Common Canonical Variates in κ Independent Groups

Goria, M. N.; Flury, Bernard D.

doi:10.2307/2291603

Cited by 4 publications

(4 citation statements)

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“…Our conclusions confirm those of Yin and Sriram (2008), who also argued that a common canonical analysis was not appropriate. A plausible explanation for the conflicting results is that the methods used by Goria and Flury (1996) only detect linear relationships, while our methods are able to identify both linear and nonlinear associations.…”

Section: Discussionmentioning

confidence: 87%

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Multivariate Association and Dimension Reduction: A Generalization of Canonical Correlation Analysis

2010

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In this article, we propose a new generalized index to recover relationships between two sets of random vectors by finding the vector projections that minimize an L(2) distance between each projected vector and an unknown function of the other. The unknown functions are estimated using the Nadaraya-Watson smoother. Extensions to multiple sets and groups of multiple sets are also discussed, and a bootstrap procedure is developed to detect the number of significant relationships. All the proposed methods are assessed through extensive simulations and real data analyses. In particular, for environmental data from Los Angeles County, we apply our multiple-set methodology to study relationships between mortality, weather, and pollutants vectors. Here, we detect existence of both linear and nonlinear relationships between the dimension-reduced vectors, which are then used to build nonlinear time-series regression models for the dimension-reduced mortality vector. These findings also illustrate potential use of our method in many other applications. A comprehensive assessment of our methodologies along with their theoretical properties are given in a Web Appendix.

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Section: Discussionmentioning

confidence: 87%

“…Based on a large sample test using a log-likelihood ratio statistic, Goria and Flury (1996) concluded that a common model fits well for the machine data with Machines 1 and 2. However, based on our analyses presented above, we believe that a common analysis is not appropriate for the machine data.…”

Section: Machine Datamentioning

confidence: 99%

Multivariate Association and Dimension Reduction: A Generalization of Canonical Correlation Analysis

2010

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“…The ratio Â = 2 W 1 = 2 W 2 still can be estimated from these designs (assuming Á ik1 ≡ Á ik2 ), but separate estimates from each sequence group must be combined to give a common estimate. Likewise, correlation analysis still can be carried out, but a variation of canonical correlation applied to a set of independent groups [51] would be needed.…”

Section: Other Designsmentioning

confidence: 99%

A practical approach for evaluating population and individual bioequivalence

Gould

2000

Statist. Med.

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Pharmacokinetic measurements provided by subjects to each of two formulations of a drug have a joint distribution that can be characterized by parameters reflecting scale and correlation as well as location. The bioavailability of the formulations can be expressed in terms of the means of the marginal distributions, their means and variances, or the marginal means and variances and the joint correlation. These expressions correspond, respectively, to ‘average’, ‘population’, and ‘individual’ bioequivalence when the joint distribution of the measurements is bivariate normal. Current proposals for assessing the degree of bioequivalence of two formulations are based on statistics that are composites of variance components and squares of expected mean differences from a mixed linear model. There are technical and practical issues associated with these proposals, particularly that they require more complicated designs than the familiar 2×2 cross‐over. This paper describes an alternative approach that can be applied with standard 2×2 cross‐over designs, and that provides evaluations of population and individual bioequivalence that should be adequate for all practical clinical purposes. The approach is based on easily computed correlation and regression coefficients whose statistical properties under normality are well known and for which non‐parametric and robust alternatives exist when normality cannot be assumed. The approach yields conclusions consistent with those obtained by the current proposals when applied to data sets supplied by the FDA. In the cases where the conclusions do not match, the new approach appears to be more consistent with the data. Copyright © 2000 John Wiley & Sons, Ltd.

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“…Recently, a set of different tools have been presented to extend single-set principal component analysis (SsPCA) by giving multiple data sets an integrative consideration. The well-known methods may include the 3-way factor analysis methods, , generalized Procrustes analysis, − generalized canonical analysis (GCA), − common PCA (CPCA), − simultaneous component analysis (SCA), − et al Generalized canonical analysis (GCA) − worked on three or more sets with object as common mode, X i ( N × J i ) ( i = 1, 2, ..., C ). The common object structure, i.e., the similar variations across sets, were represented by canonical variates with maximal cross-set correlations.…”

Section: Introductionmentioning

confidence: 99%

Two-step Multiset Regression Analysis (MsRA) Algorithm

Zhao

Gao

2012

Ind. Eng. Chem. Res.

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In the present work, a multiset regression analysis strategy is developed by designing a two-step feature extraction procedure. Multiple predictor spaces, in which the same variables are measured on different sources of objects or the same number of objects is observed on different variables, are collected, preparing multiple regression data pairs in combination with response spaces. It focuses on finding the common regression structures across predictor spaces, which can be XÀY regression correlations or predictor variations closely related with each other, for the interpretation of response. Therefore, two different subspaces are separated from each other in each predictor space. One is the common subspace revealing the general regression features shared by all predictor spaces and the other is the specific subspace driven by the unique regression information that is more predictor space-dependent. This is achieved by solving a mathematical optimization problem, in which theoretical support is framed and the related statistical characteristics are analyzed. Its feasibility and performance are illustrated with both a simple numerical case and the experimental data from the literatures. From the cross-set viewpoint, the proposed approach provides a more meaningful characterization of the inherent predictor information for regression modeling. Further development and application potential are suggested.

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Common Canonical Variates in κ Independent Groups

Cited by 4 publications

References 0 publications

Multivariate Association and Dimension Reduction: A Generalization of Canonical Correlation Analysis

Multivariate Association and Dimension Reduction: A Generalization of Canonical Correlation Analysis

A practical approach for evaluating population and individual bioequivalence

Two-step Multiset Regression Analysis (MsRA) Algorithm

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