Capitalization on Chance in Rotation of Factors

Humphreys, Lloyd G.; Ilgen, Daniel R.; McGrath, Diane; Montanelli, Richard G.

doi:10.1177/001316446902900202

Cited by 61 publications

(18 citation statements)

References 7 publications

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“…It is possible to compare competing models in terms of fit indices, but it is not possible to perform statistical tests for goodness of fit. Further, Horn (1967) and Humphreys et al (1969) have claimed that the target method would fit almost any data to almost any hypothesis. However, Acito, Anderson, and Engledow (1980), using a simulation method, show that this is not so and conclude that target analysis is not "likely to mislead the researcher into believing that any arbitrary target factor pattern is consistent with an empirical correlation matrix" (p. 148).…”

Section: Limitationsmentioning

confidence: 99%

A Test of Two Consumer Response Scales in Advertising

Zinkhan¹,

Fornell²

1985

Journal of Marketing Research

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Section: Limitationsmentioning

confidence: 99%

A Test of Two Consumer Response Scales in Advertising

Zinkhan¹,

Fornell²

1985

Journal of Marketing Research

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“…The term "capitalization on chance" has come into the psychological literature to represent the fact that in some applications of least-squares estimation procedures the results can appear to provide support for hypotheses but in fact are an outcome of chance variations. Capitalization on chance was initially studied using random data (see Horn, 1967; Armstrong & Soelberg, 1%8; Humphreys et al, 1969), but more recently it has been extended to real data, In a critical evaluation of factor analytic evidence for SI theory based on research with random data as well as data from Guilford's research projects, Undheim & Horn (1977) see two crucial problems with the factor-analytic evidence advanced in support of SI theory: (1) over-extraction of factors, and (2) repeated (iterative) applications of Procrustes techniques.…”

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confidence: 99%

“…The study by Humphreys et al (1969), as well as the Norman (1%9) study using real variables, would both indicate that four or more marker variables per factor would greatly limit capitalization on chance variations. The SI research studies (Aptitude Research Projects, ARP), directed by Guilford typically have only 2 or 3 marker variables per factor.…”

mentioning

confidence: 99%

“…In the 30 or so factor-analytic studies by ARP the ratio of variables per factor ranges from 1.5 to 3.13 (Guilford & Hoepfner, 1971). A closer scrutiny of the studies, however, shows that in several instances one may select subsamples of variables and factors meeting the criteria of Humphreys et al (1969). In such instances a comparison between the fit to random target matrices and to the original SI target matrices may provide a useful test of the SI model, albeit rather piecemeal as pointed out by Undheim & Horn (1977, p. 68).…”

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confidence: 99%

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Capitalization on chance: The case of Guilford's Memory Abilities

Undheim¹

1979

Scandinavian J Psychology

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Reanalysis of a memory study originally interpreted to support J. P. Guilford's Structure‐of‐Intellect (SI) model fails to give support for the SI distinctions: (1) When capitalization on chance was limited by selecting a subsample of variables for analysis, only 3 out of 9 hypothesized factors were identified, (2) the root‐one number‐of‐factor criterion indicate that the SI model leads to a rather dramatic over‐factoring even when the factors are theoretically over‐determined, and (3) although the fit to the model is somewhat better than is expected on the basis of a completely random model, more reasonable semi‐random null‐hypotheses cannot be rejected in favor of the SI model.

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“…True, they may become gross overestimates of communalities in a sample, but this property can be kept in bounds by appropriate selection of number of observations (N) and number of variables (n). Combinations of N and n that create problems in communality estimation are also undesirable from other points of view (Humphreys, Ilgen, McGrath, and Montanelli, 1968).…”

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Note On a Criterion for the Number of Common Factors

Humphreys

Ilgen

1969

Educational and Psychological Measurement

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111

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EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT 1969, 29, 571-578. LINN (1968) has published the results of a, Monte Carlo approach to the number of factors problem involving the use of random normal deviates as additional variables in correlational matrices from which principal components are extracted. Horn (1966) has made use of an independent component analysis of random normal deviates, parallel to the analysis of the &dquo;real&dquo; variables, in order to correct the Kaiser criterion (see Horn) which assumes population values of the correlations, for capitalization on chance in the sample. This note briefly presents some results obtained from another, and more promising, variation on their procedures. Linn found that his mean square ratios, analogous to F-ratios with data from the latent roots of real variables in the numerator and of random variables in the denomination, fluctuated widely as ratios were formed from successive roots. The lack of independence arising from the fact that both the numerator and denominator were derived from the same analysis, though from independent sets of variables, is the probable cause of this variability. Horn's use of a parallel analysis thus is indicated. Horn, however, was interested in the Kaiser rule which involves the use of unities in the diagonal of the correlational matrix. The automatic use of unity for a real variable whose population communality in any particular set of measures may be zero, and for random variables whose population communalities are zero, follows

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Capitalization on Chance in Rotation of Factors

Cited by 61 publications

References 7 publications

A Test of Two Consumer Response Scales in Advertising

A Test of Two Consumer Response Scales in Advertising

Capitalization on chance: The case of Guilford's Memory Abilities

Note On a Criterion for the Number of Common Factors

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