Open AccessTHE DUTCH IDENTITY: A NEW TOOL FOR THE STUDY OF ITEM RESPONSE THEORY MODELS
Author(s) -
Holland Paul W.
Publication year - 1987
Publication title -
ets research report series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.235
H-Index - 5
ISSN - 2330-8516
DOI - 10.1002/j.2330-8516.1987.tb00231.x
Subject(s) - item response theory , latent class model , identity (music) , curse of dimensionality , local independence , structural equation modeling , econometrics , mathematics , trait , differential item functioning , sample (material) , computerized adaptive testing , log linear model , linear model , statistics , psychometrics , computer science , physics , acoustics , chemistry , chromatography , programming language
The Dutch Identity is a useful way to reexpress the basic equations of item response theory (IRT) that relate the manifest probabilities to the item response functions (IRFs) and the latent trait distribution. The identity may be exploited in several ways. For example: (a) to show how IRT models behave for large numbers of items – they are submodels of second‐order log‐linear models for 2 J tables; (b) to suggest new ways to assess the dimensionality of IRT models – factor analysis of matrices composed of second‐order interactions from log‐linear models; (c) to give insight into the structure of latent class models; and (d) to illuminate the problem of identifying the IRFs and the latent trait distribution from sample data.