### Abstract

In a multivariate growth-curve model, the estimator of the parameter matrix is a function of the matrix of the sums of squares and of the cross-products due to error. However, if the assumption of a patterned covariance matrix is valid, then the parameter estimator does not depend on the error matrix. A likelihood ratio test of this patterned covariance matrix is constructed and its distribution is discussed. A numerical example is provided in which the design consists of two treatment groups, with three repeated measures being taken of the three response variables.

Original language | English (US) |
---|---|

Pages (from-to) | 151-156 |

Number of pages | 6 |

Journal | Biometrics |

Volume | 40 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1984 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

*Biometrics*,

*40*(1), 151-156. https://doi.org/10.2307/2530753

}

*Biometrics*, vol. 40, no. 1, pp. 151-156. https://doi.org/10.2307/2530753

**A likelihood ratio test for a patterned covariance matrix in a multivariate growth-curve model.** / Chinchilli, Vernon; Carter, W. H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A likelihood ratio test for a patterned covariance matrix in a multivariate growth-curve model.

AU - Chinchilli, Vernon

AU - Carter, W. H.

PY - 1984/1/1

Y1 - 1984/1/1

N2 - In a multivariate growth-curve model, the estimator of the parameter matrix is a function of the matrix of the sums of squares and of the cross-products due to error. However, if the assumption of a patterned covariance matrix is valid, then the parameter estimator does not depend on the error matrix. A likelihood ratio test of this patterned covariance matrix is constructed and its distribution is discussed. A numerical example is provided in which the design consists of two treatment groups, with three repeated measures being taken of the three response variables.

AB - In a multivariate growth-curve model, the estimator of the parameter matrix is a function of the matrix of the sums of squares and of the cross-products due to error. However, if the assumption of a patterned covariance matrix is valid, then the parameter estimator does not depend on the error matrix. A likelihood ratio test of this patterned covariance matrix is constructed and its distribution is discussed. A numerical example is provided in which the design consists of two treatment groups, with three repeated measures being taken of the three response variables.

UR - http://www.scopus.com/inward/record.url?scp=0021395213&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021395213&partnerID=8YFLogxK

U2 - 10.2307/2530753

DO - 10.2307/2530753

M3 - Article

C2 - 6733225

AN - SCOPUS:0021395213

VL - 40

SP - 151

EP - 156

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 1

ER -