Rasch Measurement Theory

Educational and psychological measurement in the first half of the twentieth century was dominated by what I have called the Test Score Tradition (Engelhard, 2013). As its label suggests, the Test Score Tradition is dominated by sum scores with Classical Test Theory as a key example of measurement research in this tradition (Crocker and Algina, 1986). The second half of the 20th century witnessed the emergence of a Scaling Tradition that recognized the duality between items and person scores (Mosier, 1940, 1941).

As pointed out by van der Linden (2016), Rasch was one of the pioneers within the tradition that represented a paradigm shift from earlier measurement research. Rasch (1960), presented a set of ideas and methods described by Loevinger (1965) as a “truly new approach to psychometric problems” (p. 151) that can lead to “nonarbitrary measures” (p. 151). Rasch sought to develop “individual-centered statistical techniques [that] require models in which each individual is characterized separately and from which, given adequate data, the individual parameters can be estimated” (Rasch, 1960, p. xx).

Problems of invariant measurement played a central role in the development of Rasch’s measurement theory. As pointed out by Andrich (1988), Rasch presented “two principles of invariance for making comparisons that in an important sense precede though inevitably lead to measurement” (p. 18). Problems related to invariance played a key role in motivating his measurement theory. Rasch’s concept of specific objectivity and his principles of comparison form his version of the requirements for invariant measurement (Rasch, 1977). In his words,

 The comparison between two stimuli should be independent of which particular individuals were instrumental for the comparison; and it should also be independent of which stimuli within the considered class were or might also have been compared . Symmetrically, a comparison between two individuals should be independent of which particular stimuli within the class considered were instrumental for the comparison; and it should be independent of which other individuals were also compared, on the same or on some other occasion (Rasch, 1961, pp. 331–332).

 It is clear in this quotation that Rasch recognized the importance of both personinvariant item calibration, and item-invariant measurement of persons. In fact, he made them cornerstones in his quest for specific objectivity. In order to address problems related to invariance, Rasch laid the foundation for the development of a family of measurement models that are characterized by the potential to separate item and person parameters (Wright & Masters, 1982).

Andrich (1985) has made a strong and persuasive case for viewing the Rasch model as a probabilistic realization of a Guttman scale. Rasch measurement theory can be used to model the probability of dichotomous item responses as a logistic function of item difficulty and person location on the latent variable.

Figure above shows four item response functions based on the Rasch model. Model-data fit can then be based on the comparison between the observed and expected response patterns that is conceptually equivalent to other methods of evaluating a Guttman scale. Engelhard (2013) provides a description of several modeldata fit indices that can be used with the Rasch model. Rasch measurement theory (Rasch, 1960) provides a framework for meeting these requirements when acceptable model-data fit is obtained. Bond & Fox (2015) provide an accessible introduction to Rasch measurement theory.

Source: Wilson and Fisher (2017)