Growth Curve Model with Bilinear Random Coefficients

In the present paper, we derive a new multivariate model to fit correlated data, representing a general model class. Our model is an extension of the Growth Curve model (also called generalized multivariate analysis of variance model) by additionally assuming randomness of regression coefficients li...

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Bibliographic Details
Published in:Sankhya. Series. A 2022-08, Vol.84 (2), p.477-508
Main Authors: Imori, Shinpei, von Rosen, Dietrich, Oda, Ryoya
Format: Article
Language:English
Subjects:
Mathematics and Statistics
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
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Summary:In the present paper, we derive a new multivariate model to fit correlated data, representing a general model class. Our model is an extension of the Growth Curve model (also called generalized multivariate analysis of variance model) by additionally assuming randomness of regression coefficients like in linear mixed models. Each random coefficient has a linear or a bilinear form with respect to explanatory variables. In our model, the covariance matrices of the random coefficients is allowed to be singular. This yields flexible covariance structures of response data but the parameter space includes a boundary, and thus maximum likelihood estimators (MLEs) of the unknown parameters have more complicated forms than the ordinary Growth Curve model. We derive the MLEs in the proposed model by solving an optimization problem, and derive sufficient conditions for consistency of the MLEs. Through simulation studies, we confirmed performance of the MLEs when the sample size and the size of the response variable are large.
ISSN:0976-836X
0976-8378
DOI:10.1007/s13171-020-00204-5