Monday, August 16, 2010

What Is Good About Rasch Measurement?

To answer this question requires a specification of what is meant by measurement. Two main approaches to defining measurement are the traditional approach and the representational approach. The traditional approach has been widely accepted in the physical sciences since its development by Holder (1901, as cited in Michell, 1997), who synthesized the approaches of Euclid, Newton, and Dedekind. One feature of the traditional approach is that it entertains an empiricist account of number. Measurement, then, becomes the exercise of establishing a correspondence between quantitative variables in the world and numerical instruments (Mill, 1843/1973). Mill's empiricist conception of number was criticized and made to seem untenable by Frege (1884/1984), and the traditional approach to measurement was criticized by Russell (1903), who developed a representational theory of measurement. The representational theory was further advanced by Krantz, Luce, Suppes, and Tversky (1971), Suppes, Krantz, Luce, and Tversky (1989), and Luce, Krantz, Suppes, and Tversky (1990), who are its most sophisticated contemporary proponents. Michell (1994, 1997), on the other hand, has emerged as the most sophisticated contemporary proponent of the traditional theory of measurement.

On both the traditional theory and the representational theory, Rasch measurement is good because it is an example of additive conjoint measurement. Rasch measurement satisfies two conditions that are necessary in order for an attribute to be quantitative. First, the attribute must possess additivity. Second, the attribute must possess ordinality. The Rasch model possesses additivity because the difference between the manifest level and the latent level involves the additive measurement of two different latent variables -- one for the person, one for the item. The Rasch model possesses ordinality because person and item variables can be explicity compared at the latent level as being higher or lower than one another.

Rasch measurement is good partly because it stands in contrast to a ridiculous version of the representational theory that has gained ascendance within psychology: namely, operationism -- that is, the idea that a variable is completely defined by the operations or measurements used to recognize it. There may be some ontological differences between the traditional theory and the Krantz et al. representational theory regarding the state of the world, whether the variables to be measured are quantitative or qualitative, but neither of these theories is completely subjective and idealistic (in the Berkeleyan sense) in the way that operationism is. Operationism permits quantification of anything whatsoever, albeit in a wholly arbitrary way. Operationism thus exemplifies a strong Pythagorean tendency within psychology, supposing as it does that numbers can be applied to anything. The operations used to generate the numbers, however, may represent nothing other than themselves. Operationism justifies applying a rule--any rule--to empirical reality. Applying a different rule may result in a different result, but both rules are right by fiat, because they define what they purport to represent.

It may be a mistake to claim that Rasch measurement is an idealization. According to the traditional theory, an idealization is not measurement. Within any given application, however, measurement may be impossible. Indeed, Kant (1786/1970) and Searle (1994) seem to think that psychological variables such as consciousness are inherently non-quantitative. For the representational theory, applying numbers to a qualitative reality in a systematic and rigorous way is the model for measurement. Thus, the representational theory entails no quivering reflections on whether psychology can ever be a quantitative science. The traditional theory does entail such reflections, however, because, within this theory, whether any given attribute is quantitative is an empirical question to which the answer may be "no".

If psychological variables turn out to be non-quantitative, this does not entail that psychology cannot be a science. First, psychological variables will continue to have predictive power and thus practical utility. The correlation between any number of psychological traits and criterion variables, for example, ranges from 0.3 to 0.5 (Mischel [1968] has called this the personality coefficient). Explanations for these regularities, however, will have to be acknowledged as being speculative and theoretical, bringing psychology into close alliance with philosophy. The search for quantitative variables, however, may represent the wave of the future for a potentially quantitative scientific psychology.

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