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Growth curve (statistics) : ウィキペディア英語版
Growth curve (statistics)

The growth curve model in statistics is a specific multivariate linear model, also known as GMANOVA (Generalized Multivariate ANalysis-Of-VAriance). It generalizes MANOVA by allowing post-matrices, as seen in the definition.
==Definition==

Growth curve model: Let X be a ''p''×''n'' matrix, A a ''p''×''q'' matrix with ''q'' ≤ ''p'', B a ''q''×''k'' matrix,C a ''k''×''n'' matrix with rank(''C'') + ''p'' ≤ ''n'' and let Σ be a positive-definite ''p''×''p'' matrix. Then
: X=ABC+\Sigma^E
defines the growth curve model, where A and C are known, B and Σ are unknown, and E is a random matrix distributed as ''N''''p'',''n''(0,''I''''p'',''n'').
This differs from standard MANOVA by the addition of C, a "postmatrix".〔

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