New Developments in Factor Analysis Underlain by Fixed Models

在一个新的固定因素模型的基础上，我开发了一个因素分析(FA)程序，在该模型中，共同和独特的因素分数被视为固定参数。这一过程可以称为联合FA(JFA)，因为所有参数都是联合估计的。提出了一种最小化JFA最小二乘函数的算法。该算法的一个特点是，只有当变量间协方差可用时，才能估计最优负荷和唯一方差。仿真研究表明，JFA能够很好地恢复真实载荷和唯一方差，并通过实际数据实例说明了JFA的有效性。理论上，JFA的一个有趣的性质是JFA可以被视为数据矩阵的高阶近似。进一步利用这一性质解释了公因子不确定性和唯一因子不确定性，它是Mulaik(1976)锥的推广形式。

I developed a factor analysis (FA) procedure underlain by a new fixed factor model in which common and unique factor scores are treated as fixed parameters. This procedure can be called joint FA (JFA), as all parameters are estimated jointly. I presented an algorithm for minimizing the least squares function of JFA. A feature of the algorithm is that the optimal loadings and unique variances can be estimated only if inter-variable covariances are available. Simulation studies showed that the true loadings and unique variances are recovered well, and the usefulness of JFA was illustrated in real data examples. A property of JFA interesting theoretically is that JFA can be regarded as higher rank approximation of a data matrix. I further used the property to give the explanation of the common and unique factor indeterminacy which is a generalized version of Mulaik's (1976) cone.