Asymptotic Properties of Induced Maximum Likelihood Estimates of Nonlinear Models for Item Response Variables: The Finite-Generic-Item-Pool Case.

Autor/in	Jones, Douglas H.
Institution	Advanced Statistical Technologies Corp., Lawrenceville, NJ.
Titel	Asymptotic Properties of Induced Maximum Likelihood Estimates of Nonlinear Models for Item Response Variables: The Finite-Generic-Item-Pool Case.
Quelle	(1985), (42 Seiten) PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Monographie
Schlagwörter	Error Patterns; Functions (Mathematics); Goodness of Fit; Item Analysis; Latent Trait Theory; Mathematical Models; Maximum Likelihood Statistics; Statistical Studies; Test Theory + Suchen Sie Ihr Suchwort? Fehlertyp; Itemanalyse; Latent-Trait-Modell; Mathematical model; Mathematisches Modell; Testtheorie
Abstract	The progress of modern mental test theory depends very much on the techniques of maximum likelihood estimation, and many popular applications make use of likelihoods induced by logistic item response models. While, in reality, item responses are nonreplicate within a single examinee and the logistic models are only ideal, practitioners make inferences using the asymptotic distribution of the maximum likelihood estimator derived as if item responses were replicated and satisfied their ideal model. This article proposes a sample space acknowledging these two realities and derives the asymptotic distribution of the induced maximum likelihood estimator. It is assumed that items, while sampled from an infinite set of items, have but a finite domain of alternate response functions. Using the proposed sample space, the statistical functional approach of von Mises is applied to derive the influence curve of the maximum likelihood estimator; to discuss related robustness properties; and to derive new classes of resistent estimators. This article's general purpose is revealing the value of these methods for uncovering the relative merits of different item response functions. Proofs and mathematical derivations are minimized to increase the accessibility of this complex subject. (Author/LMO)
Erfasst von	ERIC (Education Resources Information Center), Washington, DC