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Abstract: Stability Selectionfor Penalized CanonicalCorrelation AnalysisCharles Laurin a & Gitta Lubke ba University of Notre Dameb University of Notre Dame, Vrije UniversiteitAmsterdamPublished online: 29 Mar 2013.

To cite this article: Charles Laurin & Gitta Lubke (2013) Abstract: Stability Selectionfor Penalized Canonical Correlation Analysis, Multivariate Behavioral Research, 48:1,165-165, DOI: 10.1080/00273171.2013.752264

To link to this article: http://dx.doi.org/10.1080/00273171.2013.752264

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Multivariate Behavioral Research, 48:165, 2013

Copyright © Taylor & Francis Group, LLC

ISSN: 0027-3171 print/1532-7906 online

DOI: 10.1080/00273171.2013.752264

Abstract: Stability Selection for Penalized CanonicalCorrelation Analysis

Charles Laurin

University of Notre Dame

Gitta Lubke

University of Notre Dame, Vrije Universiteit Amsterdam

Identifying psychological correlates of healthy behavior is important in developing

behavioral interventions. Such identification might be improved by using item-level,rather than sumscore, data: for example, which items on neuroticism inventory X aremost associated with which items on nicotine dependence scale Y ? One way to find

such items is to estimate their contributions to the linear relationships between the twosets of variables X and Y .

Canonical correlation analysis is used to characterize linear relationships betweentwo sets of variables. Canonical correlation analysis identifies the linear combination Xu

that is most highly correlated with a linear combination Yv. Interpreting the canonicalvectors u and v is a long-standing difficulty of the method.

Two recent innovations from statistical learning may ease this difficulty. Penalized

canonical correlation analysis (PCCA; Witten, Tibshirani, & Hastie, 2009) generatessparse canonical vectors, that is, most components equal 0. This is a form of variable

selection; variables that contribute least to the canonical correlation tend to have com-ponents of 0. Independently, bootstrap stability selection (BSS) has been developed to

apply resampling to variable selection (Meinshausen & Bühlman, 2010). BSS leads toconsistent selections under broad assumptions.

A preliminary application of BSS to PCCA is presented. Receiver Operating Char-acteristic analyses were used to compare the accuracy of variable selections made usingPCCA versus using PCCA-with-BSS on simulated data. X and Y were simulated at

varying sample sizes and strengths of the population (first) canonical correlation.PCCA-with-BSS tended to show higher true positive rates and lower false positive

rates than PCCA alone. Decreasing the correlation or the sample size tended to decreasethe difference in performance between PCCA-with-BSS and PCCA.

Applying BSS to PCCA decreased the influence of sampling error on identifyingimportant variables. In unsimulated data, such item-level analyses could suggest newavenues for studying relationships between behavioral predictors, such as neuroticism,

and health outcomes, such as smoking.

Meinshausen, N., & Bühlmann, P. (2010). Stability selection. Journal of the Royal Statistical Society: Series B

(Statistical Methodology), 72(4), 417–473.

Witten, D. M., Tibshirani, R., & Hastie, T. (2009). A penalized matrix decomposition, with applications to sparse

principal components and canonical correlation analysis. Biostatistics, 10(3), 515–534.

Charles Laurin thanks his SMEP sponsor, Gitta Lubke, for support and feedback. Correspondence concerning

this abstract should be addressed to Charles Laurin, University of Notre Dame, 220C Haggar Hall, Notre Dame,

IN 46556. E-mail: claurin@nd.edu

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