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Robust Linear Regression in tidymodels (LTS parsnip Engine)

Source: R/parsnip_lts.R
linear_reg_lts.Rd

specProc adds the "lts" engine to parsnip::linear_reg(): the reweighted least trimmed squares (LTS) regression of robustbase::ltsReg(), which resists vertical outliers and bad leverage points. lts_fit() fits it outside of tidymodels.

Usage

lts_fit(x, y, alpha = 0.75, nsamp = 500)

Arguments

x

A numeric matrix or data frame of the predictors.

y

A numeric vector of the response.

alpha

The fraction of observations whose squared residuals are minimized, between 0.5 and 1. Default is 0.75.

nsamp

The number of random subsets. Default is 500.

Value

lts_fit() returns an object of class specproc_lts, a list with the coefficients (intercept first), the robust scale of the residuals, the fitted values, residuals, standardized residuals std_resid and the weights of the reweighted fit (1 for the observations whose standardized residual is within the cut-off). Its predict() method takes newdata.

Details

The engine is available once parsnip and specProc are both loaded, in either order. It is for regression with one outcome.

Combined with step_robpca() in a workflow, it gives the robust principal component regression of Hubert and Verboven (2003), whose robust PCA has num_comp components (see also rpcr()): the robust scores of the spectra, then the LTS regression on them. It also gives robust calibration curves from a few line intensities.

Engine arguments

  • alpha: the fraction of observations whose squared residuals are minimized, between 0.5 and 1 (default 0.75, as in rpcr()).

  • nsamp: the number of random subsets (default 500).

The main arguments of parsnip::linear_reg(), penalty and mixture, are not used. LTS uses random subsets, so use set.seed() before fitting for reproducible results.

References

  • Rousseeuw, P.J., Van Driessen, K. (2006). Computing LTS regression for large data sets. Data Mining and Knowledge Discovery, 12(1):29-45.

  • Hubert, M., Verboven, S. (2003). A robust PCR method for high-dimensional regressors. Journal of Chemometrics, 17(8-9):438-452.

See also

rpcr(), step_robpca(), parsnip::linear_reg()

Author

Christian L. Goueguel

Examples

library(parsnip)
data(forageLIBS)
lines <- forageLIBS[c("Ca", "393.3599236", "396.8602175")]  # Ca II K and H
names(lines) <- c("Ca", "CaII_393", "CaII_397")
set.seed(1)
fit <- linear_reg() |>
  set_engine("lts") |>
  fit(Ca ~ ., data = lines[1:300, ])
predict(fit, lines[301:305, ])
#> # A tibble: 5 × 1
#>   .pred
#>   <dbl>
#> 1 0.478
#> 2 0.517
#> 3 0.580
#> 4 0.533
#> 5 0.567
extract_fit_engine(fit)$coefficients
#>   (Intercept)      CaII_393      CaII_397 
#> -2.574715e+00  4.387295e-05  6.141614e-06