### 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.

Original language | English (US) |
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Article number | 18 |

Journal | Frontiers in Neuroinformatics |

Volume | 8 |

Issue number | MAR |

DOIs | |

State | Published - Mar 3 2014 |

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### All Science Journal Classification (ASJC) codes

- Neuroscience (miscellaneous)
- Biomedical Engineering
- Computer Science Applications

### Cite this

*Frontiers in Neuroinformatics*,

*8*(MAR), [18]. https://doi.org/10.3389/fninf.2014.00018

**A variant of sparse partial least squares for variable selection and data exploration.** / Hunt, Megan J.Olson; Weissfeld, Lisa; Boudreau, Robert M.; Aizenstein, Howard; Newman, Anne B.; Simonsick, Eleanor M.; Van Domelen, Dane R.; Thomas, Fridtjof; Yaffe, Kristine; Rosano, Caterina.

Research output: Contribution to journal › Article

*Frontiers in Neuroinformatics*, vol. 8, no. MAR, 18. https://doi.org/10.3389/fninf.2014.00018

}

TY - JOUR

T1 - A variant of sparse partial least squares for variable selection and data exploration

AU - Hunt, Megan J.Olson

AU - Weissfeld, Lisa

AU - Boudreau, Robert M.

AU - Aizenstein, Howard

AU - Newman, Anne B.

AU - Simonsick, Eleanor M.

AU - Van Domelen, Dane R.

AU - Thomas, Fridtjof

AU - Yaffe, Kristine

AU - Rosano, Caterina

PY - 2014/3/3

Y1 - 2014/3/3

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=84896930988&partnerID=8YFLogxK

U2 - 10.3389/fninf.2014.00018

DO - 10.3389/fninf.2014.00018

M3 - Article

AN - SCOPUS:84896930988

VL - 8

JO - Frontiers in Neuroinformatics

JF - Frontiers in Neuroinformatics

SN - 1662-5196

IS - MAR

M1 - 18

ER -