Convergence of the Conditional Distribution of the Maximum Likelihood Estimate, Given Latent Trait, to the Asymptotic Normality: Observations Made through the Constant Information Model.
Abstract
The Constant Information Model can be used when we substitute a subset of equivalent, binary items, whose item characteristic functions are unknown, for the 'Old Test', or a subset of test items whose operating characteristics are known, in estimating the operating characteristics of item response. In so doing, it has been suggested that we choose items whose common discrimination power is low, so that the interval of latent trait, for which their common item characteristic function in the Constant Information Model assumes positive values, is wide enough to cover the ability levels of all the examinees on which the operating characteristics of new items are to be estimated. This suggestion needs more investigation and precision, however, since it is expected from theory that the convergence of the conditional distribution of the maximum likelihood estimate, given latent trait, to the normality is slow for the values of latent which are close to the two endpoints of the above interval, in comparison with those close to the midpoint. In this paper, through a simulation study , the speed of convergence of the conditional distribution of the maximum likelihood estimate to the normality at various levels of latent trait is observed, using 20 hypothetical test sessions, in each of which 10 equivalent, binary test items are given. As was expected, the conditional distribution of the maximum likelihood estimate is skewed for the values of latent trait close to the two endpoints of the interval and the convergence is slower.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1979
- Accession Number
- ADA077706
Entities
People
- Fumiko Samejima
Organizations
- University of Tennessee