[3] Coombs, C.H., 1964, A theory of data, New York: Wiley.

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1 Bibliography [1] Birnbaum, A., 1968, Some latent trait models and their use in inferring an examinee s ability, In F.M. Lord & M.R. Novick (Eds.), Statistical theories of mental test scores (pp ), Reading (Mass.) Addison-Wesley. [2] Bol, G.W., 1994, Implicational scaling in child language acquisition: The order of production of Dutch verb constructions, In M. Verrips & F. Wijnen (Eds.), Papers from the Dutch-German colloquium on language acquisition (Amsterdam Series in Child Language Development), Amsterdam: University of Amsterdam, Institute for General Linguistics.

2 [3] Coombs, C.H., 1964, A theory of data, New York: Wiley. [4] De Jong, A., Molenaar, I.W., 1987, An application of Mokken s model for stochastic cumulative scaling in psychiatric research, Journal of Psychiatric Research, 21, [5] De Koning, E., Sijtsma, K., Hamers, J.H.M., 2001, Comparison of four IRT models when analyzing two tests for inductive reasoning, Manuscript submitted for publication. [6] Dzhafarov, E.N., Gluhovsky, 2005, Notes on selective influence, probabilistic causality, and probabilistic dimensionality, Manuscript submitted for publication.

3 [7] Edwards, A.L., 1957, Techniques of attitude scale construction, New York: Appleton-Century-Crofts. [8] Green, B.F., 1954, Attitude measurement, In G. Lindzey (Ed.), Handbook of social psychology, volume I (pp ), Cambridge (Mass.): Addison-Wesley. [9] Guttman, L., 1944, A basis for scaling qualitative data, American Sociological Review, 9,

4 [10] Guttman, L., 1950, The basis for scalogram analysis, In S.A. Stouffer, L. Guttman, E.A. Suchman, P.F. Lazarsfeld, S.A. Star, & J.A. Clausen (Eds.), Measurement and prediction (pp ), Princeton, NJ: Princeton University Press. [11] Hambleton, R.K., Swaminathan, H., & Rogers, H.J., 1991, Fundamentals of item response theory, Newbury Park, CA: Sage Publications. [12] Kelderman, H., Rijkes, C.P.M., 1994, Loglinear multidimensional IRT models for polytomously scored items, Psychometrika, 59,

5 [13] Kingma, J., 1984, A comparison of four methods of scaling for the acquisition of early number concept, The Journal of General Psychology, 110, [14] Kingma, J., Loth, F.L., 1985, The validation of a developmental scale for seriation, Educational and Psychological Measurement, 45, [15] Kingma, J., Ten Vergert, E.M., 1985, A nonparametric scale analysis of the development of conservation, Applied Psychological Measurement, 9,

6 [16] Kraaikamp, H.J.M., 1992, Difficult roles. Psychometric research of the reliability and validity of the Groningen Social Restriction Scale for psychiatric patients, Ph.D. thesis, University of Groningen, The Netherlands. [17] Laros, J.A., Tellegen, P.J., 1991, Construction and validation of the SON-R 5 1/2 17, the Snijders-Oomen non-verbal intellegence test, Groningen, The Netherlands: Wolters-Noordhoff.

7 [18] Lazarsfeld, P.F., 1950, The logical and mathematical foundation of latent structure analysis, In S.A. Stouffer, L. Guttman, E.A. Suchman, P.F. Lazarsfeld, S.A. Star, & J.A. Clausen (Eds.), Measurement and prediction (pp ), Princeton, NJ: Princeton University Press. [19] Levine, M.V., 2003, Dimension in latent variable models, Journal of Mathematical Psychology, 47, [20] Lewin, K., 1951, Field theory in social science; selected theoretical papers, D. Cartwright (Ed.), New York: Harper & Row.

8 [21] Lewis, C., 1983, Bayesian inference for latent abilities, In S.B. Anderson & J.S. Helmick (Eds.), On educational testing (pp ), San Francisco: Jossey-Bass. [22] Matalon, B., 1965, L analyse hiérarchique, Paris: Gauthier-Villars, Mouton. [23] Mokken, R.J., 1971, A theory and procedure of scale analysis, The Hague, Mouton/Berlin: De Gruyter. [24] Mokken, R.J., Lewis, C., 1982, A nonparametric approach to the analysis of dichotomous item responses, Applied Psychological Measurement, 6,

9 [25] Rasch, G., 1960, Probabilistic models for some intelligence and attainment tests, (Studies in mathematical psychology I), Copenhagen: Nielsen & Lydiche (for Danmarks Paedagogiske Institut). [26] Reckase, M.D., 1997, A linear logistic multidimensional model for dichotomous item response data, In W.J. van der Linden, R.K. Hambleton (Eds.), Handbook of modern item response theory (pp ), New York: Springer. [27] Rivas Moya, T., 1999, Mokken scale analysis: An application to items of numerical inductive reasoning, Paper presented at the European Meeting of the Psychometric Society, Lueneburg, Germany.

10 [28] Sijtsma, K., Molenaar, I.W., 2002, Introduction to nonparametric item response theory, Thousand Oaks, CA: Sage Publications. [29] Sixtl, F., 1967, Messmethoden der Psychologie, Weinheim: Julius Beltz. [30] Torgerson, W.S., 1958, Theory and methods of scaling, New York: Wiley. [31] Verweij, A.C., Sijtsma, K., Koops, W., 1996, A Mokken scale for transitive reasoning suited for longitudinal research, International Journal of Behavioral Development, 19,

11 [32] Verweij, A.C., Sijtsma, K., Koops, W., 1999, An ordinal scale for transitive reasoning by means of a deductive strategy, International Journal of Behavioral Development, 23,

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