Open AccessMONOTONE PROPERTIES OF A GENERAL DIAGNOSTIC MODEL
Author(s) -
Xu Xueli
Publication year - 2007
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.2333-8504.2007.tb02067.x
Subject(s) - monotonic function , monotone polygon , property (philosophy) , econometrics , simple (philosophy) , mathematics , statistics , mathematical analysis , philosophy , geometry , epistemology
Monotonicity properties of a general diagnostic model (GDM) are considered in this paper. Simple data summaries are identified to inform about the ordered categories of latent traits. The findings are very much in accordance with the statements made about the GPCM (Hemker, Sijtsma, Molenaar, & Junker, 1996, 1997). On the one hand, by fitting a GDM with equal slopes across items, the observed total score X + = Σ j : q jk = 1 x j demonstrates the monotone likelihood ratio (MLR) property in individual coordinate at the cost of losing model fit. On the other hand, fitting a GDM without slope restriction increases the model fit but by sacrificing MLR property. Trade‐offs between these two situations should be considered in practice.