(Dp 1979-22) On the Maximum Likelihood Method of Factor Analysis
Rao's solution of the estimation equations in the maximum likelihood method of factor analysis is derived in this paper in a model wherein Morrison's specific-factor variate ei is replaced by ¦Ä1U1 and the covariance structure, by the correlation pattern. The correlation pattern is used, at times, in classifying variables according to the criteria, which are specified in section 1 of this paper. The following innovations are recommended in this paper: 1. The use of ¦Ä12 as an indicator of dependence or independence of the ith variable and the other variables in the given set. 2. The application of simultaneous tests of independence among variables having a multivariate normal distribution (see page 3) as part of the factor analysis technique (maximum likelihood method) to determine the validity of the classification of the variables and thereby solve the following problems: (a) indeterminacy due to the non-uniqueness of solutions of the estimation equations (b) subjectivity of analysis done with or without the common practice of rotating the factor loading matrix, as observed by Scott. These test may by used independently of factor analysis in classifying variables into independent groups. This implies the exclusion of variables which are correlated with independent variables.
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