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Information matrix estimation procedures for cognitive diagnostic models
Author(s) -
Liu Yanlou,
Xin Tao,
Andersson Björn,
Tian Wei
Publication year - 2019
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/bmsp.12134
Subject(s) - covariance matrix , estimator , estimation of covariance matrices , mathematics , matrix (chemical analysis) , scatter matrix , covariance , statistics , fisher information , inverse , algorithm , materials science , geometry , composite material
Two new methods to estimate the asymptotic covariance matrix for marginal maximum likelihood estimation of cognitive diagnosis models ( CDM s), the inverse of the observed information matrix and the sandwich‐type estimator, are introduced. Unlike several previous covariance matrix estimators, the new methods take into account both the item and structural parameters. The relationships between the observed information matrix, the empirical cross‐product information matrix, the sandwich‐type covariance matrix and the two approaches proposed by de la Torre (2009, J. Educ. Behav. Stat ., 34 , 115) are discussed. Simulation results show that, for a correctly specified CDM and Q ‐matrix or with a slightly misspecified probability model, the observed information matrix and the sandwich‐type covariance matrix exhibit good performance with respect to providing consistent standard errors of item parameter estimates. However, with substantial model misspecification only the sandwich‐type covariance matrix exhibits robust performance.