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.

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.

```
## Via GitHub:
# install.packages("devtools")
::install_github("petersonR/sparseR")
devtools
# or via CRAN
install.packages("sparseR")
```

`library(sparseR)`

```
data(iris)
set.seed(1321)
<- sparseR(Sepal.Width ~ ., data = iris, k = 1, seed = 1)
srl
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`

.