A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts. (English) Zbl 1468.62181

Summary: In the common factor model the observed data is conceptually split into a common covariance producing part and an uncorrelated unique part. The common factor model is fitted to the data itself and a new method is introduced for the simultaneous estimation of loadings, unique variances, factor scores, and unique parts. The method is based on Minimum Rank Factor Analysis and allows for the percentage of explained common variance to be computed. Taking into account factor indeterminacy, an explicit description of the complete class of solutions for the factor scores and unique parts is given. The method is evaluated in a simulation study and fitted to a dataset in the literature.


62-08 Computational methods for problems pertaining to statistics
62H25 Factor analysis and principal components; correspondence analysis
62P15 Applications of statistics to psychology
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