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Biometrika 1990 77(4):773-785; doi:10.1093/biomet/77.4.773
© 1990 by Biometrika Trust
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Three-dimensional biplots

J. C. GOWER

AFRC Institute of Arable Crops Research Rothamsted Experimental Station, Harpenden, Hertfordshire AL5 2JQ, U.K.

The biplot of a two-way table is discussed as a diagnostic tool for investigating bilinear models with additive terms for rows and columns and at least one multiplicative term. The full biplot is three dimensional with the points representing row effects concentrated in a plane orthogonal to another plane containing the points representing the column effects. Projections onto suitable directions in these planes give the row, column and multiplicative constants of the model. Extensions to more complex models, practical details and implications for interactive computer graphics are discussed.

Key Words: Bilinear model • Biplot • Diagnostic • Graphical methods • Multiplicative model


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