From STAT-L Mon Oct 1 00:00:00 1993 Date: Sat, 2 Oct 1993 16:47:00 EST Reply-To: Stat-l Discussion List Sender: Stat-l Discussion List From: John Uebersax Subject: Rasch model software and FAQ This message has three parts: (1) some frequently asked questions about the Rasch model, (2) a list of current software, and (3) references. The information here is mainly oriented to consulting statisticians, rather than people who want do delve into the theoretical aspects. Attention is restricted to models for dichotomous data. Thank you to the following people who provided valuable assistance with this material: Harold Ayabe, David Delong, Travis Gee, Joop Hox, Brian Junker, Dennis Roberts, Magnus Stenbeck, and Robert Terry. (Thank you also to anyone whose name I may have inadvertently left out). ***NOTE: This file is 411 lines long*** FREQUENTLY ASKED QUESTIONS (FAQ) ABOUT THE RASCH MODEL 1. What is the Rasch model? The Rasch model is a data analysis tool for creating multi-item scales. One view is that it jointly locate items and subjects on a continuum. For example, in the figure below, i1, i2, and i3 denote three dichotomous (scored right or wrong) items, and s1, s2, and s3 denote three subjects. The location of subjects on the continuum corresponds to their ability level. The item locations correspond to their difficulty levels. If a person's ability level exceeds an item's difficulty level, the person will (generally) pass the item. i1 i2 i3 <-----+---*---+----*----+---*----> trait level s1 s2 s3 2. What is the Rasch model used for? The Rasch model can be used for measurement (i.e., locating a person on the latent continuum) or exploratory data analysis (e.g., understanding the structure of items or selecting a useful subset). It permits identification of items or behaviors that are ordered (e.g., what is the sequence of skills one attains in becoming a computer programmer). In that sense, it is similar to Guttman scaling; however, unlike a Guttman scale, a Rasch scale allows that (with reference to the figure above), there is a certain probability that, for example, subject s2 might answer item i1 incorrectly or i2 correctly. A Rasch scale is thus similar to a Guttman scale with allowance for measurement error. An article by Safrit, Cohen and Costa (1989) gives an excellent introduction showing practical applications of the Rasch and related models. 3. What are related methods? The Rasch model is subsumed under the larger heading of item response theory (IRT); other essentially synonymous terms for IRT are latent trait models and modern psychometric theory. Various models of this larger set differ according to whether the response function (the probability of a positive response given various ability levels) follows a logistic or a normal ogive curve (the two are very similar). Models also differ in the number of parameters allowed for the response function of each item. The Rasch model is the same as a 1-parameter logistic (1PL) latent trait model. Other IRT models include 2 and 3 parameter logistic models (2PL, 3PL) and 1, 2, and 3 parameter normal ogive (1PN, 2PN, and 3PN) models. The normal ogive models follow from a simple model that involves response thresholds and normally distributed measurement error. The logistic models are generally justified as close and computationally convenient approximations to the normal ogive model. The Rasch or 1PL model, however, can be viewed as deriving directly from a different theoretical model. 4. When do you use the Rasch model? The Rasch model is fairly simple IRT model. That is an advantage and a disadvantage. The disadvantage is that such a simple model may not fit the data. The advantage is that, if you only have a small number of subjects, it may be better to use a simpler model with fewer parameters. 5. Are there limiting assumptions? The first limiting assumption with the usual Rasch model is that there is only one latent dimension underlying the items; that is not a severe limitation, since one can easily eliminate items that appear to violate the assumption. Second, because it is a "one parameter" model, the Rasch model makes an assumption analogous to equal measurement error for each item. 6. Are there variations on the Rasch model? The Rasch model has been extended to items with ordered response levels, and to multidimensional latent traits. 7. Are there different estimation methods? Most programs use one of three estimation methods: joint maximum likelihood (ML), conditional ML, and marginal ML. Joint ML (also sometimes called unconditional ML) jointly estimates the locations of items and subjects on the trait continuum. Conditional ML estimates item locations by making "distribution free" assumptions. Marginal ML estimation assumes a prior distribution of subject abilities (usually a normal distribution), and estimates item locations based on this distribution. The consensus is that all three methods usually give comparable results. Some are more computationally demanding than others, however, and the number of items may affect which is used. Any will produce satisfactory results in most applied situations. Conditional ML estimation is sometimes favored by statisticians, because of interesting technical properties. For example, it is possible to obtain the conditional ML estimates by a variety of methods, including loglinear analysis (e.g., Kelderman, 1984) and special forms of latent class analysis (Lindsay, Clogg & Grego, 1990). It is also possible to closely approximate the Rasch model with so-called heuristic estimation procedures. This is briefly discussed at the end of the software list below. 8. What are some good texts or references for more information? Hambleton, Swamination & Rogers (1991) give a good overview of logistic IRT methods, including the Rasch model. Andrich (1988) provides a good and affordable (part of the Sage "Quantitative Applications" series) introduction to the Rasch model. Wright and Stone (1979) also give a good introduction to the Rasch model. Rasch (1960/1980), of course, is an obvious source to consult. Lord & Novick (1968) remains an important source for IRT methods in general. 9. What software should I use or recommend? Any of the programs listed below should be adequate to estimate the Rasch model. Some estimate more complex 2-parameter and 3-parameter models as well, which may be a consideration for some applications. Perhaps the best recommendation is to use what is most easily available. Rasch and IRT models are most common in educational and psychological research. At a large university, there is a good chance that someone in the Educational Psychology or Psychology departments already has one of these programs. RASCH MODEL SOFTWARE Much of the following list can be found in Hambleton, Swaminathan and Rogers (1985), pp. 48-50 and 159-160. Some of that information has been updated here, and a few other programs noted. ----------------------------------------------------------------- PC-BILOG $345 PC-MULTILOG $200 ----------------------------------------------------------------- Scientific Software 1525 East 53rd St Suite 906 Chicago, IL 60615 phone: 800-247-6113 312-684-4920 fax: 312-684-4979 Comments: 1, 2, and 3PL models; marginal ML estimation. ----------------------------------------------------------------- LOGIMO ----------------------------------------------------------------- Henk Kelderman Department of Educational Measurement University of Twente Postbus 217 7500 AE Enschede The Netherlands Comments: Loglinear formulation of Rasch model; conditional ML estimation. ----------------------------------------------------------------- RASCAL $175 ----------------------------------------------------------------- Assessment Systems Corporation 2233 University Avenue Suite 200 St. Paul, MN 55114 Phone: 612-647-9220 Fax: 612-647-0412 email: asc@mr.net Comments: Joint ML estimation; another program, ASCAL ($400) estimates 1, 2, and 3PL models. ----------------------------------------------------------------- BIGSTEPS $550 ----------------------------------------------------------------- MESA Press 5835 S. Kimbark Ave Chicago, IL 60637-1609 Phone: 312-702-1596 Fax: 312-702-0248 email: MESA@uchicago.edu Comments: Replaces BICAL, BIGSCALE; joint ML estimation. ----------------------------------------------------------------- PML $250 ----------------------------------------------------------------- Jan-Eric Gustafsson University of Goteborg Institute of Education S-431 20 Molndal SWEDEN Also available from the dutch company ProGamma (email: gamma.post@gamma.rug.nl). Comment: Conditional ML estimation. ----------------------------------------------------------------- RASCH 1.0 free ----------------------------------------------------------------- Germano Rossi Universita degli Studi di Verona Centro di Informatica e Calcolo Automatico via dell'Artigliere 19 I-37129 Verona ITALY email: Germano@irvuniv.bitnet The program can be obtained by ftp to rigel.oakland.edu. It is in the directory \pub\msdos\statistics and is named RASCH10.ZIP (self-extracting archive). Comment: The program appears good, but, with one data set it seemed to give incorrect results (perhaps I did not use the program correctly). My suggestion would be to contact the author and see if a new version is available, or else test it yourself to verify the results. ----------------------------------------------------------------- MIRTE ----------------------------------------------------------------- Mark Reckase American College Testing Program P.O. Box 168 Iowa City, IA 52243 Comments: 1, 2, and 3PL models; joint ML estimation. ----------------------------------------------------------------- LOGIST ----------------------------------------------------------------- Educational Testing Service Rosedale Road Princeton, NJ 08541 Comments: 1, 2, and 3PL models; joint ML estimation. ----------------------------------------------------------------- NOHARM ----------------------------------------------------------------- Colin Fraser Centre for Behavioral Studies University of New England Armidale, NSW AUSTRALIA 2351 Comment: Uses McDonald's nonlinear factor analysis model. ----------------------------------------------------------------- OTD (Optimal Test Design) $550 ----------------------------------------------------------------- Norman Verhelst National Institute for Educational Measurement P.O. Box 1034 6801 MG Arnhem The Netherlands FAX: 01131 85 52 13 56 ----------------------------------------------------------------- RIDA ----------------------------------------------------------------- Cees Glas National Institute for Educational Measurement P. O. Box 1034 6801 MG Arnhem The Netherlands Comment: Conditional or marginal ML estimation. ----------------------------------------------------------------- MIRA ----------------------------------------------------------------- Jurgen Rost Institute for Science Education Kiel University Olshausenstrasse 62 D-2300 Kiel 1 Germany Comment: Also estimates Rasch mixture model. ----------------------------------------------------------------- TESTAT (add-on module) $110 ----------------------------------------------------------------- Available from various commercial dealers. Comments: Requires SYSTAT ----------------------------------------------------------------- Other Alternatives ----------------------------------------------------------------- Frank Baker's recent book on IRT includes many programs. You can consult either the book or perhaps contact him directly to check on the programs' availability. His address is Department of Educational Psychology Univ. of Wisconsin Madison, WI 53706 Because the Rasch model can be set up as a loglinear (quasisymmetry) model, it is possible to estimate it with general software such as GLIM or SAS PROC CATMOD. Lindsay, Clogg & Grego (1991) recently described how certain latent class models could be used to estimate item parameters of the Rasch model, and that these are the same as the conditional ML estimates. In the article, they refer to a computer program they have written for this. You can contact Bruce Lindsay or Clifford Clogg at Department of Statistics Pennsylvania State University University Park, PA 16802 email (Clogg): ccc@psuvm.psu.edu PC-LISCOMP, distributed by Scientific Software (see address above for PC-BILOG), although generally thought of as a tool for structural equation modeling, can probably be used to estimate normal-ogive IRT models. Lord and Novick (1968; pp. 377-378) noted how factor analysis can be used to approximate results of 1PN and 2PN IRT models. Bock & Lieberman (1970), applying this "heuristic" approach, factor analyzed matrices of tetrachoric correlations and obtained results that closely approximated results of marginal ML estimation. This alternative would require software that calculates tetrachoric correlations, and probably a reasonably flexible factor analysis program (e.g., LISREL or EQS). REFERENCES Andrich D. (1988). Rasch models for measurement. Newbury Park, CA: Sage. Bock RD, Lieberman M. (1970). Fitting a response curve model for dichotomously scored items. Psychometrika, 35, 179-198. Hambleton RK, Swaminathan H. (1985). Item response theory. Boston: Kluwer-Nijohoff (pp. 144-147, 7.8 Approximate Estimation Procedures) Hambleton RK, Swaminathan H, Rogers HJ. (1991). Fundamentals of Item Response Theory Newbury Park: Sage. Kelderman, H. (1984). Loglinear Rasch model tests. Psychometrika 49, 223-245. Lindsay B, Clogg CC, Grego J. (1991). Semiparametric estimation in the Rasch model and related exponential response models, including a simple latent class model for item analysis. JASA, 86, 96-107. Lord FM, Novick MR. (1968). Statistical theories of mental test scores. Reading, Massachusetts: Addison-Wesley. Rasch G. (1960; reprinted 1980). Probabilistic models for some intelligence and attainment tests. Chicago: University of Chicago Press. Safrit MJ, Cohen AS, Costa MG. (1989). Item response theory and the measurement of motor behavior. Research Quarterly For Exercise and Sport, 60, 325-335. Wright BD, Stone MH. (1979). Best test design: Rasch measurement. Chicago: MESA Press. --John Uebersax Bowman Gray Medical School Winston-Salem, NC 27157 uebersax@phs.bgsm.wfu.edu =========================================================================