EQUATING LOGISTIC ABILITY SCALES BY A WEIGHTED LEAST SQUARES METHOD

TOMOKAZU HAEBARA

doi:10.4992/psycholres1954.22.144

TOMOKAZU HAEBARA

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JOURNAL FREE ACCESS

1980 Volume 22 Issue 3 Pages 144-149

DOI https://doi.org/10.4992/psycholres1954.22.144

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Published: December 30, 1980 Received: April 25, 1980 Available on J-STAGE: February 24, 2009 Accepted: - Advance online publication: - Revised: -
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Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : BIRNBAUM, A. 1968 Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord & M. R. Novick, Statistical theories of mental test scores. Reading, Mass.: Addison-Wesley.
DIXON, L. C. W. 1972 Nonlinear optimisation. London: English Universities Press.
DOUGLASS, J. B. 1980 Applying latent trait theory to a classroom examination system: Model comparison and selection. Paper presented at the meeting of the American Educational Research Association, Boston, April 1980.
HAEBARA, T. 1979 A method for investigating item bias using Birnbaum's three parameter logistic model (ITP Occasional Papers No. 25). Iowa City: University of Iowa, Iowa Testing Programs.
HAMBLETON, R. K., SWAMINATHAN, H., COOK, L. L., EIGNER, D. R., & GIFFORD, J. A. 1978 Developments in latent trait theory: Models, technical issues, and applications. Review of Educational Research, 48, 467-510.
MARCO, G. L. 1977 Item characteristic curve solutions to three intractable testing problems. Journal of Educational Measurement, 14, 139-160.
SHIBA, S. 1978 Construction of a scale for acquisition of word meanings (Bulletin of Faculty of Education, Vol. 17, Pp. 47-58). University of Tokyo. (In Japanese with English abstract)
SHIBA, S., NOGUCHi, H., & HAEBARA, T. 1978 A stratified adaptive test of verbal ability. Japanese Journal of Educational Psychology, 26, 229-238. (In Japanese with English abstract)
SHIBA, S., NOGUCHI, H., & OHAMA, K. 1980 The efficiency of preliminary measurement by means of a short form of the stratified adaptive test in measuring verbal ability (Bulletin of Faculty of Education, Vol. 19, Pp. 27-34). University of Tokyo. (In Japanese with English abstract)
WOOD, R. L., WINGERSKY, M. S., & LORD, F. M. 1976 LOGIST: A computer program for estimating examinee ability and item characteristic curve parameters (ETS RM 76-6). Princeton, N. J.: Educational Testing Service.

Right : BIRNBAUM, A. 1968 Some latent trait models and their use in inferring an examinee's ability.In F.M. Lord & M.R. Novick, Statistical theories of mental test scores. Reading, Mass.: Addison-Wesley.
DIXON, L. C. W. 1972 Nonlinear optimisation. London: English Universities Press.
DOUGLASS, J. B. 1980 Applying latent trait theory to a classroom examination system: Model comparison and selection. Paper presented at the meeting of the American Educational Research Association, Boston, April 1980.
HAEBARA, T. 1979 A method for investigating item bias using Birnbaum's three-parameter logistic model (ITP Occasional Papers No.25). Iowa City: University of Iowa, Iowa Testing Programs.
HAMBLETON, R. K., SWAMINATHAN, H., COOK, L. L., EIGNER, D. R., &GIFFORD, J. A. 1978 Developments in latent trait theory: Models, technical issues, and applications. Review of Educational Research, 48, 467-510.
MARCO, G. L. 1977 Item characteristic curve solutions to three intractable testing problems.Journal of Educational Measurement, 14, 139-160.
SHIBA, S. 1978 Construction of a scale for acquisition of word meanings (Bulletin of Faculty of Education, Vol.17, Pp.47-58). University of Tokyo.(In Japanese with English abstract)
SHIBA, S., NOGUCHI, H., &HAEBARA, T. 1978A stratified adaptive test of verbal ability. Japanese Journal of Educational Psychology, 26, 229-238.(In Japanese with English abstract)
SHIBA, S., NOGUCHI, H., &OHAMA, K. 1980 Theefficiency of preliminary measurement by means of ashort form of the stratified adaptive test in measuringverbal ability (Bulletin of Faculty of Education, Vol.19, Pp.27-34). University of Tokyo.(In Japanese with English abstract)
WOOD, R. L., WINGERSKY, M. S., &Loan, F. M.1976 LOGIST: A computer program for estimating examinee ability and item characteristic curve parameters (ETS RM 76-6). Princeton, N. J.: Educational Testing Service.

Date of correction: February 24, 2009 Reason for correction: - Correction: PDF FILE Details: -

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : BIRNBAUM, A. 1968 Some latent trait models and their use in inferring an examinee's ability.In F.M. Lord & M.R. Novick, Statistical theories of mental test scores. Reading, Mass.: Addison-Wesley.
DIXON, L. C. W. 1972 Nonlinear optimisation. London: English Universities Press.
DOUGLASS, J. B. 1980 Applying latent trait theory to a classroom examination system: Model comparison and selection. Paper presented at the meeting of the American Educational Research Association, Boston, April 1980.
HAEBARA, T. 1979 A method for investigating item bias using Birnbaum's three-parameter logistic model (ITP Occasional Papers No.25). Iowa City: University of Iowa, Iowa Testing Programs.
HAMBLETON, R. K., SWAMINATHAN, H., COOK, L. L., EIGNER, D. R., &GIFFORD, J. A. 1978 Developments in latent trait theory: Models, technical issues, and applications. Review of Educational Research, 48, 467-510.
MARCO, G. L. 1977 Item characteristic curve solutions to three intractable testing problems.Journal of Educational Measurement, 14, 139-160.
SHIBA, S. 1978 Construction of a scale for acquisition of word meanings (Bulletin of Faculty of Education, Vol.17, Pp.47-58). University of Tokyo.(In Japanese with English abstract)
SHIBA, S., NOGUCHI, H., &HAEBARA, T. 1978A stratified adaptive test of verbal ability. Japanese Journal of Educational Psychology, 26, 229-238.(In Japanese with English abstract)
SHIBA, S., NOGUCHI, H., &OHAMA, K. 1980 Theefficiency of preliminary measurement by means of ashort form of the stratified adaptive test in measuringverbal ability (Bulletin of Faculty of Education, Vol.19, Pp.27-34). University of Tokyo.(In Japanese with English abstract)
WOOD, R. L., WINGERSKY, M. S., &Loan, F. M.1976 LOGIST: A computer program for estimating examinee ability and item characteristic curve parameters (ETS RM 76-6). Princeton, N. J.: Educational Testing Service.

Right : BIRNBAUM, A. 1968 Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord & M. R. Novick, Statistical theories of mental test scores. Reading, Mass.: Addison-Wesley.
DIXON, L. C. W. 1972 Nonlinear optimisation. London: English Universities Press.
DOUGLASS, J. B. 1980 Applying latent trait theory to a classroom examination system: Model comparison and selection. Paper presented at the meeting of the American Educational Research Association, Boston, April 1980.
HAEBARA, T. 1979 A method for investigating item bias using Birnbaum's three-parameter logistic model (ITP Occasional Papers No.25). Iowa City: University of Iowa, Iowa Testing Programs.
HAMBLETON, R. K., SWAMINATHAN, H., COOK, L. L., EIGNER, D. R., & GIFFORD, J. A. 1978 Developments in latent trait theory: Models, technical issues, and applications. Review of Educational Research, 48, 467-510.
MARCO, G. L. 1977 Item characteristic curve solutions to three intractable testing problems. Journal of Educational Measurement, 14, 139-160.
SHIBA, S. 1978 Construction of a scale for acquisition of word meanings (Bulletin of Faculty of Education, Vol.17, Pp.47-58). University of Tokyo.(In Japanese with English abstract)
SHIBA, S., NOGUCHI, H., & HAEBARA, T. 1978 A stratified adaptive test of verbal ability. Japanese Journal of Educational Psychology, 26, 229-238.(In Japanese with English abstract)
SHIBA, S., NOGUCHI, H., & OHAMA, K. 1980 The efficiency of preliminary measurement by means of a short form of the stratified adaptive test in measuring verbal ability (Bulletin of Faculty of Education, Vol.19, Pp.27-34). University of Tokyo.(In Japanese with English abstract)
WOOD, R. L., WINGERSKY, M. S., & LORD, F. M.1976 LOGIST: A computer program for estimating examinee ability and item characteristic curve parameters (ETS RM 76-6). Princeton, N. J.: Educational Testing Service.

Abstract

A general procedure for equating logistic ability scales that involves the use of a loss function and an optimization process is formulated. As one of the optimum estimation procedures, a weighted least squares method is introduced and applied to an achievement scale and an intelligence scale. An advantage of the method over previously proposed methods is that highly discriminating items tend to affect equating more strongly than less discriminating items.

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