SOME CONTRIBUTIONS TO MAXIMUM LIKELIHOOD FACTOR ANALYSIS
SOME CONTRIBUTIONS TO MAXIMUM LIKELIHOOD FACTOR ANALYSIS
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DOI：
10.1007/bf02289658
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发表时间：
1967-01-01
期刊：
影响因子：
3
通讯作者：
JORESKOG, KG
中科院分区：
文献类型：
--
作者：
JORESKOG, KG
给出了因子分析中极大似然解的一种新的计算方法。该方法考虑了似然函数在所有唯一方差均为正的参数空间的点上可能不具有最大值的事实。取而代之的是，可以在参数空间的边界上达到最大值，其中一个或多个唯一方差为零。事实证明，这种不适当的(Heywood)解的出现频率比通常预期的要高。提出了一种处理此类不当解决方案的一般程序。所提出的方法使用两个小的经验数据集进行了说明，并报告了从许多其他数据集获得的分析结果。这些分析表明，新的计算方法收敛速度很快，可以非常准确地确定最大似然解。该方法得到的副产品是估计的唯一方差的方差-协方差矩阵的大样本估计。这可用于为共同性和唯一方差设置近似置信度区间。
A new computational method for the maximum likelihood solution in factor analysis is presented. This method takes into account the fact that the likelihood function may not have a maximum in a point of the parameter space where all unique variances are positive. Instead, the maximum may be attained on the boundary of the parameter space where one or more of the unique variances are zero. It is demonstrated that such improper (Heywood) solutions occur more often than is usually expected. A general procedure to deal with such improper solutions is proposed. The proposed methods are illustrated using two small sets of empirical data, and results obtained from the analyses of many other sets of data are reported. These analyses verify that the new computational method converges rapidly and that the maximum likelihood solution can be determined very accurately. A by-product obtained by the method is a large sample estimate of the variance-covariance matrix of the estimated unique variances. This can be used to set up approximate confidence intervals for communalities and unique variances.