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Residuals in GMANOVA–MANOVA model with rank restrictions on parameters

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Abstract

Residuals in the GMANOVA–MANOVA model with rank restrictions on the mean parameters is considered. The main objective is to define residuals useful for evaluating the reduced rank restriction model. We decompose linear spaces into four subspaces as it can be done for the Extended Growth Curve model with two “profiles”. The new residuals are defined by orthogonal projections on these subspaces. It is discussed how the new residuals can be used to test model assumptions.

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Acknowledgements

The research of Felix Wamono is supported by the Swedish International Development and Cooperation Agency (SIDA) in collaboration with Makerere University, under SIDA-Makerere University Cooperation Agreement, Project 316. Dietrich von Rosen is supported by the Swedish Research Council (2017-03003). We are very grateful for the comments made by an anonymous referee which improved the presentation.

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Authors and Affiliations

  1. Department of Mathematics and School of Statistics and Planning, Makerere University, Kampala, Uganda

    Felix Wamono

  2. Department of Energy and Technology, Swedish University of Agricultural Sciences, Uppsala, Sweden

    Dietrich von Rosen

  3. Department of Mathematics, Linköping University, Linköping, Sweden

    Martin Singull

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  1. Felix Wamono
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  2. Dietrich von Rosen
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  3. Martin Singull
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Correspondence to Felix Wamono.

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Wamono, F., von Rosen, D. & Singull, M. Residuals in GMANOVA–MANOVA model with rank restrictions on parameters. J. Korean Stat. Soc. 51, 223–244 (2022). https://doi.org/10.1007/s42952-021-00138-0

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  • DOI: https://doi.org/10.1007/s42952-021-00138-0

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