An Algorithm for Converting Ordinal Scale Measurement Data to Interval/Ratio Scale

Educational and Psychological Measurement

Volumn 70, Issue 1, 2010, Pages 74-90

  Granberg Rademacker, J Scott ^a  

^a MINNESOTA STATE UNIVERSITY   (United States)

Author keywords

data measurement; Markov chain Monte Carlo; measurement theory

Indexed keywords

EID: 84993820450     PISSN: 00131644     EISSN: None     Source Type: Journal    
DOI: 10.1177/0013164409344532     Document Type: Article

References (40)

1. Agresti, A. (2001). Analysis of ordinal categorical data. New York: Wiley.
2. Carpini, M.X.D., & Keeter, S. (1993). Measuring political knowledge: Putting first things first. American Journal of Political Science, 37, 1179-1206.
3. Charette, M.F., & Meng, R. (1998). The determinants of literacy and numeracy, and the effect of literacy and numeracy on labour market outcomes. Canadian Journal of Economics/ Revue Canadienne d'Economique, 31, 495-517.
4. Converse, J.M., & Presser, S. (1986). Survey questions: Handcrafting the standardized quesionnaire. Beverly Hills, CA: Sage.
5. Davenport, C., & Armstrong, D. (2004). Democracy and the violation of human rights: A statistical analysis from 1976 to 1996. American Journal of Political Science, 48, 538-554.
6. Eaves, L., Erkanli, A., Silberg, J., Angold, A., Maes, H.H., & Foley, D. (2005). Application of Bayesian inference using Gibbs sampling to item-response theory modeling of multi-symptom genetic data. Behavior Genetics, 35, 765-780.
7. Embretson, S.E., & Reise, S.P. (2000). Item response theory for psychologists. Mahwah, NJ: Lawrence Erlbaum.
8. Fischer, G.H. (1995). Derivations of the Rasch model. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 15-38). New York: Springer-Verlag.
9. Fowler, F., Jr. (2002). Survey research methods. Thousand Oaks, CA: Sage.
10. Gaito, J. (1980). Measurement scales and statistics: Resurgence of an old misconception. Psychological Bulletin, 87, 564-567.
11. Gill, J. (2002). Bayesian methods: A social and behavioral sciences approach. Boca Raton, FL: Chapman & Hall/CRC.
12. Goren, P. (2004). Political sophistication and policy reasoning: A reconsideration. American Journal of Political Science, 48, 462-478.
13. Hambleton, R.K., & Swaminathan, H. (1985). Item response theory: Principles and applications. Boston: Kluwer-Nijhoff.
14. Hand, D.J. (1996). Statistics and the theory of measurement. Journal of the Royal Statistical Society, Series A, 159, 445-492.
15. Harwell, M.R., & Gatti, G.G. (2001). Rescaling ordinal data to interval data in educational research. Review of Educational Research, 71, 105-131.
16. Iman, R.L., & Conover, W.J. (1979). The use of the rank transform in regression. Technometrics, 21, 499-509.
17. Jacoby, W. (1991). Data theory and dimensional analysis. Newbury Park, CA: Sage.
18. Jacoby, W. (1995). The structure of ideological thinking in the American electorate. American Journal of Political Science, 39, 314-335.
19. Jacoby, W. (1999). Levels of measurement and political research: An optimistic view. American Journal of Political Science, 43, 271-301.
20. Jacoby, W. (2000). Issue framing and public opinion on government spending. American Journal of Political Science, 44, 750-767.
21. Jones, B.S., & Sobel, M.E. (2000). Modeling direction and intensity in semantically balanced ordinal scales: An assessment of congressional incumbent approval. American Journal of Political Science, 44, 174-185.
22. Kalton, G. (1983). Introduction to survey sampling. Beverly Hills, CA: Sage.
23. King, G., Murray, C.J.L., Salomon, J.A., & Tandon, A. (2003). Enhancing the validity of cross-cultural comparability of measurement in survey research. American Political Science Review, 97, 567-583.
24. Kruskal, J.B. (1964). Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115-129.
25. Leonard, T. (2000). A course in categorical data analysis. Boca Raton, FL: Chapman & Hall/ CRC.
26. Mondak, J.J. (2001). Developing valid knowledge scales. American Journal of Political Science, 45, 224-238.
27. Narens, L., & Luce, R.D. (1986). Measurement: The theory of numerical assignments. Psychological Bulletin, 99, 166-180.
28. Przeworski, A., & Teune, H. (1966). Equivalence in cross-national research. Public Opinion Quarterly, 30, 551-568.
29. Stevens, S.S. (1946). On the theory of scales of measurement. Science, 103, 677-680.
30. Stevens, S.S. (1951). Mathematics, measurement, and psychphysics. In S. S. Stevens (Ed.), Handbook of experimental psychology (pp. 1-49). New York: Wiley.
31. Stevens, S.S. (1966). A metric for the social consensus. Science, 151, 530-541.
32. Stevens, S.S. (1968). Measurement, statistics, and the schemapiric view. Science, 161, 849-856.
33. Thissen, D., Steinberg, L., & Wainer, H. (1993). Detection of differential item functioning using the parameters of the item response models. In P. W. Holland & H. Wainer (Eds.), Differential item functioning (pp. 67-114). Hillsdale, NJ: Lawrence Erlbaum.
34. Tillinghast, D.S. (1980). Direct magnitude estimate scales in public opinion surveys. Public Opinion Quarterly, 44, 377-384.
35. Townsend, J.T., & Ashby, F.G. (1984). Measurement scales and statistics: The misconception misconcieved. Psychological Bulletin, 96, 394-401.
36. Tukey, J.W. (1961). Data analysis and behavioral science or learning to bear the quantitative man's burden by shunning badmandments. In L. V. Jones (Ed.), The collected works of John W. Tukey (Vol. 3, pp. 187-389). Belmont, CA: Wadsworth.
37. Velleman, P.F., & Wilkinson, L. (1993). Nominal, ordinal, interval, and ratio typologies are misleading. American Statistician, 47, 65-72.
38. Weisberg, H.F., Krosnick, J.A., & Bowen, B.D. (1996). An Introduction to survey research, polling, and data analysis. Thousand Oaks, CA: Sage.
39. Wilson, T.P. (1971). Critique of ordinal variables. Social Forces, 49, 432-444.
40. Zumbo, B.D., & Zimmerman, D.W. (1993). Is the selection of statistical methods governed by level of measurement? Canadian Psychology, 34, 390-400.