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Historical Background for Multidimensional Item Response Theory (MIRT)

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Multidimensional Item Response Theory

Part of the book series: Statistics for Social and Behavioral Sciences ((SSBS))

Abstract

Multidimensional item response theory (MIRT) is the result of the convergence of ideas from a number of areas in psychology, education, test development, psychometrics, and statistics. Two general themes underlie the influence of these ideas on the development of MIRT. The first theme is that as our understanding of these areas increases, it becomes clear that things are more complicated than originally thought. The second theme is that the complexity can be represented by models or theories, but these theories and models are idealizations of reality. Because they are idealizations, they can likely be proven false if tested using a large number of observations. Nevertheless, the models can give useful approximations with many practical applications.

It is common in the development of scientific theories to collect data about a phenomenon and then to develop an idealized model of the phenomenon that is consistent with the data. The idealized model is usually presented as a mathematical equation. An example of this approach to theory development is reported in Asimov (1972, p. 158). He describes Galileo in a church observing the swing of lamps hanging from the ceiling by long chains. These lamps were swinging like pendulums, and Galileo is reported to have recorded the length of time it took to make one full swing using his own pulse rate. From these observations, he developed a mathematical formula that related the length of the chain to the length of time for each swing (period) of a pendulum.

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Notes

  1. 1.

    The approximation formula for the period of an ideal simple pendulum is \(p = 2\pi \sqrt{\frac{\mathrm{length } } {g}}\), where g is the acceleration due to gravity. The approximation holds when the angle of swing is small.

  2. 2.

    The original presentations of factor analytic and IRT models used a wide variety of symbols to represent the parameters of the models. To make comparisons of the models easier, the symbols have been changed to a common set. This means that the symbols used here may not match those in the original article.

  3. 3.

    Whitely now publishes under the name Embretson.

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Authors and Affiliations

  1. Counseling, Educational, Psychology, and Special Education Department, Michigan State University, 461 Erickson Hall, East Lansing, MI, 48824-1034, USA

    Mark D. Reckase

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Correspondence to Mark D. Reckase .

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Reckase, M.D. (2009). Historical Background for Multidimensional Item Response Theory (MIRT). In: Multidimensional Item Response Theory. Statistics for Social and Behavioral Sciences. Springer, New York, NY. https://doi.org/10.1007/978-0-387-89976-3_3

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