Linear Discriminant Analysis for Prediction of Group Membership: A User-Friendly Primer

Abstract

In psychology, researchers are often interested in the predictive classification of individuals. Various models exist for such a purpose, but which model is considered a best practice is conditional on attributes of the data. Under certain conditions, linear discriminant analysis (LDA) has been shown to perform better than other predictive methods, such as logistic regression, multinomial logistic regression, random forests, support-vector machines, and the K-nearest neighbor algorithm. The purpose of this Tutorial is to provide researchers who already have a basic level of statistical training with a general overview of LDA and an example of its implementation and interpretation. Decisions that must be made when conducting an LDA (e.g., prior specification, choice of cross-validation procedures) and methods of evaluating case classification (posterior probability, typicality probability) and overall classification (hit rate, Huberty’s I index) are discussed. LDA for prediction is described from a modern Bayesian perspective, as opposed to its original derivation. A step-by-step example of implementing and interpreting LDA results is provided. All analyses were conducted in R, and the script is provided; the data are available online.