What is forward selection?
Forward selection is a method used in statistical modeling and feature selection to build a prediction model by iteratively adding predictors or variables to a model, based on their statistical significance. The process starts with an empty model and sequentially adds one variable at a time based on a predefined criterion, typically the significance level of the variable.
To explain how forward selection works, here are the steps to perform it:
1. Start with an empty model: Begin the process with a model that does not include any predictors or variables.
2. Select the best predictor: Add the predictor that has the highest statistical significance, typically based on p-values from hypothesis tests or other criteria. This variable is chosen based on its ability to explain the variation in the outcome variable.
3. Assess the model: Fit the model with the selected predictor and evaluate its performance using appropriate metrics such as adjusted R-squared, AIC, BIC, or cross-validation.
4. Iterate the process: Repeat steps 2 and 3 by adding one predictor at a time to the existing model. Choose the next best predictor based on its significance and repeat the evaluation process.
5. Stop criterion: Continue adding predictors until a stopping criterion is met. This criterion can vary depending on the context and goals of the analysis. It could be based on the statistical significance of the added variables, the model's performance, or other criteria. Common approaches include using a predetermined number of variables or reaching a desired level of performance.
6. Final model selection: Once the stopping criterion is met, the final model consists of the predictors that were selected during the forward selection process. This model is used for inference or prediction, depending on the objectives of the analysis.
It's worth noting that forward selection has its limitations, such as possible omission of important predictors if they are not considered early in the process, and the risk of overfitting if the stopping criterion is not carefully chosen. Therefore, it is important to interpret the results cautiously and consider potential biases or issues that might arise during the selection process.