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Title: Growth curve model with bilinear random coefficient Authors:  Shinpei Imori - Hiroshima University (Japan) [presenting]
Dietrich von Rosen - Swedish University of Agricultural Sciences (Sweden)
Ryoya Oda - Hiroshima University (Japan)
Abstract: The growth curve model is a classical model useful to analyze repeated measurements data, where response variables are obtained in matrix form. Each row of the response matrix can represent observations on the same time point and each column of the response matrix is assumed to be independently distributed is a conventional framework of the model. However, if each column of the response matrix represents observations on the same space point, this assumption may not be appropriate. However, if we consider an unstructured covariance matrix for the response variables, the number of unknown parameters is greater than the sample size. We solve this problem by introducing a bilinear random coefficient to the (extended) growth curve model, which induces a Kronecker product covariance structure of the response matrix in the growth curve model. An explicit maximum likelihood estimator of the unknown parameters is presented, even when the covariance matrix of the random coefficient is non-negative definite.