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The present study aims at disclosing a methodological prejudice which has misled factor analysis since its beginning. Simple structure, the guiding principle for factor rotation (Thurstone, 1935/1947), is regarded as a questionable dogma. The Thurstone principle impedes the discovery of latent sources of variance on which manifest empirical variables are based. This criticism is elucidated by theoretical considerations and by verbatim quotations of critical authors. The present calamity of factorial research is deemed to be due to general flaws of methodical reasoning. Onesided mathematical formalization in the discipline has lost its objectives by ignoring ordinary sources of knowledge and linguistic processing. The problem of simple structure cannot be solved by circumplex and structural equation procedures which suffer from the same flaws as simple structure modelling. A paradigm change is overdue. An alternative factor transformation modeling complex structures is demanded, it will be delineated in chapter 2. This chapter is a sequel of chapter 1 (Ertel, 2009) in which varimax, the procedure of factor rotation commonly used to generate simple structure, is replaced with varimin. Varimin aims at manifesting interacting aspects of latent structural components. The model of complexity which is outlined by initial factor extractions is optimized. The new method raises a number of issues of which five are discussed at length. Are varimin factors interpretable Can latent sources of covariance, being complex already by initial solutions, be rendered more complex? Have simple structure solutions in common practice not been tolerable, to say the least? Varimin factor loadings are often bipolar. How to interpret the bipolarity of varimin factors? Does varimin reveal contributions of variance originating from methodical sources? Ten empirical applications of varimin transformation serve as examples. Particular features of transformation to complex structure, revealing latent sources of covariance (by varimin), are compared with pertinent results obtained from transformations to simple structure (by varimax). Varimax will remain useful merely for clustering objectives. Attention is also drawn to limitations of the methodical innovation. Eighteen matrices with intercorrelations of eight subtest variables of the intelligence test IST, widely used in Germany, were subjected to principal component analysis, the resulting factors were rotated by varimin towards optimal complex structure. The 18 varimin solutions were aggregated, two factors resulted: VariminF1 represented a general factor g (‘general or basic intelligence’), variminF2 represented an achievementmodifying factor, obviously dependent on preceding educational training and learning (‘learning assets’, l). The validity of variminF1, general intelligence, was ascertained by high correlations between g and test scores of general intelligence, operationalized by culturefree tests CFT und FRT. The interpretation of variminF2 found support by significant correlations with learningdependent school grades and scores in orthography and arithmetic. The 18 PCAfactors were also transformed by varimax to simple structure. This transformation caused a splitting up of initial g into two seemingly separate factors, called ‘fluid’ and ‘crystallized’ intelligence by convention. In addition, differences between varimax F1 (fluid) and F2 (crystallized) regarding correlations with external criteria (general intelligence vs. school grades, training scores in orthography and arithmetic) which should have emerged were missing. The aggregate of varimax results yielded an unexpected third factor with considerable weight which, however, turned out to be an artifact of simple structure. Apparently, simple structure modelling of intelligence test data blends general intelligence with learning effects. Rotation of intelligence data to simple structure does not reveal, as it should, independent c
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Thurstone's principle of simple structure is rejected and replaced by its converse, the principle of complex structure. Varimax, the popular simple structure rotation of factors, is replaced by varimin, a novel procedure taking account of the complexity of investigated variables (s. Ertel, 2011). An exploratory factor analysis of a similarity matrix of 16 kinship terms showed that expected semantic features (sex, generation, nuclear family, lineality) manifest themselves by varimin rotation,while distorted clusters of kinship terms are obtained by varimax rotation. Varimin rotation was also applied to five PCAfactors obtained from 30 facet variables of NEOPIR (Ostendorf & Angleitner, 2004). As expected, variminrotated factors do not replicate the BigFive factors neuroticism, extraversion, etc., they rather reveal basic componential features (usually called „dimensions‟): activation level (highlow), activation slope (ascendingdescending), source of regulation (endodynamic exodynamic), phenomenal quality (endomodalexomodal), and functionality (eufunctional vs. dysfunctional). The wellknown BigFive factors represent clusters of those features rather than simple dimensions. Sensation seeking, internalexternal control, i. e. further constructs of simple structure oriented research, are likewise conceivable as patterns of functioning based on those five componential features. The validity of the five features obtained by varimin has largely been confirmed by rankings of the 30 NEOPIR facets using the features as judgmental criteria. Replacing Thurstonian simple structure by procedures aiming at complex structure might help to generate a systemic architecture in the personality and individual differences domains. More psychological functioning might be made transparent by modelling patterns of basic features.
Psychology  Psychological Research  Data Collection  Indentity  Personality
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Exploratory factor analysis (EFA) is a statistical tool for digging out hidden factors which give rise to the diversity of manifest objectives in psychology, medicine and other sciences. EFA had its heyday as psychologist Leon Thurstone (1935 and 1948) based EFA on what he called the “principle of simple structure” (SS). This principle, however, was erroneous from the beginning what remained unrecognized despite subsequent inventions of more sophisticated statistical tools such as confirmatory analysis and structural equation modeling. These methods are highly recommended today as tolerable routes to model complexities of observation. But they did not remove the harmful errors that SS had left behind. Five chapters in this book demonstrate and explain the trouble. In chapter 2 the ailment of SS is healed by introducing an unconventional factor rotation, called Varimin. Varimin gives variables of an analysis an optimal opportunity to manifest functional interrelations underlying correlational observations. Ten applications of Varimin (in chapter 2) show that its results are superior to results obtained by the conventional Varimax procedure. Further applications are presented for sports achievements (chapter 3), intelligence (chapter 4), and personality (chapter 5). If Varimin keeps on standing the tests new theoretical building blocks will arise together with conceptual networks promoting a better understanding of the domains under study. Readers may check this prognosis by themselves using the statistical tool (Varimin) which is provided by open access in the internet.
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