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Maximum Likelihood Estimation of Simultaneous Pairwise Linear Structural Relationships
Author(s) -
Bolfarine Heleno,
Rojas Manuel Galea
Publication year - 1995
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710370604
Subject(s) - mathematics , estimator , pairwise comparison , restricted maximum likelihood , expectation–maximization algorithm , covariance matrix , statistics , covariance , maximization , measure (data warehouse) , set (abstract data type) , maximum likelihood , wald test , fisher information , matrix (chemical analysis) , maximum likelihood sequence estimation , mathematical optimization , statistical hypothesis testing , computer science , data mining , materials science , composite material , programming language
Abstract The problem of assessing the relative calibrations and relative accuracies of a set of p instruments, each designed to measure the same characteristic on a common group of individuals is considered by using the EM algorithm. As shown, the EM algorithm provides a general solution for this problem. Its implementation is simple and in its most general form requires no extra iterative procedures within the M step. One important feature of the algorithm in this set up is that the error variance estimates are always positive. Thus, it can be seen as a kind of restricted maximization procedure. The expected information matrix for the maximum likelihood estimators is derived, upon which the large sample estimated covariance matrix for the maximum likelihood estimators can be computed. The problem of testing hypothesis about the calibration lines can be approached by using the Wald statistics. The approach is illustrated by re‐analysing two data sets in the literature.