Theory and applications of nonparametric regression in item response theory
Douglas, Jeffrey A.
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Permalink
https://hdl.handle.net/2142/22148
Description
Title
Theory and applications of nonparametric regression in item response theory
Author(s)
Douglas, Jeffrey A.
Issue Date
1995
Doctoral Committee Chair(s)
Stout, William F.
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Psychology, Psychometrics
Language
eng
Abstract
The simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered. In particular, the joint asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation is investigated under relatively unrestrictive assumptions on the underlying item response theory model as both test length and sample size increase. A large deviation probability inequality is given for ordinal ability estimation. The mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in the item characteristic curve estimates over all items and ability levels converges to zero with probability equal to one.
Smoothed SIBTEST, a nonparametric DIF detection procedure amalgamates SIBTEST and kernel smoothed item characteristic curve estimation. This procedure assesses DIF as a function of the latent trait $\theta$ that the test is designed to measure. Smoothed SIBTEST estimates this function with increased efficiency while providing hypothesis tests of local and global DIF. By contrast with most nonparametric procedures, matched examinee score cells are not needed, so sparse cell problems are avoided. The performance of smoothed SIBTEST is studied via simulation and real data analysis.
Methods are developed to investigate the fit of parametric item response theory models, by comparing them to models fit under nonparametric assumptions. The techniques are largely graphical but are made inferential through the use of resampling from the estimated parametric model. Identifiability and consistent estimation of IRT models are discussed and shown to be vital to the performance and interpretation of differences between two fitted IRT models. The techniques are illustrated with a simulated example.
The local behavior of item pair covariances conditional on a unidimensional latent trait are studied. Conditional covariance functions are estimated using kernel smoothing. Several models are developed to explain special situations in which the assumption of local independence is violated and real data examples which arguably correspond to these models are given.
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