A Likelihood Ratio Test for a Patterned Covariance Matrix in a Multivariate Growth-Curve Model

Biometrics ◽  
1984 ◽  
Vol 40 (1) ◽  
pp. 151 ◽  
Author(s):  
Vernon M. Chinchilli ◽  
Walter H. Carter
Keyword(s):  
Covariance Matrix ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Growth Curve ◽  
Ratio Test ◽  
Growth Curve Model ◽  
Curve Model ◽  
Patterned Covariance ◽  
Patterned Covariance Matrix

scholarly journals Growth curve model for analyzing the effects of Calcium foliar feed on the wilting rate of post-harvest rose flowers

2021 ◽  
Vol 8 (2) ◽  
pp. 1181-1197
Author(s):  
Justine Dushimirimana ◽  
Stanislas Muhinyuza ◽  
Joseph Nzabanita
Keyword(s):  
Growth Curve ◽  
Growth Curves ◽  
Quadratic Functions ◽  
Ratio Test ◽  
Growth Curve Model ◽  
Policy Makers ◽  
Treatment Groups ◽  
Post Harvest ◽  
Curve Model ◽  
Wilting Rate

Cut rose flowers contribute to the economy and development of the export markets for several developing countries. Despite this contribution, profitable production of rose flowers is limited by wilting which leads to lower production. This paper aims to investigate the effects of Calcium foliar feed on the wilting rate of post-harvest rose flowers using the Growth Curve Model. This method was applied to the data consisting of wilting scores on five treatment groups. The Likelihood ratio test was used to test the growth curve and the equality of the growth curves in all groups. Results revealed that the expected growth curves for all groups followed different quadratic functions. The results also revealed that the wilting rate increased with the increase of calcium concentration compared to the control. This leads to a useful model for policy-makers or further analyses.

scholarly journals Estimation of parameters in the extended growth curve model with a linearly structured covariance matrix

2012 ◽  
Vol 16 (1) ◽  
pp. 13-32
Author(s):  
Joseph Nzabanita ◽  
Dietrich von Rosen ◽  
Martin Singull
Keyword(s):  
Covariance Matrix ◽  
Growth Curve ◽  
Estimation Procedure ◽  
Inner Product ◽  
Dispersion Matrix ◽  
Growth Curve Model ◽  
Estimation Of Parameters ◽  
Curve Model ◽  
Extended Growth Curve Model ◽  
Residual Space

In this paper the extended growth curve model with two terms and a linearly structured covariance matrix is considered. We propose an estimation procedure that handles linearly structured covariance matrices. The idea is first to estimate the covariance matrix when finding the inner product in a regression space and thereafter re-estimate it when it should be interpreted as a dispersion matrix. This idea is exploited by decomposing the residual space, the orthogonal complement to the design space, into three orthogonal subspaces. Studying residuals obtained from projections of observations on these subspaces yields explicit consistent estimators of the covariance matrix. An explicit consistent estimator of the mean is also proposed and numerical examples are given.

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