Efficient estimation in image factor analysis

The image factor analytic model (IFA), as related to Guttman's image theory, is considered as an alternative to the traditional factor analytic model (TFA). One advantage with IFA, as compared with TFA, is that more factors can be extracted without yielding a perfect fit to the observed data. Several theorems concerning the structural properties of IFA are proved and an iterative procedure for finding the maximum likelihood estimates of the parameters of the IFA-model is given. Substantial experience with this method verifies that Heywood cases never occur. Results of an artificial experiment suggest that IFA may be more factorially invariant than TFA under selection of tests from a large battery. The first part of this work was done at the University of Uppsala, Sweden and supported by the Swedish Council for Social Science Research. The second part was done at Educational Testing Service and supported by a grant (NSF-GB-1985) from the National Science Foundation to Educational Testing Service. The author is indebted to Mr. G. Gruvaeus, who wrote many of the computer programs, checked the mathematical derivations and gave other invaluable assistance throughout the work.