TY - BOOK
T1 - On the estimation of the proportion of masters in criterion-referenced testing
AU - van der Linden, Wim J.
PY - 1981
Y1 - 1981
N2 - J.A. Emrick's (1971) model is a latent class model of mastery testing that can be used to estimate the proportion of masters in a given population. A. Hamerle (1980), in a recent paper on this model, has proposed an estimator for the proportion of masters that is claimed to constitute a maximum likelihood approach. It is indicated that Hamerle is not quite correct in his presentation of Emrick's model and that his estimator is not maximum likelihood. An estimator is provided using the method of moments; this estimator appears to have the same shape as Hamerle's estimator, but should be interpreted differently since it is derived under the correct version of Emrick's model. An attractive property of the method of moments is that it also yields simple estimators for the present model if the two success parameters are unknown. It appears that these estimators can be used for tests consisting of three or more items. Results of extensive Monte Carlo studies indicate that the estimators possess excellent statistical properties.
AB - J.A. Emrick's (1971) model is a latent class model of mastery testing that can be used to estimate the proportion of masters in a given population. A. Hamerle (1980), in a recent paper on this model, has proposed an estimator for the proportion of masters that is claimed to constitute a maximum likelihood approach. It is indicated that Hamerle is not quite correct in his presentation of Emrick's model and that his estimator is not maximum likelihood. An estimator is provided using the method of moments; this estimator appears to have the same shape as Hamerle's estimator, but should be interpreted differently since it is derived under the correct version of Emrick's model. An attractive property of the method of moments is that it also yields simple estimators for the present model if the two success parameters are unknown. It appears that these estimators can be used for tests consisting of three or more items. Results of extensive Monte Carlo studies indicate that the estimators possess excellent statistical properties.
KW - Mastery tests
KW - Foreign countries
KW - Maximum likelihood statistics
KW - Criterion referenced tests
KW - Monte Carlo methods
KW - Estimation (Mathematics)
KW - Mathematical model
KW - Latent trait theory
M3 - Report
T3 - Twente Educational Memorandum
BT - On the estimation of the proportion of masters in criterion-referenced testing
PB - University of Twente
CY - Enschede, The Netherlands
ER -