Latent Class Models for the Analysis of Rankings

In this papers several latent class models for the analysis of rank order data are developed and discussed. These models try to accommodate the rationale of individual choice models to the situation in which a large number of respondents is sampled from a non-homogeneous population. By considering these individual choice models as statistical error theories, these models may be seen to fall within the domain of general latent structure analysis and as such, they may provide a viable alternative to the more traditional scaling methods for the analysis of rankings.

[1]  John I. Yellott,et al.  GENERALIZED THURSTONE MODELS FOR RANKING - EQUIVALENCE AND REVERSIBILITY , 1980 .

[2]  R. Beaver Weighted Least-Squares Analysis of Several Univariate Bradley-Terry Models , 1977 .

[3]  A. Mattenklott A Stochastic Model for Paired Comparisons of Social Stimuli. Mimeograph Series No. 81-2. , 1981 .

[4]  R. Redner,et al.  Mixture densities, maximum likelihood, and the EM algorithm , 1984 .

[5]  J. Yellott The relationship between Luce's Choice Axiom, Thurstone's Theory of Comparative Judgment, and the double exponential distribution , 1977 .

[6]  H. D. Block,et al.  Random Orderings and Stochastic Theories of Responses (1960) , 1959 .

[7]  Ralph A. Bradley,et al.  RANKING IN TRIPLE COMPARISONS , 1959 .

[8]  R. Plackett The Analysis of Permutations , 1975 .

[9]  P. Bentler,et al.  Significance Tests and Goodness of Fit in the Analysis of Covariance Structures , 1980 .

[10]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS , 1952 .

[11]  E. Zermelo Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung , 1929 .

[12]  Thomas Jech The Ranking of Incomplete Tournaments: A Mathematician's Guide to Popular Sports , 1983 .

[13]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS THE METHOD OF PAIRED COMPARISONS , 1952 .

[14]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

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

[16]  R. A. Bradley Another interpretation of a model for paired comparisons , 1965, Psychometrika.

[17]  K. Jöreskog Structural analysis of covariance and correlation matrices , 1978 .