| Aspect | Rasch Dichotomous Model | Item Response Theory: One-Parameter Logistic Model |
|---|---|---|
| Abbreviation | Rasch | 1-PL IRT, also 1PL |
| Motivation | Prescriptive: Distribution-free person ability estimates and distribution-free item difficulty estimates on a linear 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: incidental parameters |
| Items, agents, prompts, probes, multiple-choice questions, etc.: structural parameters | Item i of difficulty Di, or Item ι (Greek iota) of difficulty δi in logits |
Itemi 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 a linear 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, Murdoch Univ., 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 |
Rasch dichotomous model vs. One-parameter Logistic Model … Rasch Measurement Transactions, 2005, 19:3 p. 1032
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