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Confidence ellipsoids for ASCA models based on multivariate regression theory
Author(s) -
Liland Kristian Hovde,
Smilde Age,
Marini Federico,
Næs Tormod
Publication year - 2018
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.2990
Subject(s) - multivariate statistics , ellipsoid , variance (accounting) , regression , permutation (music) , statistics , mathematics , regression analysis , confidence interval , econometrics , multivariate analysis , computer science , physics , accounting , astronomy , acoustics , business
In analysis of variance simultaneous component analysis, permutation testing is the standard way of assessing uncertainty of effect level estimates. This article introduces an analytical solution to the assessment of uncertainty through classical multivariate regression theory. We visualize the uncertainty as ellipsoids, contrasting these to data ellipsoids. This is further extended to multiple testing of effect level differences. Confirmatory and intuitive results are observed when applying the theory to previously published data and simulations.