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Thegrowth curve model instatistics is a specific multivariate linear model, also known as GMANOVA (Generalized Multivariate Analysis-Of-Variance).^[1] It generalizesMANOVA by allowing post-matrices, as seen in the definition.

Growth curve model:^[2] LetX be ap×nrandom matrix corresponding to the observations,A ap×q withindesign matrix withq ≤ p,B aq×k parameter matrix,C ak×n between individual design matrix with rank(C) + p ≤ n and letΣ be apositive-definitep×p matrix. Then

${\displaystyle X=ABC+{\mathrm{\Sigma }}^{1/2}E}$

defines the growth curve model, whereA andC are known,B andΣ are unknown, andE is a random matrix distributed asN_p,n(0,I_p,_n).

This differs from standardMANOVA by the addition ofC, a "postmatrix".^[3]

Many writers have considered the growth curve analysis, among them Wishart (1938),^[4] Box (1950)^[5] and Rao (1958).^[6] Potthoff and Roy in 1964;^[3] were the first in analyzinglongitudinal data applying GMANOVA models.

GMANOVA is frequently used for the analysis of surveys, clinical trials, and agricultural data,^[7] as well as more recently in the context of Radar adaptive detection.^[8][9]

Inmathematical statistics,growth curves such as those used in biology are often modeled as beingcontinuousstochastic processes, e.g. as beingsample paths thatalmost surely solvestochastic differential equations.^[10] Growth curves have been also applied in forecasting market development.^[11] When variables are measured with error, aLatent growth modeling SEM can be used.

• Davidian, Marie; David M. Giltinan (1995).Nonlinear Models for Repeated Measurement Data. Chapman & Hall/CRC Monographs on Statistics & Applied Probability.ISBN 978-0-412-98341-2.
• Kshirsagar, Anant M.; Smith, William Boyce (1995).Growth curves. Statistics: Textbooks and Monographs. Vol. 145. New York: Marcel Dekker, Inc.ISBN 0-8247-9341-2.
• Pan, Jianxin; Fang, Kaitai (2007).Growth curve models and statistical diagnostics. Mathematical Monograph Series. Vol. 8. Beijing: Science Press.ISBN 9780387950532.
• Timm, Neil H. (2002). ""The general MANOVA model (GMANOVA)" (Chapter 3.6.d)".Applied multivariate analysis. Springer Texts in Statistics. New York: Springer-Verlag.ISBN 0-387-95347-7.
• Vonesh, Edward F.; Chinchilli, Vernon G. (1997).Linear and Nonlinear Models for the Analysis of Repeated Measurements. London: Chapman and Hall.{{cite book}}: CS1 maint: publisher location (link)

• Analysis of variance
• Statistical forecasting
• Multivariate time series
• Ordinary differential equations
• Exponentials
• Biostatistics
• Growth curves

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