If the ratio m/p tends to zero, where m is the number of factors m and p the number of observable variables, then the inverse diagonal element of the inverted observable covariance matrix (σ pjj) -1 tends to the corresponding unique variance ψ jj for almost all of these (Guttman, 1956). If the smallest singular value of the loadings matrix from Common Factor Analysis tends to infinity as p increases, then m/p tends to zero. The same condition is necessary and sufficient for (σ pjj) -1 to tend to ψ jj for all of these. Several related conditions are discussed. © 2006 The Psychometric Society.
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The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for indeterminate factor-error covariances to be arbitrarily small, for mean square convergence of the regression predictor of factor scores, and for the existence of a unique determinate factor and error variable. The determinate factor and error variable are uncorrelated and satisfy the defining assumptions of factor analysis. Several examples are given to illustrate the results.
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A previous study found a variety of unusual sexual interests to cluster in a five-factor structure, namely submission/masochism, forbidden sexual activities, dominance / sadism, mysophilia, and fetishism (Schippers et al., 2021). The current study was an empirical replication to examine whether these findings generalized to a representative population sample. An online, anonymous sample (N = 256) representative of the Dutch adult male population rated 32 unusual sexual interests on a scale from 1 (very unappealing) to 7 (very appealing). An exploratory factor analysis assessed whether similar factors would emerge as in the original study. A subsequent confirmatory factor analysis served to confirm the factor structure. Four slightly different factors of sexual interest were found: extreme, illegal and mysophilic sexual activities; light BDSM without real pain or suffering; heavy BDSM that may include pain or suffering; and illegal but lower-sentenced and fetishistic sexual activities. The model fit was acceptable. The representative replication sample was more sexually conservative and showed less sexual engagement than the original convenience sample. On a fundamental level, sexual interest in light BDSM activities and extreme, forbidden, and mysophilic activities seem to be relatively separate constructs.
