How can you use partial least squares regression to select models?

4 What are some criteria for choosing the number of components?

When selecting the number of components in PLS, there are several criteria to consider, depending on the objective and nature of the data. Cross-validation is a method of evaluating the model's performance on different subsets of data. On the other hand, R-squared measures how well the model explains the variation in the response variable, with 0 meaning no explanation and 1 meaning perfect explanation. Additionally, AIC or BIC are information criteria that penalize the model's complexity and favor simpler models, based on the likelihood function. By using these criteria, you can select the number that minimizes prediction error, maximizes R-squared value, or minimizes AIC or BIC value.

5 How can you implement PLS in R?

R is a popular programming language for statistical analysis and data visualization. It has several packages that can help you implement PLS in your data. One of them is the pls package, which provides functions for fitting and evaluating PLS models. To use the pls package, you need to install it from CRAN and load it into your R session. Then, you can use the plsr function to fit a PLS model to your data, specifying the response variable, the predictor variables, the number of components, and the validation method. For example, the following code fits a PLS model with 3 components and 10-fold cross-validation to the iris data set, which contains measurements of four features and one species for 150 flowers:

# install and load the pls package
install.packages("pls")
library(pls)
# fit a PLS model with 3 components and 10-fold cross-validation to the iris data
iris.pls <- plsr(Species ~ ., data = iris, ncomp = 3, validation = "CV")
# print the summary of the model
summary(iris.pls)        

The summary of the model shows the coefficients, the R-squared values, and the cross-validation errors for each component. You can also use the plot function to visualize the results, such as the loadings, the scores, and the validation plots. For example, the following code plots the cross-validation errors for each component:

# plot the cross-validation errors for each component
plot(RMSEP(iris.pls))        

The plot shows that the cross-validation error decreases as the number of components increases, but it also shows that there is little difference between 2 and 3 components. Therefore, you might want to choose 2 components as the optimal number for your model, to avoid overfitting and reduce complexity.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?