Influence in canonical correlation analysis

The perturbation theory of the generalized eigenproblem is used to derive influence functions of each squared canonical correlation coefficient and the corresponding canonical vector pair. Three sample versions of these functions are described and some properties are noted. As particular applications, the influence function of the squared multiple correlation coefficient and influence functions of eigenvalues and eigenvectors in correspondence analysis are obtained. Three numerical examples are briefly discussed.We thank the Editor and the anonymous reviewers for their helpful comments. This research was carried out with the financial support of the Italian Ministry of the University and the National Research Council.     

Recalled parental behavior and objective personality measures: a canonical analysis.

Information about an individual's past relationships with his parents is an important component in psychological assessment procedures. To systematically connect these relationships and personality, two groups of college students completed an objective inventory designed to assess parental child rearing behaviors. Canonical correlational analysis was employed to relate these measures to the CPI and MMPI. A recalled parental behavior component described as Acceptance vs. Hostile Detachment/Involvement emerged as being highly related to aspects of both personality inventories, with greater recalled acceptance (and lesser recalled hostility) being associated with the more positive aspects of personality. Additional findings are enumerated.     

Part and bipartial canonical correlation analysis

Extending the definitions of part and bipartial correlation to sets of variates, the notion of part and bipartial canonical correlation analysis are developed and illustrated.     

Redundancy analysis an alternative for canonical correlation analysis

A component method is presented maximizing Stewart and Love's redundancy index. Relationships with multiple correlation and principal component analysis are pointed out and a rotational procedure for obtaining bi-orthogonal variates is given. An elaborate example comparing canonical correlation analysis and redundancy analysis on artificial data is presented.A Fortran IV program for the method of redundancy analysis described in this paper can be obtained from the author upon request.     

Generalized canonical correlation analysis of matrices with missing rows: a simulation study

A method is presented for generalized canonical correlation analysis of two or more matrices with missing rows. The method is a combination of Carroll’s (1968) method and the missing data approach of the OVERALS technique (Van der Burg, 1988). In a simulation study we assess the performance of the method and compare it to an existing procedure called GENCOM, proposed by Green and Carroll (1988). We find that the proposed method outperforms the GENCOM algorithm both with respect to model fit and recovery of the true structure. The research of Michel van de Velden was partly funded through EU Grant HPMF-CT-2000-00664. The authors would like to thank the associate editor and three anonymous referees for their constructive comments and suggestions that led to a considerable improvement of the paper.     

Generalizations of the partial,part and bipartial canonical correlation analysis

Theg ₁- andg ₂-bipartial canonical correlation analyses are developed as generalizations of the partial, part, and bipartial canonical correlation analysis. Illustrative examples are provided.     

Relationships between redundancy analysis,canonical correlation,and multivariate regression

This paper attempts to clarify the nature of redundancy analysis and its relationships to canonical correlation and multivariate multiple linear regression. Stewart and Love introduced redundancy analysis to provide non-symmetric measures of the dependence of one set of variables on the other, as channeled through the canonical variates. Van den Wollenberg derived sets of variates which directly maximize the between set redundancy. Multivariate multiple linear regression on component scores (such as principal components) is considered. The problem is extended to include an orthogonal rotation of the components. The solution is shown to be identical to van den Wollenberg's maximum redundancy solution.This research was supported in part by U.S. Environmental Protection Agency contract 68-02-3402. The author gratefully acknowledges the stimulation of Maurice Tatsuoka and Beth Dawson-Saunders in first interesting him in redundancy analysis, as well as a useful change suggested by Warren Sarle.     

Interpreting canonical correlation analysis through biplots of structure correlations and weights

This paper extends the biplot technique to canonical correlation analysis and redundancy analysis. The plot of structure correlations is shown to the optimal for displaying the pairwise correlations between the variables of the one set and those of the second. The link between multivariate regression and canonical correlation analysis/redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients. This plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables. An example is used to show how the proposed biplots may be interpreted.     

The second order approximation to sample influence curve in canonical correlation analysis

A second order approximation to the sample influence curve (SIC) in canonical correlation analysis has been derived in the literature. However, it does not seem satisfactory for some cases. In this paper, we present a more accurate second order approximation. As a particular case, the proposed method is exact for the SIC of the squared multiple correlation coefficient. An example is given. The authors are most grateful to the associate editor and three reviewers for valuable comments and suggestions which improved the presentation of the paper considerably. The first author was partly supported by a RGC earmarked research grant of Hong Kong.     

Marriage and personality: a genetic analysis

There is substantial evidence that married people fare better than their unmarried peers on many life outcome variables. The authors asked whether self-selection might partially explain these benefits through genetic influences on personality contributing to propensity to marry. Using a population-based sample of 4,225 women and 2,869 men that included 2,527 complete twin pairs, the authors investigated the phenotypic associations between personality and propensity to marry, the heritability of propensity to marry, and the extent of genetic influence on the link between personality and propensity to marry. The results suggest that propensity to marry is heritable and that the phenotypic link between personality and propensity to marry is genetically influenced.     

Age patterns of childbearing: a canonical analysis

A cross-sectional study of maternal age-specific birthrates was conducted in an attempt to gain insight into age patterns of childbearing. The age specific fertility rates were considered as the dependent variable set. These 6 variables consisted of 1970 live births to women in the age groups 15-19, 20-24, 25-29, 30-34, 35-39, and 40-44. The age-specific fertility rates were calculated for each of the 338 New York City health areas that are the sampling units. The canonical analysis used is a multivariate method of exploring these patterns which provides a means for dealing with some of the difficult analytical problems encountered. The relationships of fertility patterns with sets of variables reflecting housing, income and occupation, education and labor force participation, marital patterns, and ethnicity are explored for New York City neighborhoods. 3 dimensions of childbearing emerged with high consistency across the variable sets - roughly describable as early, middle and late fertility. The 1st pattern - high early fertility and particularly teen-age childbearing - is identified with the poorest areas of the city. The income, occupation, education and unemployment figures in these areas are consistent with a minimal preceived penalty for early childbearing. The 2nd dimension - birthrates of women ages 25-34 - identifies another distinctive group of areas. Many low income women at this age continue to bear children at moderate rates; middle income women bear the children they postponed having in the earlier years. The late childbearing group seems best understood as attributable to religious and ethnically related differences among areas. The 1st dimension is the most important for the perspective of the impact on population growth.     

A unified approach to multiple‐set canonical correlation analysis and principal components analysis

Multiple‐set canonical correlation analysis and principal components analysis are popular data reduction techniques in various fields, including psychology. Both techniques aim to extract a series of weighted composites or components of observed variables for the purpose of data reduction. However, their objectives of performing data reduction are different. Multiple‐set canonical correlation analysis focuses on describing the association among several sets of variables through data reduction, whereas principal components analysis concentrates on explaining the maximum variance of a single set of variables. In this paper, we provide a unified framework that combines these seemingly incompatible techniques. The proposed approach embraces the two techniques as special cases. More importantly, it permits a compromise between the techniques in yielding solutions. For instance, we may obtain components in such a way that they maximize the association among multiple data sets, while also accounting for the variance of each data set. We develop a single optimization function for parameter estimation, which is a weighted sum of two criteria for multiple‐set canonical correlation analysis and principal components analysis. We minimize this function analytically. We conduct simulation studies to investigate the performance of the proposed approach based on synthetic data. We also apply the approach for the analysis of functional neuroimaging data to illustrate its empirical usefulness.     

The wit: a personality analysis

Fifty-eight undergraduate psychology students were group tested on 12 variables thought to be related to the successful prediction of wit. In addition to a score on wit, scores on creativity, verbal fluency, need for play, need for impulsivity, self-confidence, dominance, exhibition, change, autonomy, personal adjustment, authoritarianism, and sex group were obtained. The results were analyzed in a stepwise multiple regression analysis. A significant Pearson product-moment correlation was obtained between wit and creativity (p < .01) and between wit and personal adjustment (p < .05). The multiple regression analysis indicated that creativity was the best single significant predictor of wit. Personal adjustment, in combination with creativity, provided the next highest significant contribution. The results are discussed and suggestions for further research are posited.     

Typological personality research by configural frequency analysis

After discussing diverse concepts of types or syndromes the definition of types, according to configural frequency analysis (CFA), is given. A type, in this theory, is assumed to be a configuration of categories belonging to different attributes. This configuration should occur with a probability which is higher than the conditional probability for given univariate marginal frequencies. The conditional probability is computed under the null hypothesis of independence of the attributes. Types are identified by simultaneous conditional binomial tests and interpreted by means of an interaction structure analysis in a multivariate contingency table. Two further versions of CFA are explained. By prediction CFA it is possible to predict certain configurations by other ones while by c-sample CFA it is possible to discriminate between populations by means of configurations. The procedures are illustrated by an example concerning the responses of patients to lumbar punctures.     

State of the aRt personality research: A tutorial on network analysis of personality data in R

Network analysis represents a novel theoretical approach to personality. Network approaches motivate alternative ways of analyzing data, and suggest new ways of modeling and simulating personality processes. In the present paper, we provide an overview of network analysis strategies as they apply to personality data. We discuss different ways to construct networks from typical personality data, show how to compute and interpret important measures of centrality and clustering, and illustrate how one can simulate on networks to mimic personality processes. All analyses are illustrated using a data set on the commonly used HEXACO questionnaire using elementary R-code that readers may easily adapt to apply to their own data.     

Coping styles and personality: a biometric analysis

Previous research suggests that coping styles are modestly heritable and that this genetic influence is shared in large part with genetic influences on personality. To test this hypothesis, we estimated the heritable basis of the Coping Inventory for Stressful Situations in a sample of 91 monozygotic and 80 dizygotic twin pairs. Task-oriented, emotion-oriented, and social diversion coping styles were modestly heritable (h(2)=.17 to .20), whereas the use of distraction appeared to be influenced solely by environmental factors. Multivariate analyses showed that genetic contributions to coping styles were, at best, only modestly related to genetic contributions to personality (r=-.03 to .35). Environmental contributions to personality were unrelated to environmental factors in coping style. These results suggest that coping style is not merely a manifestation of basic personality traits but does support the possibility that the genetic factors in personality influences have a modest influence on an individual's preferred coping style or strength (e.g., rigidity vs flexibility).     

Assessing and interpreting personality change and continuity in patients treated for major depression

Structural, mean- and individual-level, differential, and ipsative personality continuity were examined in 599 patients treated for major depression assigned to 1 of 6 forms of a 6-month pharmaco-psychotherapy program. Covariation among traits from the Five Factor model remained invariant across treatment, and patients described themselves as slightly more extraverted, open to experience, agreeable and conscientious, and substantially more emotional stable after treatment. Trait changes were only to a small extent explained by changes in depression severity. There was evidence for differential, individual-level, and ipsative stability, with stable personality profiles in terms of shape and to a lesser extent in terms of scatter and elevation. Traits remain relatively stable, except for emotional stability, despite the depressive state and the psychopharmacological interventions.