An Overview of Nonlinear Factor Analysis and its Relationship to Item Response Theory (SR-95-03)
by Andre F. De Champlain, Law School Admission Council

Executive Summary

Item response theory (IRT) models have been used extensively to address educational measurement and psychometric concerns pertaining to a host of areas such as differential item functioning, equating, and computer-adaptive testing due to their many advantages, such as item and ability parameter invariance across test-taker subgroups and item pools, respectively. Another approach, which is gaining popularity in educational measurement, is the one that treats IRT as a special case of nonlinear factor analysis (NLFA). Several authors have shown that these models are mathematically equivalent (Goldstein & Wood, 1989; Knol & Berger, 1991; McDonald, 1967, 1989, 1994). It would therefore appear reasonable to make use of NLFA models to examine a multitude of educational measurement problems that had been, until quite recently, looked at solely from an IRT perspective.

The purpose of this paper is to provide a brief overview of some of the research that has examined the relationship between IRT and NLFA and to outline three NLFA models, emphasizing their major strengths and weaknesses for practical applications. More precisely, McDonald’s (1967, 1982b) polynomial approximation to a normal ogive model, Christoffersson’s (1975)/Muthen’s (1984) factor analytic model for dichotomous variables, as well as Bock and Aitkin’s (1981)/Bock, Gibbons, and Muraki’s (1988) full-information factor analytic model, will be summarized. Also, the items from two LSAT forms will be calibrated using these three models in order to assess the degree of comparability of the IRT parameter estimates using these procedures.

An Overview of Nonlinear Factor Analysis and its Relationship to Item Response Theory (SR-95-03)

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