Two procedures for Rasch, sample-free, item calibration are reviewed and compared for accuracy. Andersen's (1972) theoretically ideal "conditional" procedure is impractical for calibrating more than 10 or 15 items. A simplified alternative procedure for conditional estimation practical for 20 or 30 items which produces equivalent estimates is developed. When more than 30 items are analyzed recourse to Wright's (1969) widely used "unconditional" procedure is inevitable but that procedure is biased. A correction factor which makes the bias negligible is identified and demonstrated.
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References
1.
Andersen, E. B.Asymptotic properties of conditional maximum likelihood estimators. Journal of the Royal Statistical Society. 1970, 32, 283-301.
2.
Andersen, E. B.The asymptotic distribution of conditional likelihood ratio tests. Journal of the American Statistical Association, 1971, 66 (335), 630-33.
3.
Andersen, E. B.The numerical solution of a set of conditional estimation equations. The Journal of the Royal Statistical Society; Series B, 1972, 34 (1), 42-54.
4.
Andersen, E. B.Conditional Inference and Models for Measuring. Cophenhagen, Denmark: Mentalhygiejnisk Forlag, 1973.
5.
Birnbaum, A.Estimation of an ability. In F. Lord and M. Novick (Eds.), Statistical Theories of Mental Test Scores . Reading, Mass.: Addison-Wesley , 1968.
6.
Bock, R. D.Estimating item parameters and latent ability when responses are scored in two or more nominal categories . Psychometrika, 1972, 37, 29-51.
7.
Rasch, G.Probabilistic Models for Some Intelligence and A ttainment Tests. Copenhagen, Denmark: Denmarks Paedagogiske Institut, 1960.
8.
Rasch, G.On general laws and the meaning of measurement in psychology. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics, 1961, 4, 321-33.
9.
Rasch, G.An individualistic approach to item analysis. In P. F. Lazarsfeld and N. W. Henry (Eds.), Readings in Mathematical Social Sciences. Chicago: Science Research Associates, 1966. (a)
10.
Rasch, G.An item analysis which takes individual differences into account. British Journal of Mathematical and Statistical Psychology, 1966, 19, 49-57. (b)
11.
Wright, B. D. and Panchapakesan, N.A procedure for sample-free item analysis, EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 1969, 29, 23-48.