Quantifying Optimization Bias in Model Evaluation when using Cross-Validation in Psychological Science: A Monte Carlo Simulation Study

Psychological scientists are increasingly using machine learning to advance applied or basic science goals. Cross-validation is commonly used for training, selecting, and evaluating machine learning algorithms. Although cross-validation is often described as a tool that necessarily prevents overly optimistic estimates of a final model’s performance in new data, not all approaches to cross-validation offer accurate evaluation in all data contexts. Prior work in other fields has established that k-fold cross-validation can provide upwardly biased model evaluation. The extent of this optimization bias in data contexts typical of psychological science is not known. This Monte Carlo simulation study characterizes optimization bias in model evaluation when using three different approaches to cross-validation — k-fold cross-validation, k-fold cross-validation with a test set, and nested k-fold cross-validation — in factorial combinations of sample size (100; 500; 1,000), number of predictors (10; 100; 1,000), and outcome distribution (balanced, with a positive case probability of .50; unbalanced, with a positive case probability of .10). For each unique data context, 1,000 simulations were conducted by randomly sampling from multivariate normal predictor distributions and binomial outcome distributions such that predictors were known to have no population-level association with the outcome. We characterized the average, standard deviation, and maximum performance estimates resulting from model evaluation using each approach to cross-validation in each context, identifying biased evaluations as those with an Area Under the Receiver Operating Characteristic Curve (AUC) value greater than .50.