Essays on Item Response Theory

"This book deals with several aspects of item response modeling. We arranged the contributions in two parts: parametric and non-parametric IRT. Within each part, the chapters are roughly ordered as (1) historic[al] accounts and overviews, (2) new models, (3) new methods, and (4) applications and miscellaneous topics... It gives an impression of the present state of the art of IRT models and methods. It may be seen as a complementary successor to the Handbook of Modern Item Response Theory (Van der Linden & Hambleton, 1997), and we hope its contents will set a direction for future developments in IRT." (Boomsma et al. p. viii)

The reader can rejoice that six chapters in this book focus on the Rasch model. Chapter 1, "The life of Georg Rasch as a mathematician and as a statistician" by Erling Andersen and Lina Olsen, covers familiar ground, with greater detail in some parts and omissions in others, such as the considerable time Rasch spent with Ben Wright, and his 7 months in Perth, Australia, in 1974. A charming feature is a pencil sketch of Rasch by Andersen. There are valuable insights. "When teaching he [Rasch] began to call his models Models for Measurement, undoubtedly to stress that the models' main property was to measure, and that they therefore could be used to solve all sorts of measurement problems within the social sciences" (p. 21, their italics).

Georg Rasch's perspective contrasts with the IRT-oriented definition given by Jürgen Rost in Chapter 2, "The growing family of Rasch models":
"A preliminary response to the question, `What is a Rasch model?' would be: a Rasch model is an item response model aimed at measuring one or more quantitative latent variables on a metric level of measurement, and that has the properties of sufficiency, separability, specific objectivity, and latent additivity" (p. 27).

One can imagine a parallel technical definition of a yardstick or a meter rule, "a yardstick is a notched implement aimed at ...". Somehow this would obscure the essential function of a yardstick. The essence of a yardstick is that it constructs interval measures from ordinal observations, "more", "less", "longer", "shorter". Rasch models function in exactly the same way. In order to construct interval measures with yardsticks or Rasch models, all those other convenient properties of separability, etc., must hold.

Chapter 3 is Gerhard Fischer's meticulous "Gain scores revised under an IRT perspective". For most applications, try first a simple "pre-post" ability measure scatterplot, with confidence intervals.

In Chapter 5, "An IRT model for multiple raters", N. Verhelst and H.H.F.M. Verstralen posit a rater model with the distinctive feature that "person parameters may vary across items" (p. 97). This contrasts strongly with the use of rater models in high-stakes testing where decision-making requires person parameter invariance across items and raters. A key sentence is "The work reported in this chapter is an attempt to find a satisfactory answer to a long-standing practical problem: is there an easy way to handle multifacet measurement designs in an IRT framework, which yields results comparable to those of generalizability theory?" (p. 104). The challenge is that generalizability theory is concerned with partitioning variance; Rasch is concerned with constructing measures. But once measures have been constructed, variance can be partitioned (RMT 7:1 p. 283, 8:1 p. 342).

In Chapter 8, "Statistical tests for differential test functioning in Rasch's model for speed tests", M. Jansen and C. Glas continue Jansen's work with Poisson models. A statistical test is described which answers the question "Do the test parameters differ over populations?" But again, look at a scatterplot first!

Chapter 9, "Expected response functions" by Charles Lewis, "takes the uncertainty regarding item parameters into account for the purposes of estimating abilities" (p. 163). There's good news! "Concern about the effect of parameter uncertainty on inferences about [ability] in the case of the Rasch model should probably be confined to cases where the items were calibrated from fewer than 100 individuals" (p. 170). In fact, in practice, an educated guess at an item's difficulty can be good enough. (RMT 5:2 p. 141)

The editors hope that this book "will set a direction for future developments in IRT.". Will it set a direction for future developments in Rasch measurement? Only in a limited way, because two central issues in Rasch measurement, construct validity and communication of results, are entirely absent.

John Michael Linacre

Essays on Item Response Theory: Review. Boomsma A., van Duijn M.A.J., Snijders T.A. … Rasch Measurement Transactions, 2001, 15:1 p.802-3

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 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

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