Monotone Properties of a General Diagnostic Model

Abstract

ETS and the ETS logo are registered trademarks of Educational Testing Service (ETS). AbstractMonotonicity 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 + = 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.

Variance Estimation for Naep Data Using a Resampling‐based Approach: An Application of Cognitive Diagnostic Models

“…For instance, recently, Xu (2007) conducted an investigation to examine whether the monotonicity property can generally be sustained in GDM so that simple data summaries (e.g., the observed total score) can help inform the ordered categories of the latent trait and lead to the reporting of valid and reliable scaled scores. Obviously, in recent years, a parametrically complex IRT modeling framework has been called for.…”

Item Response Theory

“…He demonstrated the model using simulated as well as TOEFL iBT data. Xu (2007) Simulation studies demonstrated the accuracy of the estimation procedure, and effectiveness of model fitting and model fit evaluation procedures. They concluded that the model is a promising tool for skills diagnosis that merits further research and development.…”

“…Any linking procedure is viewed as a restriction on the item parameter space, and then rewriting the log-likelihood function together with implementation of a maximization procedure under linear or nonlinear restrictions accomplishes the linking. Xu andM. von Davier (2008c/2008d) developed an IRT linking approach for use with the GD model and applied the proposed approach to NAEP data.…”

Review of Diagnostic Measurement: Theories, Methods, and Applications

“…Specifically, simple data summaries were identified by Junker and Sijtsma to inform about the presence or absence of cognitive attributes when the full computational power needed to estimate the models is not available. Xu (2007) examined the stochastic ordering and monotonicity properties of a special case of GDM. Monotonicity of item response functions under DCMs will likely need further attention if we would like to enhance the interpretability of ability estimates or attribute estimates from such models.…”