prefmod: An R Package for Modeling Preferences Based on Paired Comparisons, Rankings, or Ratings

The first part of this paper describes a series of loglinear preference models based on paired comparisons, a method of measurement whose aim is to order a set of objects according to an attribute of interest by asking subjects to compare pairs of objects. Based on the basic Bradley-Terry specification, two types of models, the loglinear Bradley-Terry model and a pattern approach are presented. Both methods are extended to include subject and object-specific covariates and some further structural effects. In addition, models for derived paired comparisons (based on rankings and ratings) are also included. Latent classes and missing values can be included. The second part of the paper describes the package prefmod that implements the above models in R. Illustrational applications are provided in the last part of the paper.

[1]  B. Francis,et al.  Modeling heterogeneity in ranked responses by nonparametric maximum likelihood: How do Europeans get their scientific knowledge? , 2010, 1101.1425.

[2]  Regina Dittrich,et al.  Missing observations in paired comparison data , 2012 .

[3]  Reinhold Hatzinger,et al.  Fitting paired comparison models in R. , 2004 .

[4]  John Hinde,et al.  Statistical Modelling in R , 2009 .

[5]  D. Rubin INFERENCE AND MISSING DATA , 1975 .

[6]  Robert J. Beaver,et al.  On Extending the Bradley-Terry Model to Incorporate Within-Pair Order Effects , 1977 .

[7]  David Firth,et al.  Bradley-Terry Models in R: The BradleyTerry2 Package , 2012 .

[8]  Douglas E. Critchlow,et al.  Paired comparison, triple comparison, and ranking experiments as generalized linear models, and their implementation on GLIM , 1991 .

[9]  Murray Aitkin,et al.  A general maximum likelihood analysis of overdispersion in generalized linear models , 1996, Stat. Comput..

[10]  A. Mallet A maximum likelihood estimation method for random coefficient regression models , 1986 .

[11]  David Firth,et al.  Generalized nonlinear models in R: An overview of the gnm package , 2007 .

[12]  Regina Dittrich,et al.  Modelling dependencies in paired comparison data a log-linear approach , 2002 .

[13]  S. Fienberg,et al.  Log linear representation for paired and multiple comparisons models , 1976 .

[14]  Christian Schmid,et al.  A Matlab function to estimate choice model parameters from paired-comparison data , 2004, Behavior research methods, instruments, & computers : a journal of the Psychonomic Society, Inc.

[15]  Robin Thompson,et al.  Composite Link Functions in Generalized Linear Models , 1981 .

[16]  Brian Francis,et al.  Modelling dependency in multivariate paired comparisons: A log-linear approach , 2006, Math. Soc. Sci..

[17]  C. Sinclair,et al.  GLIM for Preference , 1982 .

[18]  D. Kolb,et al.  Learning Styles and Learning Spaces: Enhancing Experiential Learning in Higher Education , 2005 .

[19]  A. Agresti,et al.  Categorical Data Analysis , 1991, International Encyclopedia of Statistical Science.

[20]  Regina Dittrich,et al.  A paired comparison approach for the analysis of sets of Likert-scale responses , 2007 .

[21]  Regina Dittrich,et al.  Modelling the effect of subject‐specific covariates in paired comparison studies with an application to university rankings , 2001 .

[22]  Achim Zeileis,et al.  Accounting for Individual Differences in Bradley-Terry Models by Means of Recursive Partitioning , 2011 .