For most practical purposes these models are the same, despite their conceptual differences.
| Aspect | Rasch Dichotomous Model | Item Response Theory: One-Parameter Logistic Model |
|---|---|---|
| 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: 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 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) |
Linacre J.M. (2005). Rasch dichotomous model vs. One-parameter Logistic Model. Rasch Measurement Transactions, 19:3, 1032
| Rasch Publications | ||
|---|---|---|
| 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 2nd. 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 |
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| Forum | Rasch Measurement Forum to discuss any Rasch-related topic |
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| Coming Rasch-related Events | |
|---|---|
| June 19-21, 2013, Wed.-Fri. | SIS 2013 Conference on Advances in Latent Variables: Methods, Models and Applications, Brescia, Italy, meetings.sis-statistica.org/index.php/sis2013/ALV |
| July 1 - Nov. 30, 2013, Mon.-Sun. | Online Course: Introduction to Rasch Measurement Theory (D. Andrich, RUMM), www.education.uwa.edu.au/ppl/courses |
| July 5 - Aug. 2, 2013, Fri.-Fri. | On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com |
| July 15, 2013, Monday | Application deadline: UIC Educational Research Methodology online graduate certificate program, www.go.uic.edu/OnlineMESA |
| July 22, 2013, Monday | Submission deadline: 2014 AERA Annual Meeting, Philadelphia PA, www.aera.net |
| Aug.1-5, 2013, Thur.-Mon. | TERA-PROMS Annual Meeting, Kaohsiung, Taiwan, tera.education.nsysu.edu.tw |
| Aug. 9 - Sept. 6, 2013, Fri.-Fri. | On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com |
| Aug. 22, 2013, Thursday. | Symposium in honor of Svend Kreiner, Copenhagen, Denmark, biostat.ku.dk/kreinersymposium |
| Sept. 4-6, 2013, Wed.-Fri. | IMEKO TC1-TC7-TC13 Symposium: Measurement Across Physical and Behavioural Sciences, Genoa, Italy, www.imeko-genoa-2013.it |
| Sept. 13 - Oct. 11, 2013, Fri.-Fri. | On-line workshop: Rasch Applications in Clinical Assessment, Survey Research, and Educational Measurement (W.P. Fisher), www.statistics.com |
| Sept. 18-20, 2013, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 23-25, 2013, Mon.-Wed. | In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 26-27, 2013, Thurs.-Fri. | In-person workshop: Advanced Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Oct. 18 - Nov. 15, 2013, Fri.-Fri. | On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
| Oct. 20 - Oct. 25, 2013, Sun.-Fri. | International Association for Educational Assessment (IAEA) 39th Annual Conference, Tel Aviv, Israel, www.iaea-2013.com |
| Dec. 11-13, 2013, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| March 12-14, 2014, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| April 3-7, 2014, Thurs.-Mon. | AERA Annual Meeting, Philadelphia PA, www.aera.net |
| May 14-16, 2014, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| May 19-21, 2013, Mon.-Wed. | In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| July 4 - Aug. 1, 2014, Fri.-Fri. | On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com |
| Aug. 8 - Sept. 5, 2014, Fri.-Fri. | On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com |
| Sept. 10-12, 2014, Wed.-Fri. | In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 12 - Oct. 10, 2014, Fri.-Fri. | On-line workshop: Rasch Applications in Clinical Assessment, Survey Research, and Educational Measurement (W.P. Fisher), www.statistics.com |
| Sept. 15-17, 2014, Mon.-Wed. | In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
| Sept. 18-19, 2014, Thurs.-Fri. | In-person workshop: Advanced Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric |
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