Psychology 840: Computational Statistics---Spring, 2007
(as of 3/13/2007)

Selected Topics in Item Response Theory

Time, Place: 9:00-11:30 Fridays, 347 Davie

Instructor: David Thissen

Tentative Schedule:

Date	Topic/Readings	Other Materials
January 12	Introduction If anyone developed an interest in shift (or perspective control) lenses, there is more on that topic here. Here is the glossary from an online C++ tutorial. Horton, N.J., Brown, E.R., & Qian, L. (2004). Use of R as a toolbox for mathematical statistical exploration. The American Statistician, 58, 343-357.	The class introduction and Computing History presentations are clickable links to .pdf files. For future classes: The local download source for R is here (the local ibiblio page is not working for me right now, but that appears to be a Mac-PC problem; it works for IE 7). Other mirrors (top entry, left side navigation bar; choose one in the USA!) may be faster; it depends on many things. Install (either) MS Visual Studio 2005 (this is v. 8) from the loaner CDs, or download and install the free Visual C++ Express Edition (and then register, at great and repeated length). Downloadable .zip archives of the NewMat10 library and our LstArray library are here.
January 19	Regression: Data Manipulation, Matrix Operations---R Bock, R.D. (1975). Chapter 4 from Multivariate statistical methods for the behavioral sciences. New York: McGraw-Hill. Readings that may be useful anytime: Bock, R.D. (1975). Chapter 2 from Multivariate statistical methods for the behavioral sciences. New York: McGraw-Hill. Bock, R.D. (1993). Chapter 2 from the unpublished drafts of Item Response Theory. Two books that have interesting sections on matrix differentiation and the derivatives for the least squares solution to regression are Searle (1982) Matrix Algebra Useful for Statistics (section here) and Schott (1997) Matrix Analysis for Statistics (section here). Feel free to suggest additional books (or the appendices common in introductory graduate statistics texts) as alternative presentations of matrix algebra?	Exercise 4.1-3 (the green bean problem) on pp. 207-208 of Chapter 4 is required. Use any software you like for the computation (but modification of my R is recommended). Due Friday Feburary 2. The Keynote presentation is here (in .pdf format). The canned regression, matrix regression, and graphics R files, and the data, are clickable here. Optional homework exercises on regression are here.
January 26, February 2	Regression: Data Manipulation, Matrix Operations---C++ Documentation for the NewMat10 matrix library from Robert Davies.	The .zip file containing the classed regression .h and .cp files is here. The collection of trial C++ what works up to the classed regression is here. More Optional homework exercises for regression are here.
February 9	IRT: Estimating Theta Thissen, D., & Orlando, M. 2001). Item response theory for items scored in two categories. In D. Thissen & H. Wainer (Eds), Test Scoring. Hillsdale, NJ: Lawrence Erlbaum Associates. (Ch. 3)	The Keynote presentation is here (in .pdf format). The IRT R file is clickable here. Optional homework exercises for IRT scoring are here.
February 9 February 16	IRT: Estimating Theta Using C++.	The Keynote presentation is here (in .pdf format). The .zip file of the C++ source files and item parameter files is clickable here. Documentation for a somewhat more elaborate version of IRTScore is here, as well as and an unpublished ms. that describes more about what it does. More Optional homework exercises for scoring are here.
February 23 March 2	Fechner/Thurstone Scaling Bock, R.D. & Jones, L.V. (1968). Chapter 2 and part of 3 from The measurement and prediction of judgment and choice. San Francisco, CA: Holden-Day.	One required (and some optional) homework exercises for scaling / probit / logit analysis. The Keynote presentation is here (in .pdf format). The Bock & Jones class R file is clickable here. The .zip file of the C++ source files for the NormalProb function development is clickable here. The .zip file of the C++ source files for the probit regression program is clickable here. A web-obtained image of Abramowitz & Stegun Page 932 is clickable here.
March 2 (part 2)	Probit MCMC Johnson, V.E. & Albert, J.H. (1999). Chapter 1, Chapter 2, and Chapter 3 from Ordinal Data Modeling. New York, NY: Springer. Specifically, pp. 53 and 58-62 of Chapter 2, and pp. 75-86 and 90-92 describe our topics. Chapter 1, along with sections 2.1-2.3, are excellent background on Bayesian inference, using likelihood topics we have discussed,	The Keynote presentation is here (in .pdf format). TheMCMC R file is clickable here. Optional homework exercises for probit MCMC are here.
March 9	IRT item parameter estimation I Bock, R.D. & Lieberman, M. (1970). Fitting a response model for n dichotomously scored items. Psychometrika, 35, 179-197. Bock, R.D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of the EM algorithm. Psychometrika, 46, 443-449. Thissen, D. (1982). Marginal maximum likelihood estimation for the one-parameter logistic model. Psychometrika, 47, 201-214.	The Keynote presentation is here (in .pdf format). The R files for Bock & Lieberman with numerical derivatives, Bock & Lieberman with analytical derivatives and Fisher scoring hessian (roll our own Newton-Raphson), a Bock & Lieberman-type algorithm for the 2PL, and Bock & Aitkin 2PL with numerical derivatives are clickable here.
Note: March 16 is part of Spring Break
March 23 (part 1)	IRT item parameter estimation II	The Keynote presentation is here (in .pdf format). The R files for Bock & Aitkin 2PL with the empirical hessian, and Bock & Aitkin 2PL with the expected value of the hessian, are clickable here. The zipped source files for the C++ implementation of the Bock-Aitkin algorithm are clickable here.
March 23 (part 2)	IRT item parameter estimation III Albert, J.H. (1992). Bayesian estimation of normal ogive item response curves using Gibbs sampling. Journal of Educational Statistics, 17, 251-269. Patz, R.J. & Junker, B.W. (1999a). A straightforward approach to Markov chain Monte Carlo methods for item response theory. Journal of Educational and Behavioral Statistics, 24, 146-178. Cowles, M.K. (2004). Review of WinBUGS 1.4. The American Statistician, 58, 330-336.	The Keynote presentation is here (in .pdf format). The R file for Albert's algorithm is clickable here. Patz & Junker's S-Plus code is "mcmcirt.zip" on this page.
March 30 April 20	Estimation for exploratory and confirmatory factor analysis Bock, R.D., & Bargmann, R. (1966). Analysis of covariance structures. Psychometrika, 46, 443-449. The 1965 L.L. Thurstone Psychometric Laboratory Research Memorandum version of this article is here. Jennrich, R.I. & Robinson, S.M.. (1969). A Newton-Raphson algorithm for maximum likelihood factor analysis. Psychometrika, 34, 111-123. Joreskog, K.G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183-202. Joreskog, K.G. (1971). Statistical analysis of sets of congeneric tests. Psychometrika, 36, 109-133. (Also an excerpt from a Lisrel manual.) Rubin, D.B. & Thayer, D.T. (1982). EM algorithms for ML factor analysis. Psychometrika, 47, 69-76. Some reading that may be useful, especially for Rubin & Thayer: Bock, R.D. (1975). Chapter 3 sections 3-4-5 from Multivariate statistical methods for the behavioral sciences. New York: McGraw-Hill.	The Keynote presentation is here (in .pdf format). The zip file containing the R code examples is clickable here. A revised downloadable .zip archive of the entire VS 2005 project for the NewMat10D library is here. The Bock & Bargmann presentation is a clickable link to .pdf file. The derivative-free and derivative-based R files are clickable links to text files, as is are the links to the .h and .cpp files for the C++. Optional homework exercises, for this. The source files for a minimal start on a C++ implementation of confirmatory factor analysis inspired by Joreskog (1969, 1971) are here.
Note: April 6 is a University Holiday
April 13 DT not yet back from the AERA/NCME meeting. Use this time to confer on projects/presentations?
April 27	Your presentations

Requirements, grading, and stuff: There will be no tests. There will be homework assignments, of two kinds: required and optional. There will be two or three assignments required of everyone. In addition, at many classes there will be a list of optional assignments provided. Over the course of the semester, each student will be required to do (at least) three of the optional assignments. This will yield a total of five (5) or six (6) homework assignments: two or three required plus three optional. Assignments will involve some level of computer programming, and a 2-4 page written (typed, please, thank you) report. The report must describe the programming in readable English, and include the results. The programming may be done collaboratively (indeed, that is encouraged); however, each student must complete a unique individual report.

A report on a programming project of your own choosing is also required. These projects may be done in pairs or triples, on topics of your choosing, with brief oral presentations on April 27. We will discuss this aspect of the course in more detail in February-March.

Class participation: For each week, the readings listed above will serve as the topical focus. This semester this class is a work in progress, representing a departure from previous incarnations of the course. As such, we will be open to suggestions and alternative reformulations as we proceed.