Estimating the parameters of a structural model for the latent traits in Rasch's model for speed tests

This article considers the multiplicative gamma model for reading speed originally proposed by Rasch (1960/1980) in his monograph Probabilistic Models for Some Intelligence and Attainment Tests. The model can be viewed as a latent trait model for a set of pure speed tests with known length, measuring the same trait but differing in test easiness. The basic model can be expanded in several ways, for instance, by incorporating a (log-linear) regression model for the latent subject parameters. The accuracy of a simultaneous estimation method for all the parameters involved, including the regression parameters, is studied using artificial data. In particular, the estimates of the parameters of the regression model obtained by this direct method is compared with the results of a so-called indirect method where the subject parameters are estimated in an intermediate step