# Overview of Recent Results in Growth-curve-type Multivariate Linear Models

• Volume: 50, Issue: 2, page 137-146
• ISSN: 0231-9721

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## Abstract

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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: $Y=\sum _{i=1}^{k}{X}_{i}{B}_{i}{Z}_{i}^{\text{'}}+e,\phantom{\rule{1.0em}{0ex}}vec\left(e\right)\sim {N}_{n×p}\left(0,\Sigma \otimes {I}_{n}\right).$ Here, matrices ${X}_{i}$ contain subgroup division indicators, and ${Z}_{i}$ corresponding regressors. If $k=1$, we speak about (ordinary) Growth Curve Model. 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 investigating different aspects or special cases of the model appeared in recent years. We will try to summarize the progress done so far.

## How to cite

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Žežula, Ivan, and Klein, Daniel. "Overview of Recent Results in Growth-curve-type Multivariate Linear Models." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 50.2 (2011): 137-146. <http://eudml.org/doc/197068>.

@article{Žežula2011,
abstract = {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: $Y=\sum ^\{k\}\_\{i=1\}X\_iB\_iZ\_i^\{\prime \}+e, \quad \operatorname\{vec\}(e)\sim N\_\{n\times p\}\left(0,\Sigma \otimes I\_n\right).$ Here, matrices $X_i$ contain subgroup division indicators, and $Z_i$ corresponding regressors. If $k=1$, we speak about (ordinary) Growth Curve Model. 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 investigating different aspects or special cases of the model appeared in recent years. We will try to summarize the progress done so far.},
author = {Žežula, Ivan, Klein, Daniel},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {growth curve model; extended growth curve model; multivariate linear model; extended growth curve model; multivariate linear models},
language = {eng},
number = {2},
pages = {137-146},
publisher = {Palacký University Olomouc},
title = {Overview of Recent Results in Growth-curve-type Multivariate Linear Models},
url = {http://eudml.org/doc/197068},
volume = {50},
year = {2011},
}

TY - JOUR
AU - Žežula, Ivan
AU - Klein, Daniel
TI - Overview of Recent Results in Growth-curve-type Multivariate Linear Models
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2011
PB - Palacký University Olomouc
VL - 50
IS - 2
SP - 137
EP - 146
AB - 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: $Y=\sum ^{k}_{i=1}X_iB_iZ_i^{\prime }+e, \quad \operatorname{vec}(e)\sim N_{n\times p}\left(0,\Sigma \otimes I_n\right).$ Here, matrices $X_i$ contain subgroup division indicators, and $Z_i$ corresponding regressors. If $k=1$, we speak about (ordinary) Growth Curve Model. 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 investigating different aspects or special cases of the model appeared in recent years. We will try to summarize the progress done so far.
LA - eng
KW - growth curve model; extended growth curve model; multivariate linear model; extended growth curve model; multivariate linear models
UR - http://eudml.org/doc/197068
ER -

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