syxi {RXshrink}

Linear and GAM Spline Predictions from a Single x-Variable

Description

Compute and display (x,y) plots with their linear and gam() spline y-predictions.

Usage

  syxi(form, data, i = 1)

Arguments

form

A "simple" regression formula [y~x] suitable for use with lm().

data

data.frame containing at least 10 observations on both variables in the formula.

i

A single integer "index" within 1:25.

Details

The gam() functon from the mgcv R-package is used to compute and, subsequently, to generate plots that visually compare the "linear" fit from lm(y~x) with a potentially "nonlinear" fit using smoothing parameters. The horizontal axis on type = "sy" plots gives potentially "straightened out" x numerical values.

Value

An output list object of class syxi:

dfname

Name of the data.frame object specified as the second argument.

xname

"xi" as Two or Three Characters.

sxname

"si" as Two or Three Characters.

dfsxf

A data.frame containing 3 variables: "yvec", "xvec", and "sxfit".

yxcor

Pearson correlation between "yvec" and "xvec".

yscor

Pearson correlation between "yvec" and "sxfit".

xscor

Pearson correlation between "xvec" and "sxfit".

lmyxc

lm() Coefficients (intercept and slope) for y ~ x.

lmysc

lm() Coefficients (intercept and slope) for y ~ sxfit.

adjR2

Adjusted R2 value from gam.sum$r.sq.

Author(s)

Bob Obenchain <[e-mail]>

References

Obenchain RL. (2022) Efficient Generalized Ridge Regression. Open Statistics 3: 1-18. doi:10.1515/stat-2022-0108

Obenchain RL. (2023) Nonlinear Generalized Ridge Regression. arXiv preprint https://arxiv.org/abs/2103.05161

Examples

  library(mgcv)
  data(longley2)
  form = GNP ~ Year
  GNPpred = syxi(form, data=longley2, i = 1)
  plot(GNPpred, type="xy")
  title(main="y = GNP on x1 = Year")
  plot(GNPpred, type="sy")
  title(main="y = GNP on Spline for Year")