Comparing linear discriminant analysis and supervised learning algorithms for binary classification-A method...

Area of Science:

• Psychology
• Machine Learning
• Statistical Analysis

Background:

• Linear Discriminant Analysis (LDA) is a standard method for two-group classification using questionnaire data.
• The reliance of LDA's predictive performance on the multivariate normality assumption requires investigation.

Purpose of the Study:

• To compare LDA with several supervised learning algorithms.
• To assess the impact of the multivariate normality assumption on LDA's performance.
• To evaluate alternative nonparametric methods for classification tasks.

Main Methods:

• Comparison of LDA with linear Support Vector Machine (SVM), Classification and Regression Trees (CART), Random Forest (RF), Probabilistic Neural Network (PNN), and ensemble k Conditional Nearest Neighbor (EkCNN).
• Evaluation of predictive performance using overall performance, discrimination, and calibration measures.
• Utilized two reference Likert-type datasets (5 and 10 predictors) and simulation studies with varying degrees of nonnormality (balanced and unbalanced scenarios).

Main Results:

• Random Forest (RF) outperformed LDA in overall performance for bimodal data.
• RF demonstrated higher discriminative ability than LDA, but poorer model calibration.
• LDA consistently performed well, often ranking second or showing only marginal differences when outperformed.

Conclusions:

• Despite RF's advantages in specific scenarios, LDA is still recommended for two-group classification tasks with questionnaire data.
• LDA's robustness and calibration make it a dependable choice, especially when normality assumptions are uncertain.