LOOCV-Cross-validation-for-regression

Leave-one-out Cross-validation for regression models

In the first example, we compare the fit among a Linear and a Quadratic model for artificially generated data. As shown in the R and Python output, the Quadratic model is a much better fit for the data as it minimizes the Root Mean Squared Error (RMSE), a medric for prediction error after cross-validation.

The R output using base R.

The Python output using Matplotlib.

They are equivalent. Cross-validation in Python can seem more straightforward providing we avoid errors and can be done as follows:

import pandas as pd
from sklearn.preprocessing import PolynomialFeatures
from sklearn.model_selection import LeaveOneOut, cross_val_score
loocv1 = LeaveOneOut()

# linear model
mod1 = PolynomialFeatures(degree = 1, include_bias = False).fit_transform(xn)
mod11 = LinearRegression().fit(mod1, yn)

loocv1 = LeaveOneOut()
scoresmod1 = cross_val_score(mod11, 
                         mod1,
                         yn, 
                         scoring = 'neg_mean_squared_error',
                         cv = loocv1)

Same example but with R code this time.

pred.cv.mod1 <- pred.cv.mod2 <- numeric(n)

for(i in 1:n) {
  
  # quadratic model
  mod1 = lm(y ~ x, subset = -i)
  pred.cv.mod1[i] = predict(mod1, data[i,])
  
  # quadratic model
  mod2 = lm(y ~ x + I(x^2), subset = -i)
  pred.cv.mod2[i] = predict(mod2, data[i,])
}

Then using R, we compare the fit among three models for binary data on a real dataset, 'mtcars'. We try to predict the binary variable 'vs' which correspond to the engine type using 'mpg' or miles per gallon. We find that the Probit model minimizes the RMSE compared to a Logistic model and a Complementary Log-log model. A graph is then generated using the library ggplot2.

The Python script for the second example is for now unfinished.