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Overview of recent results in growth-curve-type multivariate linear models. (English) Zbl 1244.62080

Summary: The Extended Growth Curve Model (ECGM) is a multivariate linear model connecting different multivariate regression models in sample subgroups through common variance matrix. It has the form: \[ Y=\sum ^{k}_{i=1}X_iB_iZ_i^{\prime }+e,\quad \mathrm{vec}(e)\sim N_{n\times p}\left(0,\Sigma \otimes I_n\right). \] Here, the matrices \(X_i\) contain subgroup division indicators, and \(Z_i\) the corresponding regressors. If \(k=1\), we speak about (ordinary) growth curve models. The model has already its age (it dates back to 1964), but it has many important applications. That is why it is still intensively studied. Many articles investigate different aspects or special cases of the model that have appeared in recent years. We will try to summarize the progress done so far.

MSC:

62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models

Software:

GenStat
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References:

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