title: A variant of sparse partial least squares for variable selection and data exploration.
abstract: When data are sparse and/or predictors multicollinear, current implementation of sparse partial least squares (SPLS) does not give estimates for non-selected predictors nor provide a measure of inference. In response, an approach termed "all-possible" SPLS is proposed, which fits a SPLS model for all tuning parameter values across a set grid. Noted is the percentage of time a given predictor is chosen, as well as the average non-zero parameter estimate. Using a "large" number of multicollinear predictors, simulation confirmed variables not associated with the outcome were least likely to be chosen as sparsity increased across the grid of tuning parameters, while the opposite was true for those strongly associated. Lastly, variables with a weak association were chosen more often than those with no association, but less often than those with a strong relationship to the outcome. Similarly, predictors most strongly related to the outcome had the largest average parameter estimate magnitude, followed by those with a weak relationship, followed by those with no relationship. Across two independent studies regarding the relationship between volumetric MRI measures and a cognitive test score, this method confirmed a priori hypotheses about which brain regions would be selected most often and have the largest average parameter estimates. In conclusion, the percentage of time a predictor is chosen is a useful measure for ordering the strength of the relationship between the independent and dependent variables, serving as a form of inference. The average parameter estimates give further insight regarding the direction and strength of association. As a result, all-possible SPLS gives more information than the dichotomous output of traditional SPLS, making it useful when undertaking data exploration and hypothesis generation for a large number of potential predictors.
authors.affiliation: Department of Biostatistics, University of Pittsburgh Pittsburgh, PA, USA.
authors.forename: Megan J
authors.initials: MJ
authors.lastname: Olson Hunt
authors.affiliation: Department of Biostatistics, University of Pittsburgh Pittsburgh, PA, USA.
authors.forename: Lisa
authors.initials: L
authors.lastname: Weissfeld
authors.affiliation: Department of Epidemiology, Center for Aging and Population Health, University of Pittsburgh Pittsburgh, PA, USA.
authors.forename: Robert M
authors.initials: RM
authors.lastname: Boudreau
authors.affiliation: Departments of Psychiatry, Bioengineering and Clinical and Translational Science, University of Pittsburgh Pittsburgh, PA, USA.
authors.forename: Howard
authors.initials: H
authors.lastname: Aizenstein
authors.affiliation: Department of Epidemiology, Graduate School of Public Health, University of Pittsburgh Pittsburgh, PA, USA.
authors.forename: Anne B
authors.initials: AB
authors.lastname: Newman
authors.affiliation: Intramural Research Program, National Institute on Aging Baltimore, MD, USA.
authors.forename: Eleanor M
authors.initials: EM
authors.lastname: Simonsick
authors.affiliation: Department of Biostatistics, Emory University Atlanta, GA, USA.
authors.forename: Dane R
authors.initials: DR
authors.lastname: Van Domelen
authors.affiliation: Department of Preventive Medicine, University of Tennessee Health Science Center Memphis, TN, USA.
authors.forename: Fridtjof
authors.initials: F
authors.lastname: Thomas
authors.affiliation: Department of Psychiatry, Neurology and Epidemiology, University of California, San Francisco San Francisco, CA, USA.
authors.forename: Kristine
authors.initials: K
authors.lastname: Yaffe
authors.affiliation: Department of Epidemiology, Center for Aging and Population Health, University of Pittsburgh Pittsburgh, PA, USA.
authors.forename: Caterina
authors.initials: C
authors.lastname: Rosano
keywords: MRI; SPLS; high-dimensional; inference; multicollinearity; network; over-fitting; tuning parameters