An Introduction to the Logic of Rasch Measurement
March 1, 2003
In an article in summer 2000 StressPoints, Patrick Palmieri provided an overview of item response theory, a contemporary approach to the development of psychometric instruments, and contrasted this approach to classical test theory, which forms the basis for most measures of trauma and its consequences. The following article presents another approach, based on probabilistic theory--the Rasch model.
Historically, the development of units of measure has taken a great deal of time. Early merchants found it necessary to have a measure of weight to conduct their businesses profitably. A system of standard units such as pounds, pints, inches or volts allows efficient communication across all realms of life, including the exchange of scientific information. In working with PTSD, we may feel that we can confidently count the number of cases that meet diagnostic criteria, but as yet there is not a consistent and universal standard for measuring the severity or intensity of the disorder. While an ever-growing number of PTSD scales yield total scores, they do not provide a constant, precise measurement of PTSD.
Developing a unit of measure requires basic rules. First, the measure must have equal intervals. For example, measuring the distance between two objects by counting the number of steps it takes for an individual to walk from object A to object B is not an accurate measurement--the stride of individuals varies. Equal-interval inches or feet as a unit of measure provides a more precise estimate of the distance between two objects. Equal-interval units can be calculated, thus creating a linear measure.
Another basic rule of developing units of measure is that the unit of measure cannot depend upon what is measured or who does the measuring. When a ruler is used to assess length or distance, it doesn't matter if the object being measured is a piece of wood or a bolt of fabric; the distance represented by an inch will remain the same. Also, it doesn't matter who is using the ruler; the inch does not vary from person to person. When units of measure stay constant regardless of the object being measured or the person performing the measurement, we can best apply statistical methods to conduct research.
The Rasch model can be used to create a consistent equal-interval measurement of a latent variable or dimension. Using the simple logistic model of Rasch, items representing the latent trait are lined up in terms of their difficulty, and persons responding to the items also have ordered measurements. Both the item difficulty and person measurement are in equal-interval units that can be depicted on a linear scale. The items that represent the latent trait do not move around on the scale if the persons being tested differ by age, gender or other characteristics. The person measurement indicates the amount of latent trait present, not a ranking of their total scores.
Assume we wish to use the Rasch model to create a measure of the latent variable PTSD. We would begin by generating a large pool of items that represent PTSD symptomatology. Next, subjects diagnosed with PTSD would be asked to rate the severity of their symptoms on a five-point response scale with categories ranging from none to severe. If the data fit the Rasch measurement model, there will be a graphic display of item ordering and person measurements. A suitable pool of items will result in a mapping of the items from those reflecting little or minor PTSD symptoms to those reflecting very severe PTSD symptoms.
There are many benefits in using Rasch measurement to create instruments to measure a latent variable or dimension. No more than 50 subjects are needed to test items if the subjects are well targeted (have varying degrees of the latent variable). The response patterns to the items can be evaluated, and unused response categories identified and diagnosed. Each item can be evaluated for how well it fits the Rasch model and how well it works with other items describing the dimension being measured through fit statistics and principal component analysis of their residuals. Item stability can be determined with differing groups of respondents. This model also is useful in identifying persons with unusual responses.
Software available for use with the Rasch model calculates the probability of the subject's responses, and produces the associated statistics and the graphical displays. To learn more about Rasch measurement, read Applying the Rasch Model: Fundamental Measurement in the Human Sciences, by Trevor G. Bond and Christine M. Fox, published by Lawrence Erlbaum (2001). For additional information, visit www.rasch.org.
Elizabeth J. Betemps is an associate professor at the University of Cincinnati.