Partial Canonical Correlation Research Articles

Association of Landscape Metrics to Surface Water Biology in the Savannah River Basin

Surface water quality for the Savannah River basin was assessed using water biology and landscape metrics. Two multivariate analyses, partial least square and canonical correlation, were used to describe how the structural variation in landscape metrics may affect surface water biology and to define the key landscape variable(s) that contribute the most to variation in surface water quality. The results showed that the key landscape metrics in this study area were: percent forest, percent of total area in agriculture (row crops + pasture) on moderately erodible soils, percent of total area with slopes greater than 3% and stream density. The first two canonical variates describe the linear combinations of the two data sets (r = 0.74 and 0.63), weighted mainly by percent of total area with slopes greater than 3%, taxa richness of sensitive insects to pollution (EPT; Ephemeroptera-Plecoptera-Trichoptera Index), algal growth potential and percent of total area in agriculture on moderately erodible soils.

Generalized covariance‐adjusted canonical correlation analysis with application to psychiatry

The lack of control over covariates in practice motivates the need for their adjustment when measuring the degree of association between two sets of variables, for which canonical correlation is traditionally used. In most studies however, there is also a lack of control over the attributes of responses for the sets of variables of interest. In particular, a portion of the response variable may be continuous and the other discrete. For such settings, the traditional partial canonical correlation approach is restrictive, since a covariate-adjustment for a set of continuous variables is assumed. By ignoring the assumption of continuous variates and proceeding with a partial canonical correlation analysis in the presence of continuous and discrete variates, results in canonical correlation estimates that are not consistent. In this paper we generalize the traditional partial canonical correlation approach to covariate-adjustment by allowing the response variables to contain continuous, as well as discrete, variates. The methodology is illustrated with a psychiatric application for examining which sleep variables relate to which depressive symptoms, as measured by commonly used constructs that presents with both continuous and discrete outcomes.

On multivariate linear regression shrinkage and reduced-rank procedures

Abstract An alternate derivation of the canonical analysis shrinkage prediction procedure of Breiman and Friedman (1997. J. Roy. Statist. Soc. B 59, 3–54) is presented for the multivariate linear model. It is based on consideration of prediction mean square error matrix, and bias of the squared sample canonical correlations. A modified procedure involving partial canonical correlation analysis is also introduced and discussed.

Physical activity and health-related fitness in youth: a multivariate analysis.

To evaluate the relationship between indicators of physical activity and health-related fitness in youth 9-18 yr. A cross-sectional sample of 356 boys and 284 girls 9-18 yr of age from phase I of the Quebec Family Study was studied. The sample was divided into three age groups by gender, 9-12, 13-15, and 16-18 yr of age. Physical activity variables included two estimates of activity, estimated daily energy expenditure (EE) and estimated moderate-to-vigorous physical activity (MVPA), and one estimate of inactivity, time spent watching television per day (TVTIME). Health-related fitness variables were the sum of six skin folds (SUM), number of sit-ups in 1 min (SITUP), physical work capacity at 150 beats x min(-1) (PWC150), and static strength of the leg (LMS). Partial canonical correlation was used to quantify the relationship between standardized (z-transformed) activity variables and health-related fitness items, controlling for age. There is a weak to moderate association between physical activity and fitness in youth. The first activity canonical variate is a function of positive loadings for EE and MVPA, with a smaller, negative loading for TVTIME. The first fitness variate generally includes positive loadings for PWC150 and SITUP, with a small negative loading for the SUM and a small positive loading for LMS. The first canonical correlations indicate that the variance shared by the fitness and activity variates ranges from 11 to 21%. There is a significant relationship between activity and health-related physical fitness, but a large part of the variability (80-90%) in fitness is not accounted for by physical activity as measured in this study.

Somatotype and indicators of metabolic fitness in youth.

The relationship between physique and metabolic fitness was examined in a sample of 413 boys and 343 girls 9-18 years of age from Phase I of the Québec Family Study. Physique was assessed using the Heath-Carter anthropometric somatotype. Indicators of metabolic fitness were plasma triglyceride levels (TG), high density lipoprotein cholesterol (HDL-C), low density lipoprotein cholesterol (LDL-C), and blood glucose levels (GLY). The sample was divided into three age groups, 9-12, 13-15, and 16-18 years of age. A partial canonical correlation analysis was used to quantify the relationship between the standardized somatotype and metabolic fitness variables (z-transformed) with age as the covariate. In both boys and girls the first canonical correlation is significant (P ⩽ 0.001) and indicates a relationship between the physique and metabolic fitness variables. By age group, the 16-18 year old boys, and the 9-12, 13-15, 16-18 year old girls demonstrate significant canonical correlations (P ⩽ 0.03). Overall, 8% to 19% of the variance in metabolic fitness can be explained by the Heath-Carter anthropometric somatotype. The makeup of the canonical variates is similar for all age groups. Generally, the physique domain is characterized by a positive loading for ectomorphy and negative loadings for endomorphy and mesomorphy. The metabolic fitness domain has a positive loading for HDL-C and negative loadings for TG, LDL-C, and GLY. The results suggest that in youth 9-18 years, a physique characterized by high endomorphy and mesomorphy is associated with higher levels of TG, LDL-C, and GLY, and lower levels of HDL-C. Am. J. Hum. Biol. 10:341-350, 1998. © 1998 Wiley-Liss, Inc.

Canonical correlation analyses for three data sets: a unified framework with application to management

Researchers in management, economics and other social sciences often find that they have very large data sets (a cross section over many firms, individuals or projects), but little theoretical knowledge of how to model the data. The common solution is to resort either to partial models that use small subsets of the data or to large linear models. In the first case, the researcher runs the risk of omitting important variables from the model. In the second case, there is a risk of specifying an inappropriate functional form of the relations among the variables. In this paper we survey, classify and apply several methodologies of generalized canonical correlation analysis (CCA) and partial canonical correlation analysis (PCCA) to estimate and analyze the relationships among several data sets. We present all the methods on a uniform basis—as optimization problems with several kinds of parameter restrictions. Further, we analyze all the methods within the convenient theoretical structure of generalized nonlinear eigenvector problems. These methods are applied to data on 310 Israeli manufacturing firms.

A Reader on Applying Statistics in Public Health and Prevention.

Contributions to this volume discuss the application of statistics in public health and prevention, dealing with subjects in the field of working conditions and occupational health, sexually transmissible disease, dental health, public health tables, the geographical distribution of diseases, intervention, and safe behaviour. Papers dealing with working conditions and occupational health include: F. Andries and C.C.J.H. Bijleveld : Working conditions, strain and stress of automation personnel : analysis of complaints and contentedness; S. van Buuren and J.L.A. van Rijckevorsel : Nonresponse imputation in public health research; A. Bloemhoff : Nonlinear partial canonical correlation analysis of health, social class and work indicators - in comparison with cumulative incidence ratio's; F.H.G. Marcelissen, D.J. van Putten and J.J. Radder : Graphical reference-profiles : a method for analysis and presentation of questionnaire data obtained in Periodic Medical and Workplace Surveys (PMWS).

Content and response-style in the construct validation of self-report inventories: A canonical analysis

A common problem in establishing the construct validity of self-report inventories is the confounding of the purported meaning of test scores with response styles such as social desirability. Partial correlation is a traditional method of controlling such confounding effects. This paper demonstrates the analytic and interpretive advantages of using canonical correlation to remove the effects of a confounding variable. To this end, the present study examined the test protocols of 64 male inpatient alcoholics to determine whether a general measure of mental health (Sulliman Scale of Social Interest) was related to inventories that assess psychopathology (MMPI and PSI) beyond what one could expect by Ss responding in a socially desirable manner. The results of partial correlation and canonical correlation analysis were contrasted, which demonstrated the spuriousness of partial correlations in controlling for social desirability.

Facteurs influen�ant la structure des groupements de macro-invert�br�s benthiques et phytophiles dans la zone littorale du Saint-Laurent (Qu�bec)

In the littoral zone of the St-Lawrence River (Quebec, Canada), benthic and phytophilous macroinvertebrates were studied in order to find and to explain relationships between structure of these animal communities and abiotic (substrate, water depth, current velocity) or biotic (marophytes species) factors. Benthos was sampled at 16 sites in spring, when there was no macrophytic vegetation, and in summer. Phytomacrofauna was sampled at 30 sites in summer. The data were analyzed using simple and partial correlations, stepwise regression, reciprocal averaging and canonical correlation analysis.

Measures of Multivariate Relationships for the Uniform Covariance Case

Simple procedures for obtaining the m.l. estimates of multiple correlation, canonical correlation, partial canonical correlation and bi-partial canonical correlation have been derived for situations where the underlying covariance structure is uniform (equal variances and equal positive covariances). It has been shown that for any even-sized p × p symmetric R matrix with intra-class correlation structure, the largest canonical correlation is identically equal to the maximum eccentricity of the p-dimensional correlation ellipsoid. Using an empirical variance con variance matrix based on attribute ratings of coffee, the computational short-cuts in the m.l. estimation of various measures of multivariate relationships have been demonstrated.

Longitudinal Analysis Of The Role Of Peer Support, Adult Models, And Peer Subcultures In Beginning Adolescent Substance Use: An Application Of Setwise Canonical Correlation Methods.

A confirmatory, longitudinal design was used with a setwise partial canonical correlation methodology to determine whether indicators of a deviant adolescent peer culture contain information about the subsequent drug use beyond that which may be obtained from knowledge of present drug use and perceived sources of supply and support. Peer culture measures did not increase prediction over a one year period. Adolescent drug use was quite stable over one year, and perceived sources of supply and support served to predict those portions of subsequent drug use not explained by present use. The results suggest that general nonconformity among peers is not a strong precursor of adolescent drug use.

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.

Self-Actualization and Adjustment in Retirement: Implications for Program Development

This study investigated the utilization of self-actualization concepts in the development of educational programs to aid suc cessful adjustment in retirement. The population sample consisted of retirees in six stratified social groups reflecting rural, urban, minority, and veteran backgrounds. Extent of self-actualization was determined by the Personal Orientation Inventory and adjust ment to retirement was measured by the Retirement Descriptive Index. A partial canonical correlation and chi square were utilized to treat the data. A positive relationship, significant at the .05 level, was found on the two combined roots for all scales on the R.D.I. and all but one scale of the P.O.I. It was concluded that self-actualizing concepts are definitely involved with successful adjustment to retirement.

BRIEF REPORT: THE DISTRIBUTION OF PARTIAL CORRELATIONS AND GENERALIZATIONS.

The distributional results of regression analysis can be obtained in a simple way through the use of idempotent matrices, as Graybill has shown. An extension of these methods is used to show the relation of the distribution of the partial correlation coefficient to that of the simple correlation. Obvious extensions are given to partial multiple and partial canonical correlations.

Partial canonical correlations

Partial canonical correlations