Abstract
The item response theory (IRT) also known as latent trait theory, is used for the development, evaluation and administration of standardized measurements; it is widely used in the areas of psychology and education. This theory was developed and expanded for over 50 years and has contributed to the development of measurement scales of latent traits. This paper presents the basic and fundamental concepts of this IRT and a practical example of the construction of scales is proposed to illustrate the feasibility, advantages and validity of IRT through a known measurement, the height. The results obtained with the practical application of IRT confirm its effectiveness in the evaluation of latent traits.
Similar content being viewed by others
References
Allen M.J., Yen W.M.: Introduction to Measurement Theory. Waveland Press, Long Grove (2002)
Andrade, D.F., Tavares, H.R., Valle, R.C.: Teoria de Resposta ao Item: conceitos e aplicações. Associação Brasileira de Estatística (ABE), 4° SINAPE (2000)
Andrich D.: A rating formulation for ordered response categories. Psychometrika 43, 561–573 (1978a)
Andrich D.: Application of a psychometric rating model to ordered categories, which are scored with successive integers. Appl. Psychol. Measur. 2, 581–594 (1978b)
Andrich D.: A general hyperbolic cosine latent trait model for unfolding polytomous responses: Reconciling Thurstone and Likert methodologies. Br. J. Math. Stat. Psychol. 49, 347–365 (1996)
Andrich D., Luo G.: A hyperbolic cosine latent trait model for unfolding dichotomous single-stimulus responses. Appl. Psychol. Measur. 17, 253–276 (1993)
Andrich, D., Luo, G.: RUMMFOLDTM for WindowsTM, A Program for Unfolding Pairwise Preferences, Computer Program. Social Measurement Laboratory, Murdoch University, Murdoch (1998)
Babbie E.: The Basics of Social Research. Wadsworth Publishing, Belmont (2005)
Baker, F.B.: The Basis of Item Response Theory, 2nd edn. ERIC Clearinghouse on Assessment and Evaluation, College Park (2001). http://edres.org/irt/
Beaton A.E., Allen N.L.: Interpreting scales through scale anchoring. J. Educ. Stat. 17, 191–204 (1999)
Bock R.D.: Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika 37, 29–51 (1972)
Bock R.D., Aitkin M.: Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika 46, 443–459 (1981)
Bock R.D., Lieberman M.: Fitting a response model for n dichotomously scored items. Psychometrika 35, 179–197 (1970)
Coombs C.H.: A Theory of Data. Wiley, New York (1964)
de Ayala R.J.: The Theory and Practice of Item Response Theory. The Guilford Press, New York (2009)
Drasgow F., Levine M.V., Tsien S.: Fitting polytomous item response theory models to multiple-choice tests. Appl. Psychol. Measur. 19, 143–165 (1995)
Embretson S., Reise S.P.: Item Response Theory for Psychologists. Lawrence Erlbaum Associates, Inc., Mahwah (2000)
Flapper S.D.P., Fortuin L., Toop P.P.M.: Towards consistent performance management systems. Int. J. Oper. Prod. Manag. 16(7), 27–37 (1996)
Greer S.A.: The Logic of Social Inquiry. Aldine Pub, Chicago (1969)
Hambleton R.K., Swaminathan H.: Item Response Theory: Principles and Applications. Kluwer-Nijhoff, Boston (1985)
Hambleton R.K., Swaminathan H., Rogers H.J.: Fundamentals of Item Response Theory. Sage, Newbury Park (1991)
Hancock G.R.: Structural equation modeling methods of hypothesis testing of latent variable means. Measur. Eval. Couns. Dev. 30, 91–105 (1997)
Hofmans J., Theuns P., Van Acker F.: Combining quality and quantity. A psychometric evaluation of the self-anchoring scale. Qual. Quant. 43, 703–716 (2009)
Hoijtink H.: A latent trait model for dichotomous choice data. Psychometrika 55, 641–656 (1990)
Hoijtink H.: The measurement of latent traits by proximity items. Appl. Psychol. Measur. 15, 153–169 (1991)
Hoyle R.H.: Introduction to the special section: structural equation modeling in clinical research. Special section: structural equation modeling in clinical research. J. Consult. Clin. Psychol. 62(3), 427–428 (1994)
Hoyle R.H.: Structural equation modeling: Concepts, issues, and applications. Sage, Thousand Oaks (1995)
Khurshid A., Sahai H.: Scales of measurements: an introduction and a selected bibliography. Qual. Quant. 27(3), 303–324 (1993)
Kingston N., Dorans N.: The analysis of item-ability regressions: an exploratory IRT model fit tool. Appl. Psychol. Measur. 9, 281–288 (1985)
Kolen M.J., Brennan R.L.: Test Equating. Springer, New York (1995)
Lalla M., Facchinetti G., Mastroleo G.: Ordinal scales and fuzzy set systems to measure agreement: an application to the evaluation of teaching activity. Qual. Quant. 38, 577–601 (2004)
Lawley D.N.: On problems connected with item selection and test construction. Proc. R. Soc. Edinb. 61, 273–287 (1943)
Lazarsfeld, P.F.: In: Stouffer, S.A., et al. (eds.) Studies in Social Psychology in World War II, vol. 4: Measurement and Prediction, chaps. 10 and 11. Princeton University Press, Princeton (1950)
Lin T.H.: Identifying optimal items in quality of life assessment. Qual. Quant. 41, 661–672 (2007)
Lord F.M.: A Theory of Test Scores. Psychometric Monograph 7. Psychometric Society, New York (1952)
Lord F.M.: Applications of Item Response Theory to Practical Testing Problems. Erlbaum, Hillsdale (1980)
Lynch R.L., Cross K.F.: Managing the corporate warriors. Qual. Prog. 23(4), 54–59 (1990)
Masters G.N.: A Rasch model for partial credit scoring. Psychometrika 47, 149–174 (1982)
Metz S.M., Wyrwich K.W., Babu A.N., Kroenke K., Tierney W.M., Wolinsky F.D.: A comparison of traditional and Rasch CUT points for assessing clinically important change in health-related quality of life among patients with asthma. Qual. Life Res. 15, 1639–1649 (2006)
Michell J.: An Introduction to the Logic of Psychological Measurement. Lawrence Erlbaum Associates, Hillsdale (1990)
Mislevy R.J., Bock R.D.: BILOG 3: Item Analysis and Test Scoring with Binary Logistic Models. Scientific Software, Inc., Chicago (1990)
Mosier C.I.: A psychometric study of meaning. J. Soc. Psychol. 13, 123–140 (1941)
Mosier C.I.: A modification of the method of successive intervals. Psychometrika 7(1), 19–29 (1942)
Muraki E.: A generalized partial credit model: application of the EM algorithm. Appl. Psychol. Measur. 16, 159–176 (1992)
Muraki E.: A generalized partial credit model. In: van der Linden, W, Hambleton, R.K. (eds) Handbook of modern item response theory, pp. 153–164. Springer, New York (1997)
Muraki E., Bock R.D.: PARSCALE: IRT Based Test Scoring and Item Analysis for Graded Open-Ended Exercises and Performance Tasks. Scientific Software, Inc., Chicago (1997)
Novick M.R.: The axioms and principal results of classical test theory. J. Math. Psychol. 3(1), 1–18 (1966)
Nunnally J.: Psychometric Theory. McGraw-Hill, New York (2005)
Ommundsen R., Larsen K.S.: Attitudes toward illegal immigration in Scandinavia and United States. Psychol. Rep. 84, 1331–1338 (1999)
Orlando M., Thissen D.: Likelihood-based item-fit indices for dichotomous item response theory models. Appl. Psychol. Measur. 24(1), 50–64 (2000)
Orlando M., Thissen D.: Further examination of the performance of S-X2, an item fit index for dichotomous item response theory models. Appl. Psychol. Measur. 27(4), 289–298 (2003)
Reckase M.D.: Unifactor latent trait models applied to multifactor tests: Results and implications. J. Educ. Stat. 4 , 207–230 (1979)
Richardson M.W.: The relationship between difficulty and the differential validity of a test. Psychometrika 1, 33–49 (1936)
Roberts J.S., Donoghue J.R., Laughlin J.E.: A general model for unfolding Unidimensional polytomous responses using item response theory. Appl. Psychol. Measur. 24(1), 3–32 (2000)
Roberts, J.S., Fang, H., Cui, W., Wang, Y.: GGUM2004: A Windows-based program to estimate parameters of the generalized graded unfolding model. Manuscript preparation (2004)
Rost J., Langeheine R.: Applications of Latent Trait and Latent Class Models in the Social Sciences. Waxmann, New York (1997)
Samejima, F.: Estimation of Latent Ability Using a Response Pattern Of Graded Scores. Psychometric Monography 34 (1969)
Samejima F.: Graded response model. In: van der Linden, W., Hambleton, R.K. (eds) Handbook of Modern Item Response Theory, pp. 85–100. Springer, New York (1997)
Singh J.: Tackling measurement problems with Item Response Theory: principles, characteristics, and assessment, with an illustrative example. J. Bus. Res. 57, 184–208 (2004)
Szeles, M.R., Fusco, A.: Item response theory and the measurement of deprivation: evidence from Luxembourg data. Qual. Quant. (2011). Online FirstTM, 4 October
Terman L.M.: The Measurement of Intelligence. Houghton Mifflin, Boston (1916)
Thissen D.: MULTILOG user’s guide: multiple categorical item analysis and test scoring using item response theory. Scientific Software Int., Chicago (1991)
Thomson, W.: Lord Kelvin. In: Popular Lectures and Addresses, vol. 1. Macmillan and Company, London (1891)
Thurstone L.L.: A law of comparative judgments. Psychol. Rev. 34, 278–286 (1928)
Thurstone L.L.: Motion Pictures and the Attitudes of Children. University of Chicago Press, Chicago (1932)
Tucker L.R.: Maximum validity of a test with equivalent items. Psychometrika 11, 1–13 (1946)
Van Schuur, W.H., Post, W.J.: MUDFOLD. A Program for Multiple Unidimensional Unfolding [Software Manual]. ProGAMMA, Groningen (1998)
Veer K.V.D., Ommundsen R., Hak T., Larsen K.S.: Meaning shift of items in different language versions. A cross-national validation study of the illegal aliens scale. Qual. Quant. 37, 193–206 (2003)
Wilson M.: Constructing Measures: An Item Response Modeling Approach. Erlbaum, Mahwah (2005)
Wilson M., Allen D.D., Li J.C.: Improving measurement in health education and health behavior research using item response modeling: Comparison with the classical test theory approach. Health Educ. Res. 21(1), 19–32 (2006)
Wright, B., Mead, R.: BICAL: Calibrating Items and Scales with the Rasch Model, Research Memorandum 23. University of Chicago, Department of Education, Statistical Laborator, Chicago (1977)
Zimowski M.F., Muraki E., Mislevy R.J., Bock R.D.: BILOG-MG: Multiple-Group IRT Analysis and Test Maintenance for Binary Items. Scientific Software, Inc., Chicago (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bortolotti, S.L.V., Tezza, R., de Andrade, D.F. et al. Relevance and advantages of using the item response theory. Qual Quant 47, 2341–2360 (2013). https://doi.org/10.1007/s11135-012-9684-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11135-012-9684-5