Determining the accuracy of item parameter standard error of estimates in BILOG-MG 3

Authors

Michael Toland, University of Nebraska at LincolnFollow

Date of this Version

July 2008

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirement For the Degree of Doctor of Philosophy. Major: Psychological Studies in Education. Under the Supervision of Professor Rafael J. De Ayala
Lincoln, Nebraska: July 7, 2008
Copyright (c) 2008 Michael Toland.

Abstract

This study was conducted to determine the accuracy of item parameter standard error of estimates (SEEs) produced by BILOG-MG 3 by examining their performance under a variety of conditions. The Factors manipulated in this study were type of underlying difficulty (b) distribution, type of underlying discrimination (a) distribution, type of underlying lower asymptote (c) distribution, test length (I), type of underlying latent trait (θ) distribution, sample size (J), and the number of quadrature points. Results showed that the accuracy of the estimated SEb under the 1PL, 2PL, and 3PL models depended on the magnitude of the b parameter being estimated. Under the 1PL model, the accuracy of the estimated SEb was related to the underlying b and θ distributions as well as I. The 2PL model results showed that the accuracy of the estimated SEb was related to I, but no other factors in this study had an impact on the accuracy of estimation of SEb under this model. For the 3PL model, results showed that the accuracy of the estimated SEb tended to be impacted by I, while certain combinations of J, I, underlying b distribution, and underlying a distribution had consistently uniform accuracy of estimation of SEb across the range of b parameters studied. When considering the accuracy of the estimated SEa, the 2PL and 3PL model results showed that the accuracy depended upon the magnitude of the a parameter being estimated, while an increase in I increased the accuracy of the estimated SEa under the 2PL and 3PL models. Moreover, 2PL and 3PL model results showed the accuracy of the estimated SEa was related to the underlying item a, b, and θ distributions as well as J and I, when the entire range of a parameters was considered. The accuracy of the estimated SEc under the 3PL model was independent of the magnitude of the item c parameter being estimated and unaffected by any combination of factors studied. The implications and limitations of these results are discussed.