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Information Matrices and Standard Errors for MLEs of Item Parameters in IRT

Published online by Cambridge University Press:  01 January 2025

Ke-Hai Yuan ,
Ying Cheng  and
Jeff Patton
Ke-Hai Yuan*
Affiliation:
University of Notre Dame
Ying Cheng
Affiliation:
University of Notre Dame
Jeff Patton
Affiliation:
University of Notre Dame
*
Requests for reprints should be sent to Ke-Hai Yuan, University of Notre Dame, Notre Dame, IN 46556, USA. E-mail: kyuan@nd.edu
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Abstract

The paper clarifies the relationship among several information matrices for the maximum likelihood estimates (MLEs) of item parameters. It shows that the process of calculating the observed information matrix also generates a related matrix that is the middle piece of a sandwich-type covariance matrix. Monte Carlo results indicate that standard errors (SEs) based on the observed information matrix are robust to many, but not all, conditions of model/distribution misspecifications. SEs based on the sandwich-type covariance matrix perform most consistently across conditions. Results also suggest that SEs based on other matrices are either not consistent or perform not as robust as those based on the sandwich-type covariance matrix or the observed information matrix.

Keywords

model misspecificationMonte Carloobserved information matrixsandwich-type covariance matrixstandard errors
Type
Original Paper
Information
Psychometrika , Volume 79 , Issue 2 , April 2014 , pp. 232 - 254
Copyright
Copyright © 2013 The Psychometric Society

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