Abstract

The Extended Growth Curve model is considered. It turns out that the estimated mean of the model is the projection of the observations on the space generated by the design matrices which turns out to be the sum of two tensor product spaces. The orthogonal complement of this space is decomposed into four orthogonal spaces and residuals are defined by projecting the observation matrix on the resulting components. The residuals are interpreted and some remarks are given as to why we should not use ordinary residuals, what kind of information our residuals give and how this information might be used to validate model assumptions and detect outliers and influential observations. It is shown that the residuals are symmetrically distributed around zero and are uncorrelated with each other. The covariance between the residuals and the estimated model as well as the dispersion matrices for the residuals are also given

Published in

Scandinavian Journal of Statistics
2006, Volume: 33, number: 1, pages: 121-138
Publisher: BLACKWELL PUBLISHING

SLU Authors

• Hamid, Jemila Seid

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    

• von Rosen, Dietrich

  • Department of Energy and Technology, Swedish University of Agricultural Sciences
    

UKÄ Subject classification

Forest Science
Horticulture
Environmental Sciences related to Agriculture and Land-use


Publication identifier

DOI: https://doi.org/10.1111/j.1467-9469.2006.00464.x

Permanent link to this page (URI)

https://res.slu.se/id/publ/9679