Notes and Commentary: Regression Equations for the Latent Roots of Random Data Correlation Matrices with Unities on the Diagonal

Allen, Stuart J.; Hubbard, Raymond

doi:10.1207/s15327906mbr2103_7

Cited by 54 publications

(20 citation statements)

References 7 publications

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“…Although there were five eigenvalues greater than 1, both the scree plot method and parallel analysis supported the existence of three factors. The eigenvalues for random data were estimated using the regression equation developed by Allen and Hubbard (1986). The minimum loading used to identify items to factors was .45.…”

Section: Exploratory Factor Analysismentioning

confidence: 99%

Implicit theories, goal orientations, and perceived competence: Impact on students' achievement behavior

Leondari

Gialamas

2002

Psychology in the Schools

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The present study was designed to explore relations between implicit theories of intelligence, goal orientations, perceived competence, and school achievement. It was assumed that implicit theories of intelligence orient individuals toward particular goals, which in turn influence achievement behavior. Perceived competence was hypothesized to moderate the relationship between implicit theories, goal orientations and actual achievement. Subjects were 451 elementary and junior high school students. The results of Pearson product moment correlations and Path analysis show theoretically important intercorrelations that replicated previous research. Implicit theories were not related to academic achievement. Goal orientations had an indirect effect on achievement, which was mediated through perceived competence. Educational implications of these findings are discussed.

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Section: Exploratory Factor Analysismentioning

confidence: 99%

Implicit theories, goal orientations, and perceived competence: Impact on students' achievement behavior

Leondari

Gialamas

2002

Psychology in the Schools

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“…1), referencing published work which presents regression models or tables of threshold values to test the significance of components, or readily available programs (Allen & Hubbard 1986;Lautenschlager 1989;Buja & Eyuboglu 1992; Pohlmann unpubl. -available from the author upon request).…”

Section: The Problem Of the 'Number Of Components'mentioning

confidence: 99%

Parallel Analysis: a method for determining significant principal components

Franklin¹,

Gibson²,

Robertson³

et al. 1995

J Vegetation Science

340

229

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. Numerous ecological studies use Principal Components Analysis (PCA) for exploratory analysis and data reduction. Determination of the number of components to retain is the most crucial problem confronting the researcher when using PCA. An incorrect choice may lead to the underextraction of components, but commonly results in overextraction. Of several methods proposed to determine the significance of principal components, Parallel Analysis (PA) has proven consistently accurate in determining the threshold for significant components, variable loadings, and analytical statistics when decomposing a correlation matrix. In this procedure, eigenvalues from a data set prior to rotation are compared with those from a matrix of random values of the same dimensionality (p variables and n samples). PCA eigenvalues from the data greater than PA eigenvalues from the corresponding random data can be retained. All components with eigenvalues below this threshold value should be considered spurious. We illustrate Parallel Analysis on an environmental data set. We reviewed all articles utilizing PCA or Factor Analysis (FA) from 1987 to 1993 from Ecology, Ecological Monographs, Journal of Vegetation Science and Journal of Ecology. Analyses were first separated into those PCA which decomposed a correlation matrix and those PCA which decomposed a covariance matrix. Parallel Analysis (PA) was applied for each PCA/FA found in the literature. Of 39 analy ses (in 22 articles), 29 (74.4 %) considered no threshold rule, presumably retaining interpretable components. According to the PA results, 26 (66.7 %) overextracted components. This overextraction may have resulted in potentially misleading interpretation of spurious components. It is suggested that the routine use of PA in multivariate ordination will increase confidence in the results and reduce the subjective interpretation of supposedly objective methods.

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“…This selection criterion produced a three-factor solution. To ensure only reliable factors were retained, the factors were evaluated using both a scree test and parallel analysis (Allen & Hubbard, 1986;Longman, Cota, Holden, & Fekken, 1989). Both the scree test and parallel analysis suggested only the first two factors were reliable, and these are reported in Table 3.…”

Section: Relationship Between Mothers' and Daughters' Family Perceptionsmentioning

confidence: 99%

Family climates: Family factors specific to disturbed eating and bulimia nervosa

1999

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More than a decade of research has characterized the families of individuals with bulimia and bulimia anorexia (Anorexia Nervosa, Binge/Purging Type) as less expressive, less cohesive, and experiencing more conflicts than normal control families. This two-part study investigated variables believed more directly related to disturbed eating and bulimia as contributing to a "family climate for eating disorders." In Study 1. a nonclinical sample of 324 women who had just left home for college and a sample of 121 mothers evaluated their families. Principal-components analyses revealed the same factor structure for both students and mothers, with Family Body Satisfaction, Family Social Appearance Orientation, and Family Achievement Emphasis loading together, representing the hypothesized family climate for eating disorders: the remaining variables loaded with the more traditional family process variables (conflict, cohesion, expressiveness), representing a more general family dysfunction. As predicted, the family climate for eating disorders factor score was a more powerful predictor of disturbed eating. Study 2 extended these findings into a clin ical population, examining whether the family climate for eating disorders variables would distinguish individuals with bulimia from both depressed and healthy controls. Groups of eating-disordered patients (n = 40) and depressed (n = 17) and healthy (n = 27) controls completed family measures. The eating-disordered group scored significantly higher on family climate variables than control groups. Family process variables distinguished clinical groups (depressed and eating disordered) from healthy controls, but not from one another. Controlling for depression removed group differences on family process variables, but family climate variables continued to distinguish the eating-disordered group from both control groups. Indications for further research are discussed.

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Notes and Commentary: Regression Equations for the Latent Roots of Random Data Correlation Matrices with Unities on the Diagonal

Cited by 54 publications

References 7 publications

Implicit theories, goal orientations, and perceived competence: Impact on students' achievement behavior

Implicit theories, goal orientations, and perceived competence: Impact on students' achievement behavior

Parallel Analysis: a method for determining significant principal components

Family climates: Family factors specific to disturbed eating and bulimia nervosa

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