Scholarlink

<p>In this paper, we consider the generalized growth curve model. The tensor residual is formulated and then transformed into a matrix residual through matricization. The main objective is to analyze this residual in the generalized growth curve model. It is shown that this residual is obtained by projecting the observations onto the space orthogonal to the space generated by the design matrices. This space is decomposed into three orthogonal spaces and the new residuals are obtained by projecting the observations on the resulting spaces. The interpretation and properties of the residuals based on their first two moments are discussed. It turns out that the residuals are symmetrically distributed around zero mean and uncorrelated. The dispersion matrices of the residuals and their covariance with the estimated model are provided. A simulation study and real dataset were used to evaluate the performance of the proposed tensor residual.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Residual analysis in the generalized growth curve model

  • 期刊论文

  • 发表日期：

    2026年7月10日

查看全文
  • Justine Dushimirimana,
  • Isaac Kipchirchir Chumba,
  • Lydia Musiga,
  • Joseph Nzabanita,
  • Ronald Waliaula Wanyonyi

摘要

In this paper, we consider the generalized growth curve model. The tensor residual is formulated and then transformed into a matrix residual through matricization. The main objective is to analyze this residual in the generalized growth curve model. It is shown that this residual is obtained by projecting the observations onto the space orthogonal to the space generated by the design matrices. This space is decomposed into three orthogonal spaces and the new residuals are obtained by projecting the observations on the resulting spaces. The interpretation and properties of the residuals based on their first two moments are discussed. It turns out that the residuals are symmetrically distributed around zero mean and uncorrelated. The dispersion matrices of the residuals and their covariance with the estimated model are provided. A simulation study and real dataset were used to evaluate the performance of the proposed tensor residual.