On the estimation of the proportion of masters in criterion-referenced testing

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Abstract

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.
Original languageUndefined
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente, Faculty Educational Science and Technology
Publication statusPublished - 1981

Publication series

NameTwente Educational Memorandum
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.27

Keywords

  • Mastery Tests
  • Foreign Countries
  • Maximum Likelihood Statistics
  • IR-103601
  • Criterion Referenced Tests
  • Monte Carlo Methods
  • Estimation (Mathematics)
  • Mathematical Models
  • Latent Trait Theory

Cite this

van der Linden, W. J. (1981). On the estimation of the proportion of masters in criterion-referenced testing. (Twente Educational Memorandum; No. 27). Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology.
van der Linden, Willem J. / On the estimation of the proportion of masters in criterion-referenced testing. Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1981. (Twente Educational Memorandum; 27).
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abstract = "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.",
keywords = "Mastery Tests, Foreign Countries, Maximum Likelihood Statistics, IR-103601, Criterion Referenced Tests, Monte Carlo Methods, Estimation (Mathematics), Mathematical Models, Latent Trait Theory",
author = "{van der Linden}, {Willem J.}",
year = "1981",
language = "Undefined",
series = "Twente Educational Memorandum",
publisher = "University of Twente, Faculty Educational Science and Technology",
number = "27",

}

van der Linden, WJ 1981, On the estimation of the proportion of masters in criterion-referenced testing. Twente Educational Memorandum, no. 27, University of Twente, Faculty Educational Science and Technology, Enschede, the Netherlands.

On the estimation of the proportion of masters in criterion-referenced testing. / van der Linden, Willem J.

Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1981. (Twente Educational Memorandum; No. 27).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - On the estimation of the proportion of masters in criterion-referenced testing

AU - van der Linden, Willem 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.

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KW - Foreign Countries

KW - Maximum Likelihood Statistics

KW - IR-103601

KW - Criterion Referenced Tests

KW - Monte Carlo Methods

KW - Estimation (Mathematics)

KW - Mathematical Models

KW - Latent Trait Theory

M3 - Report

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van der Linden WJ. On the estimation of the proportion of masters in criterion-referenced testing. Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology, 1981. (Twente Educational Memorandum; 27).