A log-linear approach for modelling ordinal paired comparison data on motives to start a PhD programme

Abstract

The purpose of this paper is to propose an alternative log-linear representation of an adjacent categories (AC) paired comparison (PC) model. The AC model is well suited for modelling ordinal PC data by postulating a power relationship between the response category and the probability of preferring one object over another object. The model is applied to data collected on the motivation of Vienna students to start a doctoral programme of study.

Keywords

adjacent categories model Bradley-Terry model generalized linear models GLIM ordinal data paired comparisons R

Get full access to this article

View all access options for this article.

References

Agresti A (1990) Categorical data analysis. John Wiley, New York .

Agresti A (1992) Analysis of ordinal paired comparison data . Journal of the Royal Statistical Society: Series C (Applied Statistics) 41, 287-297 .

Aitkin M , Anderson D , Francis B , and Hinde J (1989) Statistical modelling in GLIM. Clarendon Press: Oxford .

Böckenholt U (1988) A logistic representation of multivariate paired-comparison models . Journal of Mathematical Psychology 32, 44-63 .

Böckenholt U and Dillon W (1997) Modelling within-subject dependencies in ordinal paired comparison data . Psychometrika 62, 411-434 .

Bradley RA and Terry ME (1952) Rank analysis of incomplete block designs I. The method of paired comparisons . Biometrika 39, 324-345 .

David HA (1988) The method of paired comparisons. New York: Oxford University Press .

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

Davidson RR and Beaver RJ (1977) On extending the Bradley-Terry model to incorporate within-pair order effects . Biometrics, 33, 693-702 .

10.

Dittrich R , Hatzinger R and Katzenbeisser W (1997). Fitting paired comparison models in GLIM: (I) simple models, ties and position effects . GLIM-Newsletter 27, 27-34 .

11.

Dittrich R , Hatzinger R and Katzenbeisser W (1998a) 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), 47, 511-525 .

12.

Dittrich R , Hatzinger R and Katzenbeisser W (1998b) Fitting paired comparison models in GLIM: (II) subject and object variables . GLIM-Newsletter, 28, 21-28 .

13.

Francis B , Dittrich R , Hatzinger R and Penn R (2002) Analysing partial ranks by using smoothed paired comparison methods: an investigation of value orientation in Europe . Journal of the Royal Statistical Society: Series C (Applied Statistics), 51, 319-336 .

14.

Francis B , Green M , Payne C (Eds.) (1993) The GLIM system: release 4 manual. Oxford: Clarendon Press .

15.

Gilchrist R and Green P (1993) The Theory of generalised linear models. In Francis, B. , Green M , Payne C (Eds.) The GLIM system: release 4 Manual. Oxford: Clarendon Press .

16.

Matthews JNS and Morris KP (1995) An application of Bradley-Terry-type models to the measurement of pain . Journal of the Royal Statistical Society: Series C (Applied Statistics), 44, 243-255 .

17.

Payne C (1979) A macro for calculating the correct degrees of freedom for a log-linear model of a contingency table . GLIM-Newsletter, 1, 32-33 .

18.

Rao PV and Kupper LL (1967) Ties in paired comparisons: a generalization of the Bradley-Terry model . Journal of the American Statistical Association, 62, 194-204 .

19.

Proceedings of the International Conference on Generalised Linear Models, Springer Lecture Notes in Statistics, 14, 164-178 ; New York, Heidelberg, Berlin: Springer .