Suicide risk prediction models can identify individuals for targeted intervention. Discussions of transparency, explainability, and transportability in machine learning presume complex prediction models with many variables outperform simpler models. We compared random forest, artificial neural network, and ensemble models with 1500 temporally defined predictors to logistic regression models. Data from 25,800,888 mental health visits made by 3,081,420 individuals in 7 health systems were used to train and evaluate suicidal behavior prediction models. Model performance was compared across several measures. All models performed well (area under the receiver operating curve [AUC]: 0.794-0.858). Ensemble models performed best, but improvements over a regression model with 100 predictors were minimal (AUC improvements: 0.006-0.020). Results are consistent across performance metrics and subgroups defined by race, ethnicity, and sex. Our results suggest simpler parametric models, which are easier to implement as part of routine clinical practice, perform comparably to more complex machine learning methods.