For most practical purposes these models are the same, despite their conceptual differences.
Aspect | Rasch Dichotomous Model | Item Response Theory: One-Parameter Logistic Model |
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Abbreviation | Rasch | 1-PL IRT, also 1PL |
For practical purposes | When each individual in the person sample is parameterized for item estimation, it is Rasch. | When the person sample is parameterized by a mean and standard deviation for item estimation, it is 1PL IRT. |
Motivation | Prescriptive: Distribution-free person ability estimates and distribution-free item difficulty estimates on an additive latent variable | Descriptive: Computationally simpler approximation to the Normal Ogive Model of L.L. Thurstone, D.N. Lawley, F.M. Lord |
Persons, objects, subjects, cases, etc. | Person n of ability Bn, or Person ν (Greek nu) of ability βn in logits |
Normally-distributed person sample of ability distribution θ, conceptualized as N(0,1), in probits; persons are incidental parameters |
Items, agents, prompts, probes, multiple-choice questions, etc.; items are structural parameters | Item i of difficulty Di, or Item ι (Greek iota) of difficulty δι in logits |
Item i of difficulty bi (the "one parameter") in probits |
Nature of binary data | 1 = "success" - presence of property 0 = "failure" - absence of property | 1 = "success" - presence of property 0 = "failure" - absence of property |
Probability of binary data | Pni = probability that person n is observed to have the requisite property, "succeeds", when encountering item i | Pi(θ) = overall probability of "success" by person distribution θ on item i |
Formulation: exponential form e = 2.71828 | ![]() |
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Formulation: logit-linear form loge = natural logarithm |
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Local origin of scale: zero of parameter estimates | Average item difficulty, or difficulty of specified item. (Criterion-referenced) | Average person ability. (Norm-referenced) |
Item discrimination | Item characteristic curves (ICCs) modeled to be parallel with a slope of 1 (the natural logistic ogive) | ICCs modeled to be parallel with a slope of 1.7 (approximating the slope of the cumulative normal ogive) |
Missing data allowed | Yes, depending on estimation method | Yes, depending on estimation method |
Fixed (anchored) parameter values for persons and items | Yes, depending on software | Items: depending on software. Persons: only for distributional form. |
Fit evaluation | Fit of the data to the model Local, one parameter at a time | Fit of the model to the data Global, accept or reject the model |
Data-model mismatch | Defective data do not support parameter separability in an additive framework. Consider editing the data. | Defective model does not adequately describe the data. Consider adding discrimination (2-PL), lower asymptote (guessability, 3-PL) parameters. |
Differential item functioning (DIF) detection | Yes, in secondary analysis | Yes, in secondary analysis |
First conspicuous appearance | Rasch, Georg. (1960) Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research. | Birnbaum, Allan. (1968). Some latent trait models. In F.M. Lord & M.R. Novick, (Eds.), Statistical theories of mental test scores. Reading, MA: Addison-Wesley. |
First conspicuous advocate | Benjamin D. Wright, University of Chicago | Frederic M. Lord, Educational Testing Service |
Widely-authoritative currently-active proponent | David Andrich, Univ. of Western Australia, Perth, Australia | Ronald Hambleton, University of Massachusetts |
Introductory textbook | Applying The Rasch Model.T.G. Bond and C.M. Fox | Fundamentals of Item Response Theory. R.K. Hambleton, H. Swaminathan, and H.J. Rogers. |
Widely used software | Winsteps, RUMM, ConQuest | Logist, BILOG |
Minimum reasonable sample size | 30 | 200 (Downing 2003) |
See also: Andrich, D. (2004) Controversy and the Rasch model: A characteristic of incompatible paradigms? Medical Care, 42, 7-16. Reprinted in E.V. Smith & R.M. Smith, Introduction to Rasch Measurement: Theory, Models and Applications. JAM Press, Minnesota. Ch. 7 pp 143-166.
Downing S.M. (2003) Item response theory: applications of modern test theory for assessments in medical education. Medical Education, 37:739-745.
Linacre J.M. (2005). Rasch dichotomous model vs. One-parameter Logistic Model. Rasch Measurement Transactions, 19:3, 1032
Rasch Publications | ||||
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Rasch Measurement Transactions (free, online) | Rasch Measurement research papers (free, online) | Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch | Applying the Rasch Model 3rd. Ed., Bond & Fox | Best Test Design, Wright & Stone |
Rating Scale Analysis, Wright & Masters | Introduction to Rasch Measurement, E. Smith & R. Smith | Introduction to Many-Facet Rasch Measurement, Thomas Eckes | Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. | Statistical Analyses for Language Testers, Rita Green |
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar | Journal of Applied Measurement | Rasch models for measurement, David Andrich | Constructing Measures, Mark Wilson | Rasch Analysis in the Human Sciences, Boone, Stave, Yale |
in Spanish: | Análisis de Rasch para todos, Agustín Tristán | Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez |
Forum | Rasch Measurement Forum to discuss any Rasch-related topic |
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