Nonparametric Unidimensional Unfolding for Multicategory Data

This article describes a nonparametric unidimensional unfolding model for dichotomous data (van Schuur 1984) and shows how it can be extended to multicategory data such as Likert-type rating data. This extension is analo gous to Molenaar's (1982) application of Mokken's (1970) nonparametric unidimensional cumulative scaling model. The model is illustrated with an analysis of five-point preference ratings given in 1980 to five political presi dential candidates by Democratic and Republican party activists in Missouri. . It has something to do with numbers . . . —"The Politics of Goofing Off," a review of the 1991 APSA Meeting Washington Post, August 31, 1991

[1]  Herbert Hoijtink,et al.  A latent trait model for dichotomous choice data , 1990 .

[2]  Charles Lewis,et al.  A Nonparametric Approach to the Analysis of Dichotomous Item Responses , 1982 .

[3]  Klaas Sijtsma,et al.  Rejoinder to "The Mokken Scale: A Critical Discussion" , 1986 .

[4]  E. Roskam,et al.  The Mokken Scale: A Critical Discussion , 1986 .

[5]  U. Böckenholt,et al.  Modeling Individual Differences in Unfolding Preference Data: A Restricted Latent Class Approach , 1990 .

[6]  Henry E. Brady.  Traits versus Issues: Factor versus Ideal-Point Analysis of Candidate Thermometer Ratings , 1990, Political Analysis.

[7]  Richard C. W. Kao,et al.  On a connection between factor analysis and multidimensional unfolding , 1960 .

[8]  Clyde H. Coombs,et al.  On the detection of structure in attitudes and developmental processes. , 1973 .

[9]  C. Coombs.  A theory of data. , 1965, Psychology Review.

[10]  F. Samejima.  Estimation of latent ability using a response pattern of graded scores , 1968 .

[11]  Anton K. Formann,et al.  Latent class models for nonmonotone dichotomous items , 1988 .

[12]  R. J. Mokken,et al.  A Theory and Procedure of Scale Analysis: With Applications in Political Research , 1971 .

[13]  G. Masters.  A rasch model for partial credit scoring , 1982 .

[14]  Klaas Sijtsma,et al.  Mokken scale analysis for polychotomous items: theory, a computer program and an empirical application , 1990 .

[15]  David Thissen,et al.  A response model for multiple choice items , 1984 .

[16]  Marcel A. Croon,et al.  Latent class analysis with ordered latent classe , 1990 .

[17]  Forrest W. Young,et al.  Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features , 1977 .

[18]  J. Loevinger,et al.  The technic of homogeneous tests compared with some aspects of scale analysis and factor analysis. , 1948, Psychological bulletin.

[19]  William G. Jacoby.  Data Theory and Dimensional Analysis , 1991 .

[20]  Wendelina Jantina Post.  Nonparametric unfolding models. A latent structure approach. , 1992 .

[21]  Mark L. Davison,et al.  On a metric, unidimensional unfolding model for attitudinal and developmental data , 1977 .

[22]  Georg Rasch,et al.  Probabilistic Models for Some Intelligence and Attainment Tests , 1981, The SAGE Encyclopedia of Research Design.

[23]  David Andrich,et al.  The Application of an Unfolding Model of the PIRT Type to the Measurement of Attitude , 1988 .

[24]  Rian A. W. van Blokland-Vogelesang,et al.  Unfolding and group consensus ranking for individual preferences , 1991 .

[25]  Jürgen Rost,et al.  Rating scale analysis with latent class models , 1988 .

[26]  N. Cliff,et al.  A generalization of the interpoint distance model , 1964 .

[27]  Keith T. Poole.  Least squares metric, unidimensional unfolding , 1984 .

[28]  Wayne S. DeSarbo,et al.  Simple and Weighted Unfolding Threshold Models for the Spatial Representation of Binary Choice Data , 1986 .

[29]  Hendrik van Schuur.  Sructure in political beliefs. A new model for Stochastic Unfolding with Application to European Party Activists , 1984 .