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

Area of Science:

• Statistics
• Machine Learning
• Bioinformatics

Background:

• Traditional sparse partial least squares (SPLS) lacks estimates for non-selected predictors and inference measures.
• This limitation is prominent in datasets with sparse data or multicollinear predictors.

Purpose of the Study:

• To introduce an "all-possible" SPLS approach for enhanced inference in sparse and multicollinear datasets.
• To provide a more informative output than traditional SPLS for data exploration.

Main Methods:

• Fitting SPLS models across a grid of tuning parameter values.
• Analyzing the percentage of times each predictor is selected and its average non-zero parameter estimate.

Main Results:

• Simulation confirmed that strongly associated variables were most likely to be chosen, while unassociated variables were least likely.
• Predictor selection frequency and average parameter estimate magnitude correlated with the strength of the relationship to the outcome.
• The method validated a priori hypotheses in studies relating volumetric MRI measures to cognitive test scores.

Conclusions:

• The "all-possible" SPLS method offers a valuable measure of inference by ordering predictor relationships.
• Average parameter estimates provide further insight into the direction and strength of associations.
• This approach enhances data exploration and hypothesis generation with a large number of potential predictors.