The covariance between level and shape in the latent growth curve model with estimated basis vector coefficients

A LISREL representation of the Latent Growth Curve Model is used to generate the set of equations for the expectation of the vector of means and the covariance matrix in terms of the unknown population parameters. A dependency between the covariance of the level and shape parameters and the scalings of the shape basis vector is shown. A simulation is presented based on data presented by McArdle and Hamagami (1991) to show how the covariance changes as the basis vector coefficients are rescaled. The relationship is explained in terms of the algebraic solution to a system of equations. Keywords: Latent growth curves, structural equation modeling, LISREL. unknown publishedVersion

本研究采用潜增长曲线模型（Latent Growth Curve Model）的LISREL（Linear Structural Relations）表征形式，基于未知总体参数推导得到均值向量期望与协方差矩阵的方程组。研究阐明了水平参数与形状参数的协方差同形状基向量缩放系数之间的依存关系。基于McArdle与Hamagami（1991）发布的数据集开展模拟实验，用以展示基向量系数经重新缩放时协方差的变化规律。上述依存关系可通过方程组的代数解予以阐释。关键词：潜增长曲线、结构方程建模、LISREL。未知出版版本