Hostname: page-component-6898cfcb55-zkb6p Total loading time: 0 Render date: 2026-11-11T11:25:04.013Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonparametric Unidimensional Unfolding for Multicategory Data

Published online by Cambridge University Press:  04 January 2017

Wijbrandt H. van Schuur
Get accessRights & Permissions [Opens in a new window]

Abstract

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 analogous 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 presidential candidates by Democratic and Republican party activists in Missouri.

Information

Type
Research Article
Information
Political Analysis , Volume 4 , 1992, pp. 41 - 74
Copyright
Copyright © by the University of Michigan 1993 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Andrich, D. 1988. “The Application of an Unfolding Model of the PIRT Type for the Measurement of Attitude.” Applied Psychological Measurement 12: 33–51.CrossRefGoogle Scholar
Böckenholt, V., and Böckenholt, I. 1990. “Modeling Individual Differences in Unfolding Preference Data.” Applied Psychological Measurement 14: 257–69.Google Scholar
Brady, H. E. 1990. ‘Traits versus Issues: Factor versus Ideal-Point Analysis of Candidate Thermometer Ratings.” Political Analysis 2: 97–129.Google Scholar
Coombs, C. H. 1964. A Theory of Data. New York: Wiley.Google Scholar
Coombs, C. H., and Kao, R. C. 1960. “On a Connection between Factor Analysis and Multidimensional Unfolding.” Psychometrika 25: 219–31.CrossRefGoogle Scholar
Coombs, C. H., and Smith, J. E. K. 1973. “On the Detection of Structure in Attitudes and Developmental Processes.” Psychological Review 5: 337–51.Google Scholar
Croon, M. 1990. “Latent Class Analysis with Ordered Latent Classes.” British Journal of Mathematical and Statistical Psychology 43: 171–92.Google Scholar
Davison, M. 1977. “On a Metric, Unidimensional Unfolding Model for Attitudinal and Developmental Data.” Psychometrika 42: 523–48.CrossRefGoogle Scholar
DeSarbo, W. A., and Hoffman, D. L. 1986. “The Simple and Weighted Thresholds Model for the Spatial Representation of Binary Choice Data.” Applied Psychological Measurement 10: 247–64.Google Scholar
Fischer, G. 1974. Einführung in die Theorie Psychologischer Tests. Vienna: Huber Verlag.Google Scholar
Formann, A. K. 1988. “Latent Class Analysis Models for Nonmonotone Dichotomous Items.” Psychometrika 53: 45–62.Google Scholar
Guttman, L. 1950. “The Basis for Scalogram Analysis.” In Measurement and Prediction, ed. Stouffer, S. A., Guttman, L., Suchman, E. A., Lazarsfeld, P. F., Star, S. A., and Clausen, J. A., 216–57. Princeton: Princeton University Press.Google Scholar
Hoijtink, H. 1990. “A Latent Trait Model for Dichotomous Choice Data.” Psychometrika 55: 641–56.Google Scholar
Jacoby, W. G. 1991. Data Theory and Dimensional Analysis. Sage University Papers Series on Quantitative Applications in the Social Sciences, no. 07-078. Newbury Park, Calif.: Sage.Google Scholar
Leik, R. K., and Matthews, M. 1968. “A Scale for Developmental Processes.” American Sociological Review 54: 62–75.Google Scholar
Loevinger, J. 1948. “The Technique of Homogeneous Tests Compared with Some Aspects of ‘Scale Analysis’ and Factor Analysis.” Psychological Bulletin 45: 507–30.CrossRefGoogle Scholar
McIver, J. P., and Carmines, E. G. 1981. Unidimensional Scaling. Sage University Papers Series on Quantitative Applications in the Social Sciences, no. 07-024. Beverly Hills and London: Sage.Google Scholar
Masters, G. A. 1982. “Rasch Model for Partial Credit Scoring.” Psychometrika 47: 149–74.Google Scholar
Mokken, R. J. 1970. A Theory and Procedure of Scale Analysis with Applications in Political Research. New York and Berlin: De Gruyter (Mouton).Google Scholar
Mokken, R. J., and Lewis, C. 1982. “A Nonparametric Approach to the Analysis of Dichotomous Item Responses.” Applied Psychological Measurement 6: 417–30.Google Scholar
Mokken, R. J., Lewis, C., and Sijtsma, K. 1986. “Rejoinder to ‘The Mokken Scale: A Critical Discussion.’” Applied Psychological Measurement 10: 279–85.Google Scholar
Molenaar, I. W. 1982. “Mokken Scaling Revisited.” Kwantitatieve Methoden 3: 145–64.Google Scholar
Poole, K. T. 1984. “Least Squares Metric Unidimensional Unfolding.” Psychometrika 49: 311–23.Google Scholar
Post, W. J. 1988. “Distribution of the Observed Number of Errors as Defined in the MUDFOLD Model under Statistical Independence in the Pick/Any Case.” In The Many Faces of Multivariate Analysis: Proceedings of the 1988 SMABS Conference, ed. Jansen, M. G. H. and van Schuur, W. H., 2: 255–69. Groningen: RION.Google Scholar
Post, W. J. 1992. Nonparametric Unfolding Models: A Latent Structure Approach. Leiden: DSWO Press.Google Scholar
Rapoport, R. B., Abramowitz, A. I., and McGlennon, J. 1986. Life of the Parties. Lexington: University Press of Kentucky.Google Scholar
Rasch, G. 1960. Probabilistic Models for Some Intelligence and Attainment Tests. Copenhagen: Nielsen and Lydiche.Google Scholar
Reif, K., Cayrol, R., and Niedermayer, O. 1980. “National Political Parties’ Middle Level Elites and European Integration.” European Journal of Political Research 8: 91–112.Google Scholar
Roskam, E. E., van den Wollenberg, A. L., and Jansen, P. G. W. 1986. “The Mokken Scale: A Critical Discussion.” Applied Psychological Measurement 10: 165–77.Google Scholar
Ross, J., and Cliff, N. 1964. “A Generalization of the Interpoint Distance Model.” Psychometrika 29: 167–76.CrossRefGoogle Scholar
Rost, J. 1988. “Rating Scale Analysis with Latent Class Models.” Psychometrika 53: 327–48.CrossRefGoogle Scholar
Samejima, F. 1969. “Estimation of Latent Ability Using a Response Pattern of Graded Scores.” Psychometrika Monograph Supplement 4: 1–100.Google Scholar
Sijtsma, K., Debets, P., and Molenaar, I. W. 1990. “Mokken Scale Analysis for Polychotomous Items: Theory, a Computer Program, and an Empirical Application.” Quality and Quantity 24: 173–88.Google Scholar
Takane, Y., Young, F. W., and De Leeuw, J. 1977. “Nonmetric Individual Differences Multidimensional Scaling: An Alternating Least Squares Method with Optimal Scaling Features.” Psychometrika 42: 7–67.Google Scholar
Thissen, D., and Steinberg, L. 1984. “A Model for Multiple Choice Items.” Psychometrika 49: 501–19.Google Scholar
Van Blokland-Vogelesang, R. 1991. Unfolding and Group Consensus Ranking for Individual Preferences. Leiden: DSWO Press.Google Scholar
Van Schuur, H. 1984. Structure in Political Beliefs: A New Model for Stochastic Unfolding with Application to European Party Activists. Amsterdam: CT Press.Google Scholar
Van Schuur, W. H. 1987. “Constraint in European Party Activists’ Sympathy Scores for Interest Groups: The Left-Right Dimension as Dominant Structuring Principle.” European Journal of Political Research 15: 347–62.Google Scholar
Van Schuur, W. H. 1988. “Stochastic Unfolding.” In Sociometric Research, vol. 1, Data Collection and Scaling, ed. Saris, W. E. and Gallhofer, I. N., 137–57. London: Macmillan.Google Scholar
Van Schuur, W. H. 1989. “Unfolding the German Political Parties.” In Advances in Psychology, vol. 60, New Developments in Psychological Choice Modeling, ed. De Soete, G., Feger, H., and Klauer, K. C., 259–90. Amsterdam: North-Holland.Google Scholar