: a factor with levels c("good, poor"), indicating the student's knowledge of English
FRA: a factor with levels c("good, poor"), indicating the student's knowledge of French
SPA: a factor with levels c("good, poor"), indicating the student's knowledge of Spanish
ITA: a factor with levels c("good, poor"), indicating the student's knowledge of Italian
WOR: a factor with levels c("no", "yes"), whether the student was in full-time employment while studying
DEG: a factor with levels c("no", "yes"), whether the student intended to take an international degree
SEX: a factor with levels c("female", "male")

The CEMS$schools data frame has 6 observations (one for each management school) on the following 7 variables:

Barcelona: numeric (value 0 or 1)
London: numeric (value 0 or 1)
Milano: numeric (value 0 or 1)
Paris: numeric (value 0 or 1)
St.Gallen: numeric (value 0 or 1)
Stockholm: numeric (value 0 or 1)
LAT: numeric (value 0 or 1) indicating a 'Latin' city

The variables win1.adj and win2.adj are provided in order to allow a simple way of handling ties (in which a tie counts as half a win and half a loss), which is slightly different numerically from the Davidson (1970) method that is used by Dittrich et al. (1998): see the examples.

David Firth

Royal Statistical Society datasets website, at https://rss.onlinelibrary.wiley.com/hub/journal/14679876/series-c-datasets/pre_2016.

Davidson, R. R. (1970) Extending the Bradley-Terry model to accommodate ties in paired comparison experiments. Journal of the American Statistical Association 65, 317–328.

Dittrich, R., Hatzinger, R. and Katzenbeisser, W. (1998) Modelling the effect of subject-specific covariates in paired comparison studies with an application to university rankings. Applied Statistics 47, 511–525.

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. Applied Statistics 50, 247–249.

Turner, H. and Firth, D. (2012) Bradley-Terry models in R: The BradleyTerry2 package. Journal of Statistical Software, 48(9), 1–21.

##
##  Fit the standard Bradley-Terry model, using the simple 'add 0.5'
##  method to handle ties:
##
table3.model <-  BTm(outcome = cbind(win1.adj, win2.adj),
                     player1 = school1, player2 = school2,
                     formula = ~.. , refcat = "Stockholm",
                     data = CEMS)
##  The results in Table 3 of Dittrich et al (2001) are reproduced
##  approximately by a simple re-scaling of the estimates:
table3 <- summary(table3.model)$coef[, 1:2]/1.75
print(table3)
##
##  Now fit the 'final model' from Table 6 of Dittrich et al.:
##
table6.model <-  BTm(outcome = cbind(win1.adj, win2.adj),
                     player1 = school1, player2 = school2,
                     formula = ~ .. +
                         WOR[student] * Paris[..] +
                         WOR[student] * Milano[..] +
                         WOR[student] * Barcelona[..] +
                         DEG[student] * St.Gallen[..] +
                         STUD[student] * Paris[..] +
                         STUD[student] * St.Gallen[..] +
                         ENG[student] * St.Gallen[..] +
                         FRA[student] * London[..] +
                         FRA[student] * Paris[..] +
                         SPA[student] * Barcelona[..] +
                         ITA[student] * London[..] +
                         ITA[student] * Milano[..] +
                         SEX[student] * Milano[..],
                     refcat = "Stockholm",
                     data = CEMS)
##
##  Again re-scale to reproduce approximately Table 6 of Dittrich et
##  al. (2001):
##
table6 <- summary(table6.model)$coef[, 1:2]/1.75
print(table6)
##
## Not run: 
##  Now the slightly simplified model of Table 8 of Dittrich et al. (2001):
##
table8.model <-  BTm(outcome = cbind(win1.adj, win2.adj),
                     player1 = school1, player2 = school2,
                     formula = ~ .. +
                         WOR[student] * LAT[..] +
                         DEG[student] * St.Gallen[..] +
                         STUD[student] * Paris[..] +
                         STUD[student] * St.Gallen[..] +
                         ENG[student] * St.Gallen[..] +
                         FRA[student] * London[..] +
                         FRA[student] * Paris[..] +
                         SPA[student] * Barcelona[..] +
                         ITA[student] * London[..] +
                         ITA[student] * Milano[..] +
                         SEX[student] * Milano[..],
                     refcat = "Stockholm",
                     data = CEMS)
table8 <- summary(table8.model)$coef[, 1:2]/1.75
##
##  Notice some larger than expected discrepancies here (the coefficients
##  named "..Barcelona", "..Milano" and "..Paris") from the results in
##  Dittrich et al. (2001).  Apparently a mistake was made in Table 8 of
##  the published Corrigendum note (R. Dittrich personal communication,
##  February 2010).
##
print(table8)

## End(Not run)