Pd. Wentzell et Mt. Lohnes, Maximum likelihood principal component analysis with correlated measurement errors: theoretical and practical considerations, CHEM INTELL, 45(1-2), 1999, pp. 65-85
Procedures to compensate for correlated measurement errors in multivariate
data analysis are described. These procedures are based on the method of ma
ximum likelihood principal component analysis (MLPCA), previously described
in the literature. MLPCA is a decomposition method similar to conventional
PCA, but it takes into account measurement uncertainty in the decompositio
n process, placing less emphasis on measurements with large variance. Altho
ugh the original MLPCA algorithm can accommodate correlated measurement err
ors, two drawbacks have limited its practical utility in these cases: (1) a
n inability to handle rank deficient error covariance matrices, and (2) dem
anding memory and computational requirements. This paper describes two simp
lifications to the original algorithm that apply when errors are con-elated
only within the rows of a data matrix and when all of these row covariance
matrices are equal. Simulated and experimental data for three-component mi
xtures are used to test the new methods. It was found that inclusion of err
or covariance information via MLPCA always gave results which were at least
as good and normally better than PCA when the true error covariance matrix
was available. However, when the error covariance matrix is estimated from
replicates, the relative performance depends on the quality of the estimat
e and the degree of correlation. For experimental data consisting of mixtur
es of cobalt, chromium and nickel ions, maximum likelihood principal compon
ents regression showed an improvement of up to 50% in the cross-validation
error when error covariance information was included. (C) 1999 Elsevier Sci
ence B.V. All rights reserved.