Adaptive Test by Minimum Entropy Criterion

<p>A case of inadequacy of using information function in adaptive test was demonstrated by simulation. In adaptive test, assumption of independent and identical distributions is not satisfied, and in the beginning of the test, amount of data is not enough to insure asymptotic representation of distribution of parameter estimate by information function. The simulation showed that these conditions can induce contradictive discrepancy between the true distribution of parameter estimate and the distribution represented by information function. Adaptive test by minimum entropy criterion instead of information function was proposed. Minimum entropy criterion was adopted for psychophysical measurement by Kontsevich and Tyler (1999), and the method was named Ψ method. Behavior of adaptive test by minimum entropy criterion was checked by simulation, which demonstrated that the method by minimum entropy criterion with a uniform prior distribution works as well as the one by information function with respect to estimation of ability parameter, although it induces substantial conservative biases in case of a normal prior distribution. It was pointed out that as one of Bayesian approaches, the proposed method is worth further investigation to inspect its merits and demerits in various conditions and to exploit its multidimensional characteristics.</p>