Open AccessReparameterization and invariant covariance matrices of factors in linear models
Author(s) -
Tõnu Möls,
Tatjahtman
Publication year - 2004
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.276
H-Index - 6
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2004.08.16
Subject(s) - eigenvalues and eigenvectors , covariance , mathematics , invariant (physics) , covariance matrix , permutation matrix , permutation (music) , random matrix , matrix (chemical analysis) , pure mathematics , combinatorics , statistics , mathematical physics , physics , circulant matrix , materials science , composite material , quantum mechanics , acoustics
Let the vector ζ consist of sampled random elements of factors in a linear mixed model. Let P be a permutation matrix. The covariance matrix D(ζ) is called P-invariant if D(ζ)=D(Pζ). It will be demonstrated that there is a strong correspondence between the spectrum of D(ζ) and certain reparametrization conditions on the factors. In particular, the classical reparametrization condition ∑ζi=0 has a clear presentation through the eigenvalues of D(ζ). This correspondence is useful for modelling data.