The Legacies of R. A. Fisher and K. Pearson in the Application of the Polytomous Rasch Model for Assessing the Empirical Ordering of Categories

Educational and Psychological Measurement

Volumn 73, Issue 4, 2013, Pages 553-580

  Andrich, David ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

empirical category order; ordered category formats; partial credit; polytomous Rasch model; rating scale

Indexed keywords

EID: 84879512438     PISSN: 00131644     EISSN: 15523888     Source Type: Journal    
DOI: 10.1177/0013164413477107     Document Type: Article

References (62)

1. Adams R. J.,Wu M. L.,Wilson M.The Rasch rating model and the disordered threshold controversy.Educational and Psychological Measurement. 2012;72:547-573.
2. Andersen E. B.Sufficient statistics and latent trait models.Psychometrika. 1977;42:69-81.
3. Andersen E. B.,Wøhlk L.Lecture notes in statistics: Vol. 157. Essays in item response theory. Boomsma A.van Duijn M. A. J.Sniders T. A. B., ed. New York, NY: Springer; 2001:3-24.
4. Anderson J. A.Regression and ordered categorical variables.Journal of the Royal Statistical Society Series B. 1984;46:1-30.
5. Andrich D.A rating formulation for ordered response categories.Psychometrika. 1978;43:561-574.
6. Andrich D.A model for contingency tables having an ordered response classification.Biometrics. 1979;35:403-415.
7. Andrich D.Invited contribution to the discussion on: Regression models for ordinal data, P. McCullagh.Journal of the Royal Statistical Society Series B. 1980;42:135.
8. Andrich D.Distinctive and incompatible properties of two common classes of IRT models for graded responses.Applied Psychological Measurement. 1995a;19:101-119.
9. Andrich D.Further remarks on the non-dichotomization of graded responses.Psychometrika. 1995b;60:37-46.
10. Andrich D.Models for measurement, precision and the non-dichotomization of graded responses.Psychometrika. 1995c;60:7-26.
11. Andrich D.Analysis of categorical variables in developmental research. von Eye A.Clogg C. C., ed. Orlando, FL: Academic Press; 1996:3-35.
12. Andrich D.Controversy and the Rasch model: A characteristic of incompatible paradigms?.Medical Care. 2004;42:7-16.
13. Andrich D.An expanded derivation of the threshold structure of the polytomous Rasch rating model which dispels any "threshold disorder controversy".Educational and Psychological Measurement. 2013;73:78-124.
14. Andrich D.,de Jong J. H. A. L.,Sheridan B. E.Applications of latent trait and latent class models in the social sciences. Rost J.Langeheine R., ed. GMBH: Münster, Germany: Waxmann Verlag; 1997:58-68.
15. AndrichD.StylesI. M. (2004). Final report on the psychometric analysis of the Early Development Instrument (EDI) using the Rasch model: A technical paper commissioned for the development of the Australian Early Development Instrument (AEDI). Retrieved from http://www.rch.org.au/aedi/studies/index.cfm?doc_id=14792.
16. Bock R. D.Multivariate statistical methods in behavioral research. New York, NY: McGraw-Hill; 1975:.
17. Bock R. D.,Jones L. V.The measurement and prediction of judgment and choice. San Francisco, CA: Holden Day; 1968:.
18. Bradley R. A.,Katti S. K.Optimal scaling for ordered categories.Psychometrika. 1962;27:355-374.
19. Divgi D. R.Does the Rasch model really work for multiple choice items? Not if you look closely.Journal of Educational Measurement. 1986;23:283-298.
20. Dubois B.,Burns J. A.An analysis of the meaning of the question mark response category in attitude scales.Educational and Psychological Measurement. 1975;35:869-884.
21. Edwards A. L.,Thurstone L. L.An internal consistency check for scale values determined by the method of successive intervals.Psychometrika. 1952;17:169-180.
22. Embretson S. E.,Reise S. P.Item response theory for psychologists. London, England: Erlbaum; 2000:.
23. Fisher R. A.Statistical methods for research workers. Edinburgh, Scotland: Oliver & Boyd; 1925:.
24. Fisher R. A.Statistical methods for research workers. 1934a). Statistical methods for research workers (5th ed.). Edinburgh, Scotland: Oliver & Boyd.Edinburgh, Scotland: Oliver & Boyd; 1934a:.
25. Fisher R. A.Two new properties of mathematical likelihood.Proceedings of the Royal Society A. 1934b;144:285-307.
26. Fisher R. A.The design of experiments. Oxford, England: Oliver & Boyd; 1935:.
27. Fisher R.A.Statistical methods for research workers. 1958). Statistical methods for research workers (13th ed.). New York, NY: Hafner.New York, NY: Hafner; 1958:.
28. Fisher Box J.R. A. Fisher: The life of a scientist. New York, NY: Wiley; 1978:.
29. Glas C. A. W.,Verhelst N. D.Extensions of the partial credit model.Psychometrika. 1989;54:635-659.
30. Goodman L. A.Sociological methodology. Leinhardt S., ed. San Francisco, CA: Jossey-Bass; 1981:193-239.
31. Hambleton R. K.Emergence of item response modeling in instrument development and data analysis.Medical Care. 2000;38:II-28-II-42.
32. Jansen P. G. W.,Roskam E. E.Latent trait models and dichotomization of graded responses.Psychometrika. 1986;51:69-91.
33. Koch G. G.Invited contribution to the discussion on regression models for ordinal data, P. McCullagh.Journal of the Royal Statistical Society Series B. 1980;42:137.
34. Kuhn T. S.The function of measurement in modern physical science.Isis. 1961;52:161-190.
35. Kuhn T. S.The structure of scientific revolutions. 1970). The structure of scientific revolutions (2nd ed., enlarged.) Chicago, IL: University of Chicago Press.Chicago, IL: University of Chicago Press; 1970:.
36. Likert R.A technique for the measurement of attitudes.Archives of Psychology. 1932;140:5-55.
37. Linacre J. M.Investigating rating scale category utility.Journal of Outcome Measurement. 1999;3:103-122.
38. Luo G.The relationship between the rating scale and partial credit models and the implication of disordered thresholds of the Rasch models for polytomous responses.Journal of Applied Measurement. 2005;6:443-455.
39. MacKenzie D. A.Statistics in Britain, 1865-1930. Edinburgh, Scotland: Edinburgh University Press; 1981:.
40. MagnelloM. E. (2005-2006). Karl Pearson and the origins of modern statistics: An elastician becomes a statistician. Rutherford Journal-The New Zealand Journal for the History and Philosophy of Science and Technology, 1. Retrieved from http://www.rutherfordjournal.org/current.html.
41. Masters G. N.A Rasch model for partial credit scoring.Psychometrika. 1982;47:149-174.
42. Masters G. N.,Wright B. D.Handbook of item response theory. van der Linden W. J.Hambleton R. K., ed. New York, NY: Springer; 1997:101-121.
43. McCullagh P.Regression models for ordinal data.Journal of the Royal Statistical Society Series B. 1980;42:109-142.
44. Mellenbergh G. J.Conceptual notes on models for discrete polytomous item responses.Applied Psychological Measurement. 1995;19:91-100.
45. Molenaar I. W.Item steps. Groningen, Netherlands: University of Groningen; 1983:.
46. Norton B. J.Karl Pearson and statistics: The social origins of scientific innovation.Social Studies of Science. 1978;8 (3): 3-34.
47. Ostini R.,Nering M. L.Polytomous item response models. Thousand Oaks, CA: Sage; 2006:.
48. RaschG. (1960). Probabilistic models for some intelligence and attainment tests (Reprint, with Foreword and Afterword by B. D. Wright, Chicago, IL: University of Chicago Press, 1980). Copenhagen, Denmark: Danmarks Paedogogiske Institut. Available from www.rasch.org/books.htm.
49. Rasch G.On general laws and the meaning of measurement in psychology. Proceedings of the fourth Berkeley Symposium on mathematical statistics and probability; 1961Berkeley: University of California Press; 1961. 321.
50. Rasch G.On specific objectivity: An attempt at formalising the request for generality and validity of scientific statements.Danish Yearbook of Philosophy. 1977;14:58-94.
51. Rasch G.Readings in mathematical social science. Lazarsfeld P. F.Henry N. W., ed. Chicago, IL: Science Research Associates; 1966:89-108.
52. Rasch G.Laesoe, Denmark:; 1979:.
53. Raven J. C.Matrix tests.Mental Health. 1940;1:10-18.
54. Roskam E. E.Graded responses and joining categories: A rejoinder to Andrich's "Models for measurement, precision, and the non-dichotomization of graded responses".Psychometrika. 1995;60:27-35.
55. SamejimaF. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometric Monographs, 34(2, No. 17). Retrieved from http://www.psychometrika.org/journal/online/MN17.pdf.
56. Samejima F.Handbook of modern item response theory. Van der Linden W. J.Hambleton R. K., ed. New York, NY: Springer; 1997:139-152.
57. Thissen D.,Steinberg L.A taxonomy of item response models.Psychometrika. 1986;51:567-577.
58. Von Davier M.,Rost J.Rasch models: Foundations, recent developments, and applications. Fischer G. H.Molenaar I. W., ed. New York, NY: Springer; 1995:371-379.
59. Wilson M.Constructing measures. New York, NY: Psychology Press; 2005:.
60. Wøhlk Olsen L.Essays on Georg Rasch and his contributions to statistics. Copenhagen, Denmark: University of Copenhagen, Institute of Economics; 2003:.
61. Wright B. D.,Masters G. N.Rating scale analysis: Rasch measurement. Chicago, IL: MESA Press; 1982:.
62. Zhu W.A confirmatory study of Rasch-based optimal categorization of a rating scale.Journal of Applied Measurement. 2003;3:1-15.