FACTOR-ANALYSIS FOR CLUSTERED OBSERVATIONS
FACTOR-ANALYSIS FOR CLUSTERED OBSERVATIONS
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DOI：
10.1007/bf02294421
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发表时间：
1992-12-01
期刊：
影响因子：
3
通讯作者：
MUTHEN, BO
中科院分区：
文献类型：
--
作者：
LONGFORD, NT;MUTHEN, BO
经典因子分析假设观测向量的随机样本。对于观察的聚类向量，例如大学生数据或家庭内的个人数据，可能需要考虑不同的组内和组间因子结构。定义了因子分析的两水平模型，并推导了该模型的评分算法公式。一个简单的非迭代方法的基础上分解的平方和叉积的总和进行了讨论。这种方法为迭代算法提供了一个合适的起始解，但它也是最大似然解的一个非常好的近似。更高层次的嵌套的扩展指示。与明智的应用拟牛顿方法，计算量涉及的评分算法是温和的，即使是复杂的问题，特别是，没有大尺寸的矩阵的逆。两个例子说明的方法。
Classical factor analysis assumes a random sample of vectors of observations. For clustered vectors of observations, such as data for students from colleges, or individuals within households, it may be necessary to consider different within-group and between-group factor structures. Such a two-level model for factor analysis is defined, and formulas for a scoring algorithm for estimation with this model are derived. A simple noniterative method based on a decomposition of the total sums of squares and crossproducts is discussed. This method provides a suitable starting solution for the iterative algorithm, but it is also a very good approximation to the maximum likelihood solution. Extensions for higher levels of nesting are indicated. With judicious application of quasi-Newton methods, the amount of computation involved in the scoring algorithm is moderate even for complex problems; in particular, no inversion of matrices with large dimensions is involved. The methods are illustrated on two examples.