TY - JOUR

T1 - Set theoretic latent trait model

T2 - —Theoretical consideration—

AU - Shiina, Kenpei

PY - 1990

Y1 - 1990

N2 - The set theoretic latent trait model proposed in this paper assumes that: 1) subjects and items are represented by sets of discrete abilities, 2) the sets of abilities are partially ordered with respect to their inclusion relations, and 3) the probability of correct responses is defined on the partially ordered structure as a set function of subjects and items. This model is a modified latent class model incorporating order relations among latent classes. At the same time it is a generalization of ordinary item response theory in that subjects are represented in a partially ordered structure rather than a totally ordered structure (dimension). A computer program which estimates parameters of the model and determines set structures was developed, and three simulation studies suggested the viability of the model.

AB - The set theoretic latent trait model proposed in this paper assumes that: 1) subjects and items are represented by sets of discrete abilities, 2) the sets of abilities are partially ordered with respect to their inclusion relations, and 3) the probability of correct responses is defined on the partially ordered structure as a set function of subjects and items. This model is a modified latent class model incorporating order relations among latent classes. At the same time it is a generalization of ordinary item response theory in that subjects are represented in a partially ordered structure rather than a totally ordered structure (dimension). A computer program which estimates parameters of the model and determines set structures was developed, and three simulation studies suggested the viability of the model.

KW - item response theory

KW - latent class model

KW - latent traits

KW - lattice structure

KW - sets of abilities

UR - http://www.scopus.com/inward/record.url?scp=85007947216&partnerID=8YFLogxK

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U2 - 10.5926/jjep1953.38.1_1

DO - 10.5926/jjep1953.38.1_1

M3 - Article

AN - SCOPUS:85007947216

SN - 0021-5015

VL - 38

SP - 1

EP - 8

JO - The Japanese Journal of Educational Psychology

JF - The Japanese Journal of Educational Psychology

IS - 1

ER -