N-way interaction basis

Generates a design matrix that contains all possible interactions of the input variables up to a specified maximum depth. The default "symbox" standardization, which maps inputs to \([-0.5, 0.5]^d\), is strongly recommended, as it means that the interaction terms will have smaller variance and thus be penalized more by methods like the Lasso or ridge regression (see Gelman et al., 2008).

Usage

b_inter(
  ...,
  depth = 2,
  stdize = c("symbox", "box", "scale", "none"),
  shift = NULL,
  scale = NULL
)

Arguments

...

The variable(s) to build features for. A single data frame or matrix may be provided as well. Missing values are not allowed.

depth

The maximum interaction depth. The default is 2, which means that all pairwise interactions are included.

stdize

How to standardize the predictors, if at all. The default "scale" applies scale() to the input so that the features have mean zero and unit variance, "box" scales the data along each dimension to lie in the unit hypercube, and "symbox" scales the data along each dimension to lie in \([-0.5, 0.5]^d\).

shift

Vector of shifts, or single shift value, to use. If provided, overrides those calculated according to stdize.

scale

Vector of scales, or single scale value, to use. If provided, overrides those calculated according to stdize.

Value

A matrix with the rescaled and interacted features.

References

Gelman, A., Jakulin, A., Pittau, M. G., & Su, Y. S. (2008). A weakly informative default prior distribution for logistic and other regression models.

Examples

# default: all pairwise interactions
lm(mpg ~ b_inter(cyl, hp, wt), mtcars)
#> 
#> Call:
#> lm(formula = mpg ~ b_inter(cyl, hp, wt), data = mtcars)
#> 
#> Coefficients:
#>                (Intercept)     b_inter(cyl, hp, wt)cyl  
#>                     15.225                       2.914  
#>     b_inter(cyl, hp, wt)hp      b_inter(cyl, hp, wt)wt  
#>                    -11.443                     -13.041  
#> b_inter(cyl, hp, wt)cyl:hp  b_inter(cyl, hp, wt)cyl:wt  
#>                     13.724                       6.855  
#>  b_inter(cyl, hp, wt)hp:wt  
#>                      7.050  
#> 

# how number of features depends on interaction depth
for (d in 2:6) {
    X = with(mtcars, b_inter(cyl, disp, hp, drat, wt, depth=d))
    print(ncol(X))
}
#> [1] 15
#> [1] 25
#> [1] 30
#> [1] 31
#> [1] 31