Trace Lines in Item Response Theory

The other day, in a conversation with a colleague, we all of a sudden wondered where the term "trace line" came from. The term has been around as an alternative to item characteristic curve, operating characteristic or response function for a long time. But what is the idea behind the choice of this name? And who introduced it?

Curious to know who was the first to use the name in test theory and how its meaning was defined, I went back to the early literature and have found what may be the origin of it. Paul Lazarsfeld, a pioneer in item response theory, used the name in his contribution to a 1950 volume. On page 364, he simply wrote: "The graphical picture of our functions fi(x) we shall call the trace line of item i." Nine years later, he allowed us some more insight into his motives for choosing this name: "The curves of probabilities in [our Figure] we shall call trace lines; they trace the probability for an item as a `respondent' moves along the continuum" (1959 p.493). This definition definitely accords with a dictionary definition: "a line drawn by a recording instrument." But why a dynamic interpretation of a line that only maps a set of probabilities?

It is known that Lazarsfeld was deeply struck by the fundamental distinction between manifest data and latent variables. Data are observable, but never very interesting. On the other hand, the variables we do have an interest in are never observable. Physicists used to have the same problem with sub-atomic particles. It was impossible to observe them directly, but they had data indicative of their existence. Then the Wilson cloud chamber was invented and experiments early in this century made ionized particles visible in the form of traces of condensation in saturated vapor.

Was this the analogy that Lazarsfeld had in mind?

Wim van der Linden

Lazarsfeld PF. 1950. The logical and mathematical foundation of latent structure analysis. In SA Stouffer at al. (Eds) Measurement and Prediction. Princeton NJ: Princeton University Press

Lazarsfeld PF. 1959. Latent structure analysis. In S Koch (Ed) Psychology: A study of a science. Vol 3. New York: McGraw-Hill

Trace lines in item response theory. Van der Linden WJ. Rasch Measurement Transactions 1993 7:3 p.308

Trace lines in item response theory. van der Linden WJ. … Rasch Measurement Transactions, 1993, 7:3 p.308

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