%0 Journal Article
%T High Order Tensor Forms of Growth Curve Models
%A Zerong Lin
%A Dongzhe Liu
%A Xueying Liu
%A Lingling He
%A Changqing Xu
%J Advances in Linear Algebra & Matrix Theory
%P 18-32
%@ 2165-3348
%D 2018
%I Scientific Research Publishing
%R 10.4236/alamt.2018.81003
%X In this paper, we first study the linear regression model <img src=\"Edit_b8ebabe2-7823-49b1-a4bb-38eec2167754.bmp\" alt=\"\" /> and obtain a norm-minimized estimator of the parameter vector <img src=\"Edit_195b897a-f5e7-4021-bb9c-145e631f82e2.bmp\" alt=\"\" /> by using the g-inverse and the singular value decomposition of matrix <span style=\"font-family:Verdana, Helvetica, Arial;white-space:normal;background-color:#FFFFFF;\"><em>X</em></span>. We then investigate the growth curve model (GCM) and extend the GCM to a generalized GCM (GGCM) by using high order tensors. The parameter estimations in GGCMs are also achieved in this way.
%K Tensor
%K Generalized Linear Model
%K Growth Curve Model
%K Parameter Estimation
%K Generalized Inverse
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=82800