# Implementing ranked sparsity methods with sparseR

## What is ranked sparsity?

The ranked sparsity methods such as the sparsity-ranked lasso (SRL) have been developed for model selection and estimation in the presence of interactions and polynomials (Peterson & Cavanaugh 2022)[https://doi.org/10.1007/s10182-021-00431-7]. The main idea is that an algorithm should be more skeptical of higher-order polynomials and interactions a priori compared to main effects, by a predetermined amount.

## Package overview

The sparseR package implements ranked-sparsity-based versions of the lasso, elastic net, MCP, and SCAD. We also provide a (preliminary) version of an sparsity-ranked extension to Bayesian Information Criterion (and corresponding stepwise approaches)

Additionally, sparseR has many features designed to streamline dealing with interaction terms and polynomials, including functions for variable pre-processing, variable selection, post-selection inference, and post-fit model visualization under ranked sparsity.

## Installation

## Via GitHub:
# install.packages("devtools")
devtools::install_github("petersonR/sparseR")

# or via CRAN
install.packages("sparseR")

## Example

library(sparseR)
data(iris)
set.seed(1321)

srl <- sparseR(Sepal.Width ~ ., data = iris, k = 1, seed = 1)
srl
#>
#> Model summary @ min CV:
#> -----------------------------------------------------
#>   lasso-penalized linear regression with n=150, p=18
#>   (At lambda=0.0015):
#>     Nonzero coefficients: 10
#>     Cross-validation error (deviance): 0.07
#>     R-squared: 0.62
#>     Signal-to-noise ratio: 1.64
#>     Scale estimate (sigma): 0.267
#>
#>   SR information:
#>              Vartype Total Selected Saturation Penalty
#>          Main effect     6        4      0.667    2.45
#>  Order 1 interaction    12        6      0.500    3.46
#>
#>
#> Model summary @ CV1se:
#> -----------------------------------------------------
#>   lasso-penalized linear regression with n=150, p=18
#>   (At lambda=0.0070):
#>     Nonzero coefficients: 7
#>     Cross-validation error (deviance): 0.08
#>     R-squared: 0.57
#>     Signal-to-noise ratio: 1.33
#>     Scale estimate (sigma): 0.285
#>
#>   SR information:
#>              Vartype Total Selected Saturation Penalty
#>          Main effect     6        3      0.500    2.45
#>  Order 1 interaction    12        4      0.333    3.46

For more examples and a closer look at how to use this package, check out the package website.

Many thanks to the authors and maintainers of ncvreg and recipes.