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Mokken Scale Analysis: Between the Guttman Scale and Parametric Item Response Theory

Published online by Cambridge University Press:  04 January 2017

Wijbrandt H. van Schuur
Wijbrandt H. van Schuur*
Affiliation:
Department of Sociology, University of Groningen, Grote Rozenstraat 31, 9712 TG Groningen, The Netherlands. e-mail: [email protected]
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Abstract

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This article introduces a model of ordinal unidimensional measurement known as Mokken scale analysis. Mokken scaling is based on principles of Item Response Theory (IRT) that originated in the Guttman scale. I compare the Mokken model with both Classical Test Theory (reliability or factor analysis) and parametric IRT models (especially with the one-parameter logistic model known as the Rasch model). Two nonparametric probabilistic versions of the Mokken model are described: the model of Monotone Homogeneity and the model of Double Monotonicity. I give procedures for dealing with both dichotomous and polytomous data, along with two scale analyses of data from the World Values Study that demonstrate the usefulness of the Mokken model.

Type
Research Article
Information
Political Analysis , Volume 11 , Issue 2 , Spring 2003 , pp. 139 - 163
Copyright
Copyright © Political Methodology Section of the American Political Science Association 2003 

References

Andrich, D. 1988. Rasch Models for Measurement. Newbury Park, CA: Sage.CrossRefGoogle Scholar
Andrich, D., and Douglas, G. A. 1977. “Reliability: Distinctions Between Item Consistency and Subject Separation Within the Simple Logistic Model.” Paper presented at the Annual Meeting of the American Educational Research Association, New York.Google Scholar
Bart, W. M., and Krus, D. J. 1973. “An Ordering Theoretic Method to Determine Hierarchies Among Items.” Educational and Psychological Measurement 33:291–300.Google Scholar
Birnbaum, A. 1968. “Some Latent Trait Models and Their Use in Inferring an Examinee's Ability.” In Statistical Theories of Mental Test Scores, eds. Lord, F. M. and Novick, R. Reading, MA: Addison-Wesley.Google Scholar
Carroll, J. B. 1945. “The Effect of Difficulty and Chance Success on Correlations Between Items or Between Tests.” Psychometrika 10:1–19.Google Scholar
Cingranelli, D. L., and Richards, D. L. 1999. “Measuring the Level, Pattern and Sequence of Government Respect for Physical Integrity Rights.” International Studies Quarterly 43:407–417.CrossRefGoogle Scholar
Coombs, C. H., and Lingoes, J. C. 1978. “Stochastic Cumulative Scales.” In Theory Construction and Data Analysis in the Behavioral Sciences, ed. Shye, S. San Francisco: Jossey-Bass, pp. 280–298.Google Scholar
Davenport, C. 1995. “Multidimensional Threat Perception and State Repression: An Inquiry Into Why States Apply Negative Sanctions.” American Journal of Political Science 39:683–713.CrossRefGoogle Scholar
Dayton, C. M., and MacReady, G. B. 1980. “A Scaling Model with Response Errors and Intrinsically Unscalable Respondents.” Psychometrika 45:343–356.Google Scholar
Embretson, S., and Reise, S. P. 2000. Item Response Theory for Psychologists. Mahwah, NJ: Lawrence Erlbaum.Google Scholar
Ferguson, G. A. 1941. “The Factorial Interpretation of Test Difficulty.” Psychometrika 6:323–330.Google Scholar
Ganter, B., and Wille, R. 1999. Formal Concept Analysis: Mathematical Foundations. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Guttman, L. 1950. “The Basis for Scalogram Analysis.” In Measurement and Prediction. Studies in Social Psychology in World War II, Vol. 4, eds. Stouffer, S. A. et al. Princeton, NJ: Princeton University Press, pp. 60–90.Google Scholar
Inglehart, R. 1997. Modernization and Postmodernization: Cultural, Economic and Political Change in 43 Countries. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Jacoby, W. G. 1994. “Public Attitudes Towards Government Spending.” American Journal of Political Science 38:336–361.CrossRefGoogle Scholar
Jacoby, W. G. 1995. “The Structure of Ideological Thinking in the American Electorate.” American Journal of Political Science 39:314–335.CrossRefGoogle Scholar
Kingma, J., and ten Vergert, E. 1985. “A Nonparametric Scale Analysis of the Development of Conservation.” Applied Psychological Measurement 9:375–387.CrossRefGoogle Scholar
Loevinger, J. 1948. “The Technique of Homogeneous Tests Compared with Some Aspects of ‘Scale Analysis’ and Factor Analysis.” Psychological Bulletin 45:507–530.Google Scholar
Meijer, R. R. 1994. Nonparametric Person Fit Analysis. Unpublished doctoral dissertation. Amsterdam: Free University.Google Scholar
Meijer, R. R., and Sijtsma, K. 2001. “Methodology Review: Evaluating Person Fit.” Applied Psychological Measurement 25:107–135.Google Scholar
Mokken, R. J. 1971. A Theory and Procedure of Scale Analysis with Applications in Political Research. New York: De Gruyter.CrossRefGoogle Scholar
Mokken, R. J. 1997. “Nonparametric Models for Dichotomous Responses.” In Handbook of Modern Item Response Theory, eds. van der Linden, W. J. and Hambleton, R. K. New York: Springer-Verlag, 351–367.CrossRefGoogle Scholar
Mokken, R. J., and Lewis, C. 1982. “A Nonparametric Approach to the Analysis of Dichotomous Item Responses.” Applied Psychological Measurement 6:417–430.CrossRefGoogle Scholar
Mokken, R. J., van Schuur, H. W., and Leeferink, A. J. 2001. “The Circles of Our Minds. A Nonparametric IRT Model for the Circumplex.” In Essays on item response theory, eds. Boomsma, A., van Duijn, M. A. J., and Snijders, T. A. B. New York: Springer-Verlag, pp. 339–356.CrossRefGoogle Scholar
Molenaar, I. W. 1973. “Simple Approximations to the Poisson, Binomial and Hypergeometrical Distributions.” Biometrics 29:403–407.Google Scholar
Molenaar, I. W. 1991. “A Weighted Loevinger H Coefficient Extending Mokken Scaling to Multicategory Items.” Kwantitatieve Methoden 12:97–117.Google Scholar
Molenaar, I. W. 1997a. “Lenient or Strict Application of IRT with an Eye on Practical Consequences.” In Applications of Latent Trait and Latent Class Models in the Social Sciences, eds. Rost, J. and Langeheine, R. Münster: Waxmann, pp. 38–49.Google Scholar
Molenaar, I. W. 1997b. “Nonparametric Models for Polytomous Responses.” In Handbook of Modern Item Response Theory, eds. van der Linden, W. J. and Hambleton, R. K. New York: Springer-Verlag, pp. 367–380.Google Scholar
Molenaar, I. W. and Sijtsma, K. 1988. “Mokken's Approach to Reliability Estimation Extended to Multicategory Items.” Kwantitatieve Methoden 9:115–126.Google Scholar
Molenaar, I. W., and Sijtsma, K. 2000. MSP5 for Windows. A Program for Mokken Scale Analysis for Polytomous Items. Groningen: ProGamma.Google Scholar
Niemöller, B., and van Schuur, W. H. 1983. “Stochastic Models for Unidimensional Scaling: Mokken and Rasch.” In Data Analysis and the Social Sciences, eds. McKay, D., Schofield, N., and Whiteley, P. London: Francis Pinter, pp. 120–170.Google Scholar
Post, W. J., and Snijders, T. A. B. 1993. “Nonparametric Unfolding Models for Dichotomous Data.” Methodika 7:130–156.Google Scholar
Rasch, G. 1960. Probabilistic Models for Some Intelligence and Attainment Tests. Copenhagen: Nielsen and Lydiche.Google Scholar
Richards, D. L., Gelleny, D. R., and Sacko, D. H. 2001. “Money with a Mean Streak? Foreign Economic Penetration and Government Respect for Human Rights in Developing Countries.” International Studies Quarterly 45:219–231.Google Scholar
Rosenbaum, P. R. 1984. “Testing the Conditional Independence and Monotonicity Assumptions of Item Response Theory.” Psychometrika 49:425–435.Google Scholar
Rosenbaum, P. R. 1987. “Comparing Item Characteristic Curves.” Psychometrika 52:217–233.Google Scholar
Samejima, F. 1969. “Estimation of Latent Ability Using a Response Pattern of Graded Scores.” Psychometrika Monograph 17:1–100.Google Scholar
Scarritt, J. R. 1996. “Measuring Political Change: The Quantity and Effectiveness of Electoral and Party Participation in the Zambian One-Party State, 1973-1991.” British Journal of Political Science 26:283–297.Google Scholar
Schneider, S. K., Jacoby, W. G., and Coggburn, J. D. 1997. “The Structure of Bureaucratic Decision Making in the American States.” Public Administration Review 57:240–249.Google Scholar
Schriever, B. F. 1985. Order Dependence. Unpublished doctoral dissertation. Amsterdam: Free University Press.Google Scholar
Sheridan, B., Andrich, D., and Luo, G. 2000. RUMM2010 Manual, Part 2: Extending RUMM2010. Duncraig, Western Australia: RUMM Laboratory.Google Scholar
Sheridan, B., Andrich, D., and Luo, G. 2001. RUMM2010 Manual, Part 1: Getting Started. Duncraig, Western Australia: RUMM Laboratory.Google Scholar
Shye, S. 1985. Multiple Scaling. Amsterdam: North Holland.Google Scholar
Sijtsma, K. 1998. “Beyond Mokken Scale Analysis.” In In Search of Structure. Essays in Social Science and Methodology, eds. Fennema, M., van der Eijk, C., and Schijf, H. Amsterdam: Het Spinhuis, pp. 29–44.Google Scholar
Sijtsma, K., and Molenaar, I. W. 1987. “Reliability of Test Scores in Nonparametric Item Response Theory.” Psychometrika 52:79–97.CrossRefGoogle Scholar
Sijtsma, K., and Molenaar, I. W. 2002. Introduction to Nonparametric Item Response Theory. Vol. 5 of Measurement Methods for the Social Sciences. Thousand Oaks, CA: Sage.Google Scholar
Stokman, F. N. 1977. Roll Calls and Sponsorship: A Methodological Analysis of Third World Group Formation in the United Nations. Leiden: Sijthoff.Google Scholar
Van Schuur, W. H. 1993. “Nonparametric Unfolding Models for Multicategory Data.” Political Analysis 4:41–74.Google Scholar
Van Schuur, W. H. 1997. “Nonparametric IRT Models for Dominance and Proximity Data.” In Objective Measurement: Theory into Practice, Vol. 4, eds. Wilson, M., Engelhard, G. Jr, and Draney, K. Greenwich, London: Ablex, pp. 313–331.Google Scholar
Van Schuur, W. H. 1998. “From Mokken to Mudfold and Back.” In In Search of Structure. Essays in Social Science and Methodology, eds. Fennema, M., van der Eijk, C., and Schijf, H. Amsterdam: Het Spinhuis, pp. 45–62.Google Scholar
Van Schuur, W. H., and Kiers, H. A. L. 1994. “Why Factor Analysis is Often the Wrong Model for Analyzing Bipolar Concepts, and What Model to Use Instead.” Applied Psychological Measurement 18:97–110.Google Scholar
Van Schuur, W. H., and Vis, J. C. P. M. 2002. “What Dutch Parliamentary Journalists Know About Politics.” Acta Politica 35:196–227.Google Scholar
Zinn, F. D., Henderson, D. A., Nystuen, J. D., and Drake, W. D. 1992. “A Stochastic Cumulative Scaling Method Applied to Measuring Wealth in Indonesian Villages.” Environment and Planning A 24:1155–1166.Google Scholar
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