The "common cause hypothesis" of cognitive aging: evidence for not only a common factor but also specific associations of age with vision and grip strength in a cross-sectional analysis.

A prominent hypothesis in cognitive aging is the existence of a common factor that is responsible for age-related deterioration in cognitive and noncognitive processes. A multiple indicators, multiple causes model was used to examine the nature of this common factor and its relationship to age, gender, and the apolipoprotein E (APOE) genotype. The common factor was modeled by using 10 indicator variables with 374 participants aged between 77.4 and 98.7 years. A latent factor was identified, with all indicators except blood pressure loading significantly. This factor could be established in 2 age strata within the sample. After controlling for the effects of gender, APOE, and level of education, direct effects of age were seen on visual functioning and grip strength. APOE was significantly associated with memory but not with the common factor. The findings suggest that a number of specific processes may operate concurrently with any common cause factor.     

A criterion for significant common factor variance

Up to the present only empirical methods have been available for determining the number of factors to be extracted from a matrix of correlations. The problem has been confused by the implicit attitude that a matrix of intercorrelations between psychological variables has a rank which is determinable. A table of residuals always contains error variance and common factor variance. The extraction of successive factors increases the proportion of error variance remaining to common factor variance remaining, and a point is reached where the extraction of more dimensions would contain so much error variance that the common factor variance would be overshadowed. The critical value for this point is determined by probability theory and does not take into account the size of the residuals. Interpretation of the criterion is discussed.     

Caveats of non-ipsatization of basic values: A review of issues and a simulation study

Ipsatization, or a correction of variables by their common component, is routinely applied to measures of basic values. Although ipsatization has been criticized, the consequences of non-ipsatization are rarely discussed. We show that the ipsatization of values is intertwined with their definition. A common factor involved in ipsatization was suggested to represent a nuisance variable, a response style, social desirability, or other constructs. A simulation study illustrated that within-individual centering revealed more accurate value scores when the common factor was in the data, with exception of the situation when values were consistently and positively correlated with each other. We conclude that in different conditions both applying and failing to apply ipsatization can cause bias. Therefore, no general advice in regard to ipsatization can be provided.     

An inductive exploration of the social effectiveness construct space

ABSTRACT There is no agreement regarding the nature or number of dimensions that make up the social effectiveness domain. We inductively explore the relationships between a set of social effectiveness measures with the intention of identifying an initial set of dimensions. An exploratory factor analysis of the Social Competence Inventory (SCI, Schneider, 2001 ) resulted in the identification of four factors: Social Potency, Social Appropriateness, Social Emotional Expression, and Social Reputation. A joint factor analysis between the SCI and a set of extant measures resulted in the identification of the same four factors. A fifth factor emerged when a set of scales from an emotional intelligence measure was included in the analysis, suggesting that emotional intelligence is not captured within the common factor space defined by measures of social effectiveness. This study represents a first step in the establishment of a set of common social effectiveness dimensions.     

Common region: a new principle of perceptual grouping.

A new principle of grouping is proposed that is based on elements being located within a common region of space. Demonstrations analogous to Wertheimer's original displays show that this factor strongly influences perceived grouping and is capable of overcoming the effects of other powerful grouping factors such as proximity and similarity. Grouping by common region is further shown to depend on perceived depth relations, indicating that it is influenced by processes that occur after at least some depth perception has been achieved. Further demonstrations suggest that it is dominated by the smallest background area and that it can follow a hierarchical embedding scheme. It is argued that common region cannot be reduced to the effects of proximity, closure, or any other previously known factor and therefore constitutes a genuinely new principle of grouping.     

Genetic and environmental influences on pubertal development: longitudinal data from Finnish twins at ages 11 and 14

To study sources of individual differences in pubertal development, the authors fit a sex-limitation common factor model to data reported, at ages 11 and 14 years, by 1,891 twin pairs on items that comprise the Pubertal Development Scale (PDS; A. C. Petersen, L. Crockett, M. Richards, & A. Boxer, 1988). The model divides variation into a general pubertal factor and item-specific variation and, in addition, decomposes it into constituent sources. In both boys and girls, genetic influences made the largest contribution to variance common to PDS items. Genetic and nonshared environmental factors accounted for variation specific to PDS items in boys, whereas for girls, common environmental influences were added for growth spurt and menarcheal status. For both common and item-specific variation, genetic effects were partially sex specific. Subsidiary analyses found accelerated maturation in both boys and girls who at age 14 were reared in father-absent homes.     

Convergence in mean square of factor predictors

Sufficient conditions for mean square convergence of factor predictors in common factor analysis are given by Guttman, by Williams, and by Schneeweiss and Mathes. These conditions do not hold for confirmatory factor analysis or when an error variance equals zero (Heywood cases). Two sufficient conditions are given for the three basic factor predictors and a predictor from rotated principal components analysis to converge to the factors of the model for confirmatory factor analysis, including Heywood cases. For certain model specifications the conditions are necessary. The conditions are sufficient for the existence of a unique true factor. A geometric interpretation is given for factor indeterminacy and mean square convergence of best linear factor prediction.     

A preliminary scale for assessing attitudes toward homosexuals in the military

This paper reports a factor analytical study of responses to statements of attitudes concerning lesbians and gay men in the military by 72 23.4-yr.-old members of the U.S. Marine Corps Reserve. Using exploratory factor analysis with an oblique rotation four factors were found which accounted for 64.9% of the total common variance. A factor labeled Trust accounted for 40.6% of the common variance, Comfort accounted for 8.7%, Acceptance accounted for 8.2%, and the fourth factor, Threat, accounted for 7.5%. Cronbach a ranged from .63 to .78. Validity was .75 when scores were correlated with those on the Attitudes Toward Lesbians and Gay Men scale, supporting the 4-factor interpretation. It is recommended that additional factor analyses be performed to further investigate the validity of the four factors and that of the entire scale.     

A note on the factor analysis of partial covariance matrices

A relationship is given between the joint common factor structure of two sets of variables, and the factor structure of the partial covariance matrix of one of the sets with the other partialled out.     

A note on a sufficiency condition for uniqueness of a restricted factor matrix

A counterexample is produced to a conjecture by K. G. Jöreskog concerning sufficiency conditions for uniqueness of a restricted factor matrix. A substitute condition is stated and proved for the most common situation where the restricted elements are specified to be zero.     

Common Core Thesis and Qualitative and Quantitative Analysis of Mysticism in Chinese Buddhist Monks and Nuns

This study explores the phenomenological structure of mystical experience among 139 Chinese Pure Land and Chan Buddhist monks and nuns. Semi‐structured interviews, thematic coding, and statistical analyses demonstrated that Stace's common facets of mysticism as measured by Hood's Mysticism Scale (M Scale) successfully described Buddhist experience as modified by Buddhist doctrines. Confirmatory factor analysis (CFA) revealed that these facets could be formed into Stace's three‐factor structure. A mystical introvertive unity hypothesized to be separate from an extrovertive unity instead converged in the Chinese Buddhist context. These results lend strong support to the thesis that the phenomenology of mystical experience reveals a common experiential core that can be discerned across religious and spiritual traditions. These data also demonstrated that this common core can and should be explored using mixed methods.     

Simultaneous factor analysis in several populations

This paper is concerned with the study of similarities and differences in factor structures between different groups. A common situation occurs when a battery of tests has been administered to samples of examinees from several populations.A very general model is presented, in which any parameter in the factor analysis models (factor loadings, factor variances, factor covariances, and unique variances) for the different groups may be assigned an arbitrary value or constrained to be equal to some other parameter. Given such a specification, the model is estimated by the maximum likelihood method yielding a large samplex ² of goodness of fit. By computing several solutions under different specifications one can test various hypotheses.The method is capable of dealing with any degree of invariance, from the one extreme, where nothing is invariant, to the other extreme, where everything is invariant. Neither the number of tests nor the number of common factors need to be the same for all groups, but to be at all interesting, it is assumed that there is a common core of tests in each battery that is the same or at least content-wise comparable.This research was supported by grant NSF-GB-12959 from National Science Foundation. My thanks are due to Michael Browne for his comments on an earlier draft of this paper and to Marielle van Thillo who checked the mathematical derivations and wrote and debugged the computer program SIFASP.Now at Statistics Department, University of Uppsala, Sweden.     

SYNTHESIS OF FACTOR ANALYSES: III Interbattery methods of synthesis of factor analyses

W erdelin , I. Synthesis of factor analyses. III. Interbattery methods of synthesis of factor analyses. Scand. J. Psyehol ., 1962, 3 , 196–204.—Methods of performing several factor analyses on a common sample, so that we arrive at invariant structures, are discussed. A method of rotating a factorial solution to a structure given by a previous study, and a method of checking whether two studies performed on the same sample are congruent, are given.     

Constrained least squares estimators of oblique common factors

An expression is given for weighted least squares estimators of oblique common factors, constrained to have the same covariance matrix as the factors they estimate. It is shown that if as in exploratory factor analysis, the common factors are obtained by oblique transformation from the Lawley-Rao basis, the constrained estimators are given by the same transformation. Finally a proof of uniqueness is given.The research reported in this paper was partly supported by Natural Sciences and Engineering Research Council Grant No. A6346.     

How shared are age-related influences on cognitive and noncognitive variables?

Several theories have suggested that age-related declines in cognitive processing are due to a pervasive unitary mechanism, such as a decline in processing speed. Structural equation model tests have shown some support for such common factor explanations. These results, however, may not be as conclusive as previously claimed. A further analysis of 4 cross-sectional data sets described in Salthouse, Hambrick, and McGuthry (1998) and Salthouse and Czaja (2000) found that although the best fitting model included a common factor in 3 of the data sets, additional direct age paths were significant, indicating the presence of specific age effects. For the remaining data set, a factor-specific model fit at least as well as the best fitting common factor model. Three simulated data sets with known structure were then tested with a sequence of structural equation models. Common factor models could not always be falsified--even when they were false. In contrast, factor-specific models were more easily falsified when the true model included a unitary common factor. These results suggest that it is premature to conclude that all age-related cognitive declines are due to a single mechanism. Common factor models may be particularly difficult to falsify with current analytic procedures.     

The relationship between external variables and common factors

A theorem is presented which gives the range of possible correlations between a common factor and an external variable (i.e., a variable not included in the test battery factor analyzed). Analogous expressions for component (and regression component) theory are also derived. Some situations involving external correlations are then discussed which dramatize the theoretical differences between components and common factors.Support by the National Research Council of Canada (NRC Grant No. A4640) and the University of British Columbia (UBC Humanities and Social Sciences Grant 26-9718) is gratefully acknowledged.This paper is based in part on the author's Ph.D. dissertation. I am particularly grateful to my dissertation advisor, Dr. Peter H. Schönemann. Thanks also to the editor and the anonymous reviewers, who contributed many helpful comments and suggestions.     

Some Mathematical Properties of the Matrix Decomposition Solution in Factor Analysis

A new factor analysis (FA) procedure has recently been proposed which can be called matrix decomposition FA (MDFA). All FA model parameters (common and unique factors, loadings, and unique variances) are treated as fixed unknown matrices. Then, the MDFA model simply becomes a specific data matrix decomposition. The MDFA parameters are found by minimizing the discrepancy between the data and the MDFA model. Several algorithms have been developed and some properties have been discussed in the literature (notably by Stegeman in Comput Stat Data Anal 99:189–203, 2016), but, as a whole, MDFA has not been studied fully yet. A number of new properties are discovered in this paper, and some existing ones are derived more explicitly. The properties provided concern the uniqueness of results, covariances among common factors, unique factors, and residuals, and assessment of the degree of indeterminacy of common and unique factor scores. The properties are illustrated using a real data example.     

A feasible method for standard errors of estimate in maximum likelihood factor analysis

A jackknife-like procedure is developed for producing standard errors of estimate in maximum likelihood factor analysis. Unlike earlier methods based on information theory, the procedure developed is computationally feasible on larger problems. Unlike earlier methods based on the jackknife, the present procedure is not plagued by the factor alignment problem, the Heywood case problem, or the necessity to jackknife by groups. Standard errors may be produced for rotated and unrotated loading estimates using either orthogonal or oblique rotation as well as for estimates of unique factor variances and common factor correlations. The total cost for larger problems is a small multiple of the square of the number of variables times the number of observations used in the analysis. Examples are given to demonstrate the feasibility of the method.The research done by R. I. Jennrich was supported in part by NSF Grant MCS 77-02121. The research done by D. B. Clarkson was supported in part by NSERC Grant A3109.     

Testing Models of Psychopathology in Preschool-aged Children Using a Structured Interview-based Assessment

A number of studies have found that broadband internalizing and externalizing factors provide a parsimonious framework for understanding the structure of psychopathology across childhood, adolescence, and adulthood. However, few of these studies have examined psychopathology in young children, and several recent studies have found support for alternative models, including a bi-factor model with common and specific factors. The present study used parents’ (typically mothers’) reports on a diagnostic interview in a community sample of 3-year old children (n?=?541; 53.9 % male) to compare the internalizing-externalizing latent factor model with a bi-factor model. The bi-factor model provided a better fit to the data. To test the concurrent validity of this solution, we examined associations between this model and paternal reports and laboratory observations of child temperament. The internalizing factor was associated with low levels of surgency and high levels of fear; the externalizing factor was associated with high levels of surgency and disinhibition and low levels of effortful control; and the common factor was associated with high levels of surgency and negative affect and low levels of effortful control. These results suggest that psychopathology in preschool-aged children may be explained by a single, common factor influencing nearly all disorders and unique internalizing and externalizing factors. These findings indicate that shared variance across internalizing and externalizing domains is substantial and are consistent with recent suggestions that emotion regulation difficulties may be a common vulnerability for a wide array of psychopathology.