Simple estimators for the simple latent class mastery testing model

Research output: Book/ReportReportOther research output

6 Downloads (Pure)

Abstract

Latent class models for mastery testing differ from continuum models in that they do not postulate a latent mastery continuum but conceive mastery and non-mastery as two latent classes, each characterized by different probabilities of success. Several researchers use a simple latent class model that is basically a simultaneous application of the binomial error model to both mastery classes. W. A. Reulecke (1977) presents a version of this model that assumes that non-masters guess blindly, with a probability of success equal to the reciprocal of the number of alternatives. Assuming a loss ratio, these models enable the derivation of an optimal cutting score for separating masters from non-masters. To compute this cutting score, the model parameters must be estimated. J. A. Emrick and F. N. Adams (1969) suggest a method that is based on the average inter-item correlation but which, due to its assumptions, is only of restricted applicability. The sample applies to the maximum likelihood method in as much as this involves estimation equations that can be solved iteratively. In this paper, the method of moments is used to obtain "quick and easy" estimates. An endpoint that assumes that the parameters can simply be estimated from the tails of the sample distribution is discussed. A Monte Carlo experiment demonstrates that the method of moments yields excellent estimators and beats the endpoint method uniformly.
Original languageUndefined
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente, Faculty Educational Science and Technology
Publication statusPublished - Jun 1980

Publication series

NameTwente Educational Memorandum
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.19

Keywords

  • Cutting Scores
  • Guessing (Tests)
  • Models
  • Estimation (Mathematics)
  • Probability
  • Foreign Countries
  • Latent Trait Theory
  • IR-103610
  • Mastery Tests
  • Maximum Likelihood Statistics
  • Error Patterns

Cite this

van der Linden, W. J. (1980). Simple estimators for the simple latent class mastery testing model. (Twente Educational Memorandum; No. 19). Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology.
van der Linden, Willem J. / Simple estimators for the simple latent class mastery testing model. Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1980. (Twente Educational Memorandum; 19).
@book{df43ded790b74086a255437e666dba49,
title = "Simple estimators for the simple latent class mastery testing model",
abstract = "Latent class models for mastery testing differ from continuum models in that they do not postulate a latent mastery continuum but conceive mastery and non-mastery as two latent classes, each characterized by different probabilities of success. Several researchers use a simple latent class model that is basically a simultaneous application of the binomial error model to both mastery classes. W. A. Reulecke (1977) presents a version of this model that assumes that non-masters guess blindly, with a probability of success equal to the reciprocal of the number of alternatives. Assuming a loss ratio, these models enable the derivation of an optimal cutting score for separating masters from non-masters. To compute this cutting score, the model parameters must be estimated. J. A. Emrick and F. N. Adams (1969) suggest a method that is based on the average inter-item correlation but which, due to its assumptions, is only of restricted applicability. The sample applies to the maximum likelihood method in as much as this involves estimation equations that can be solved iteratively. In this paper, the method of moments is used to obtain {"}quick and easy{"} estimates. An endpoint that assumes that the parameters can simply be estimated from the tails of the sample distribution is discussed. A Monte Carlo experiment demonstrates that the method of moments yields excellent estimators and beats the endpoint method uniformly.",
keywords = "Cutting Scores, Guessing (Tests), Models, Estimation (Mathematics), Probability, Foreign Countries, Latent Trait Theory, IR-103610, Mastery Tests, Maximum Likelihood Statistics, Error Patterns",
author = "{van der Linden}, {Willem J.}",
year = "1980",
month = "6",
language = "Undefined",
series = "Twente Educational Memorandum",
publisher = "University of Twente, Faculty Educational Science and Technology",
number = "19",

}

van der Linden, WJ 1980, Simple estimators for the simple latent class mastery testing model. Twente Educational Memorandum, no. 19, University of Twente, Faculty Educational Science and Technology, Enschede, the Netherlands.

Simple estimators for the simple latent class mastery testing model. / van der Linden, Willem J.

Enschede, the Netherlands : University of Twente, Faculty Educational Science and Technology, 1980. (Twente Educational Memorandum; No. 19).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Simple estimators for the simple latent class mastery testing model

AU - van der Linden, Willem J.

PY - 1980/6

Y1 - 1980/6

N2 - Latent class models for mastery testing differ from continuum models in that they do not postulate a latent mastery continuum but conceive mastery and non-mastery as two latent classes, each characterized by different probabilities of success. Several researchers use a simple latent class model that is basically a simultaneous application of the binomial error model to both mastery classes. W. A. Reulecke (1977) presents a version of this model that assumes that non-masters guess blindly, with a probability of success equal to the reciprocal of the number of alternatives. Assuming a loss ratio, these models enable the derivation of an optimal cutting score for separating masters from non-masters. To compute this cutting score, the model parameters must be estimated. J. A. Emrick and F. N. Adams (1969) suggest a method that is based on the average inter-item correlation but which, due to its assumptions, is only of restricted applicability. The sample applies to the maximum likelihood method in as much as this involves estimation equations that can be solved iteratively. In this paper, the method of moments is used to obtain "quick and easy" estimates. An endpoint that assumes that the parameters can simply be estimated from the tails of the sample distribution is discussed. A Monte Carlo experiment demonstrates that the method of moments yields excellent estimators and beats the endpoint method uniformly.

AB - Latent class models for mastery testing differ from continuum models in that they do not postulate a latent mastery continuum but conceive mastery and non-mastery as two latent classes, each characterized by different probabilities of success. Several researchers use a simple latent class model that is basically a simultaneous application of the binomial error model to both mastery classes. W. A. Reulecke (1977) presents a version of this model that assumes that non-masters guess blindly, with a probability of success equal to the reciprocal of the number of alternatives. Assuming a loss ratio, these models enable the derivation of an optimal cutting score for separating masters from non-masters. To compute this cutting score, the model parameters must be estimated. J. A. Emrick and F. N. Adams (1969) suggest a method that is based on the average inter-item correlation but which, due to its assumptions, is only of restricted applicability. The sample applies to the maximum likelihood method in as much as this involves estimation equations that can be solved iteratively. In this paper, the method of moments is used to obtain "quick and easy" estimates. An endpoint that assumes that the parameters can simply be estimated from the tails of the sample distribution is discussed. A Monte Carlo experiment demonstrates that the method of moments yields excellent estimators and beats the endpoint method uniformly.

KW - Cutting Scores

KW - Guessing (Tests)

KW - Models

KW - Estimation (Mathematics)

KW - Probability

KW - Foreign Countries

KW - Latent Trait Theory

KW - IR-103610

KW - Mastery Tests

KW - Maximum Likelihood Statistics

KW - Error Patterns

M3 - Report

T3 - Twente Educational Memorandum

BT - Simple estimators for the simple latent class mastery testing model

PB - University of Twente, Faculty Educational Science and Technology

CY - Enschede, the Netherlands

ER -

van der Linden WJ. Simple estimators for the simple latent class mastery testing model. Enschede, the Netherlands: University of Twente, Faculty Educational Science and Technology, 1980. (Twente Educational Memorandum; 19).