CEMS {BradleyTerry2}

Dittrich, Hatzinger and Katzenbeisser (1998, 2001) Data on Management School Preference in Europe

Description

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

Usage

CEMS

Format

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

Details

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.

Author(s)

David Firth

Source

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

References

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.

Examples

##
##  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)