Reparameterization and invariant covariance matrices of factors in linear models | Zendy

Tõnu Möls | Zendy; Tatyahtman | Zendy

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Reparameterization and invariant covariance matrices of factors in linear models

Author(s) -

Tõnu Möls,

Tatyahtman

Publication year - 2004

Publication title -

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.

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