Linear latent variable models and covariance structures
Linear latent variable models and covariance structures
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DOI：
10.1016/0304-4076(89)90044-4
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发表时间：
1989-05
影响因子：
6.3
通讯作者：
T. W. Anderson
中科院分区：
文献类型：
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作者：
T. W. Anderson
观察到的向量被视为潜在（不可观察）向量变量的线性组合。加载矩阵是矢量参数的函数；一个潜在向量的协方差矩阵可以依赖于另一个向量参数，并且其他潜在向量的协方差矩阵是不受限制的正定矩阵；不同的潜在向量是不相关的。观测向量的协方差矩阵是两个参数向量和潜向量的协方差矩阵的函数。对潜在变量为正态分布时的最大似然估计量进行了刻画。如果不同的潜在变量是独立的（而不仅仅是不相关的），则在正态下导出的最大似然估计量的渐近分布通常是有效的。一个潜在向量只需要有一个有概率极限的样本协方差矩阵。协方差结构的检验也具有渐近鲁棒性。
The observed vector is taken as a linear combination of latent (unobservable) vector variables. The loading matrices are functions of a vector parameter; the covariance matrix of one latent vector may depend on another vector parameter and the covariance matrices of the other latent vectors are unrestricted positive definite matrices; and the different latent vectors are uncorrelated. The covariance matrix of the observed vector is a function of the two parameter vectors and the covariance matrices of the latent vectors. The maximum likelihood estimator when the latent variables are normally distributed is characterized. The asymptotic distribution of the maximum likelihood estimator derived under normality is shown to be valid generally if the different latent variables are independent (not just uncorrelated). One latent vector is only required to have a sample covariance matrix that has a probability limit. Tests of the covariance structure are also asymptotically robust.