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Numerical approximation of the observed information matrix with Oakes' identity
Author(s) -
Chalmers R. Philip
Publication year - 2018
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.12127
Subject(s) - estimator , mathematics , covariance matrix , identity (music) , matrix (chemical analysis) , monte carlo method , identity matrix , algorithm , computer science , numerical approximation , mathematical optimization , numerical analysis , statistics , eigenvalues and eigenvectors , mathematical analysis , physics , materials science , acoustics , composite material , quantum mechanics
An efficient and accurate numerical approximation methodology useful for obtaining the observed information matrix and subsequent asymptotic covariance matrix when fitting models with the EM algorithm is presented. The numerical approximation approach is compared to existing algorithms intended for the same purpose, and the computational benefits and accuracy of this new approach are highlighted. Instructive and real‐world examples are included to demonstrate the methodology concretely, properties of the estimator are discussed in detail, and a Monte Carlo simulation study is included to investigate the behaviour of a multi‐parameter item response theory model using three competing finite‐difference algorithms.