Whitely and Dawis (1974) recently discussed, in this journal, the nature of objectivity with the Rasch model. They made several good points. However, their paper contained some unfortunate misunderstandings and errors. One important misunderstanding concerns the estimation procedure necessary to calibrate items according to the Rasch model. The authors recommend a two-stage estimation procedure which is actually unnecessary and impractical. As a result they conclude that only huge sample sizes make it possible to apply the Rasch model to real data. Since the Rasch model can be and has been applied productively to sets of data as small as 100 persons, and under those circumstances lead to useful results, it is important to correct that misunderstanding and the incorrect conclusion drawn from it. Whitely and Dawis recommend beginning parameter estimation with a least squares method based on item by score-group frequencies. This crude method was first used by Rasch in the 1950's and presented in his 1960 book. It is neither the most convenient nor the most efficient method of estimation and it is unnecessary as a beginning. Far preferable is to begin directly with the unconditional maximum likelihood procedure described by Wright and Panchapakesan (1969) and Wright and Douglas (1975b). Most researchers applying the Rasch model today are using some version of the computer program for unconditional maximum likelihood estimation written by Wright and Panchapakesan in 1965. The danger to them of being misled by the recommendation of Whitely and Dawis is slight.* However, newcomers to the topic who take the Whitely-Dawis recommendation seriously will be led astray. Perhaps because they focused their attention on the least squares method of estimation, Whitely and Dawis conclude that huge sample sizes are necessary for useful item calibration using the Rasch model. This conclusion is based on their incorrect statement that each and every possible score group has to be inhabited by a substantial number of persons for the estimation procedure to proceed. This is untrue. In fact, a set of items may be calibrated even when all the persons in the calibration sample have earned one and the same score. Even the least squares method allows estimation of the relative difficulties of a set of items from merely the log-odds success that any single score group obtains on each item. No additional score groups are necessary for a set of unbiased least squares estimates. The same, of course, is true for the unconditional maximum likelihood procedure. It is only when the researcher wishes, and wisely so, to test the fit of his data to the Rasch model, that more than one score group is needed. In order to evaluate fit, at least two score groups must be available so that the separate estimates of each item difficulty within each score group can be compared with one another to see if they are
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