Abstract
The test information function serves important roles in latent trait models and in their applications. Among others, it has been used as the measure of accuracy in ability estimation. A question arises, however, if the test information function is accurate enough for all meaningful levels of ability relative to the test, especially when the number of test items is relatively small (e.g., less than 50). In the present paper, using the constant information model and constant amounts of test information for a finite interval of ability, simulated data were produced for eight different levels of ability and for twenty different numbers of test items ranging between 10 and 200. Analyses of these data suggest that it is desirable to consider some modification of the test information function when it is used as the measure of accuracy in ability estimation.
Similar content being viewed by others
References
Birnhaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord & M. R. Novick (Eds.),Statistical theories of mental test scores (Chapters 17–20, pp. 395–479). Reading, MA: Addison Wesley.
Kendall, M. G., & Stuart, A. (1961).The advanced theory of statistics. Vol. 2. New York: Hafner.
Lord, F. M. (1983). Unbiased estimators of ability parameters, of their variances and of their parallel-form reliability.Psychometrika, 48, 233–245.
Lord, F. M., & Novick, M. R. (1968).Statistical theories of mental test scores. Reading, MA: Addison Wesley.
Samejima, F. (1972). A general model for free-response data.Psychometrika Monograph, No. 18, 37 (1, Pt. 2).
Samejima, F. (1979a). Constant information model: a promising item characteristic function (Office of Naval Research Report, 79-1). Arlington, VA: Office of Naval Research.
Samejima, F. (1979b). Convergence of the conditional distribution of the maximum likelihood estimate, given latent trait, to the asymptotic normality: Observations made through the constant information model (Office of Naval Research Report, 79-3). Arlington, VA: Office of Naval Research.
Samejima, F. (1982). Information loss caused by noise in models for dichotomous items (Office of Naval Research Report, 82-1). Washington, DC: Office of Naval Research.
Samejima, F. (1983). The constant information model on the dichotomous response level. In D. J. Weiss (Ed.),New horizons in testing (pp. 287–308). New York: Academic Press.
Samejima, F. (1987). Bias function of the maximum likelihood estimate of ability for discrete item responses (Office of Naval Research Report, 87-1). Arlington, VA: Office of Naval Research.
Samejima, F. (1993a). An approximation for the bias function of the maximum likelihood estimate of a latent variable for the general case where the item responses are discrete,Psychometrika, 58, 119–138.
Samejima, F. (1993b). The bias function of the maximum likelihood estimate of ability for the dichotomous response level,Psychometrika, 58, 195–209.
Author information
Authors and Affiliations
Additional information
This research was supported by the Office of Naval Research (N00014-77-C-0360, N00014-87-K-0320, N00014-91-J-1456). I would like to thank one of my former assistants, Barbara Livingston, for help with this manuscript.
Rights and permissions
About this article
Cite this article
Samejima, F. Some critical observations of the test information function as a measure of local accuracy in ability estimation. Psychometrika 59, 307–329 (1994). https://doi.org/10.1007/BF02296127
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02296127