## 2 Materials and Methods
### Model Development
#### 2.3.1 Model Selection  
The model performance between existing models must be compared to validate the effectiveness of the proposed framework on crash severity assessment. Unsuitable assessment methods may result in underfitting or overfitting of the prediction results. Six ML models were used for severity classification in this study. Each model is briefly described as follows:  
1. The Bayesian ordered logit model (BOL) is an elegant parametric model that has the basic formulation of logit models with parameter estimation conducted by Bayesian inference [15]. The Bayes method overcomes the uncertainty of the maximum likelihood and reduces overfitting. The parametric modeling could analytically measure the influence of factors based on parameter estimation compared with other ML methods, which helps in the interpretation of the marginal effects on the probabilities of injury severity.
2. A multilayer perceptron (MLP) is a fully connected feed-forward artificial neural network, which uses back propagation for multilayer training with a relatively simple structure and is widely used in roadway safety evaluation. In this study, this approach can be regarded as the baseline model for comparison.
3. A support vector machine (SVM) is a supervised ML method that uses kernel functions to map data features to a high-dimensional feature space, which in turn enables classification prediction [43]. The SVM model has excellent generalization and efficiently solves nonlinear problems with medium-sized training sets. In addition, this model can obtain satisfactory results when dealing with datasets with a large number of features.
4. Random forest (RF) is a well-known tree-based method that uses multiple decision trees for classification and prediction [13]. The model randomly selects the same amount of data for training and several features for tree construction. With these two stochastic selections, this model does not require complex hyperparameter tuning and efficiently performs with large sample sizes, which is consistent with the datasets in this study.
5. A deep neural network (DNN) is a deep learning algorithm with more than one hidden layer in feedforward networks [44]. This method interacts with features through several fully connected layers that are interlinked by weighted connections. Each connected node is regarded as a nonlinear calculation module that converts the input information with an optimization algorithm to form a critical decision threshold. In this study, dropout regularization was applied to leave the biases unregularized and avoid overfitting in training.
6. The local cascade ensemble model (LCE) is a hybrid ensemble method for handling the bias-variance tradeoff. This method combines the bagging method to generate the aggregate predictors and the boosting method to learn weak classifiers. Furthermore, a divide-and-conquer approach is utilized in LCE to learn different parts of the training data, which can be locally applied for cascade generalization. The latest studies have proven that LCE outperforms the state-of-the-art classifiers on the UCI and UEA datasets [45]. Although, to our knowledge, limited studies have applied this model for roadway safety modeling, its utilization in IR assessment is promising.  
Former applications have proven that model predictions can be enhanced by 5-20% through hyperparameter tuning and cross-validation (CV) regardless of the model used [46]. To identify the best model, the Bayes optimization method was adopted in this framework to generate information from previous optimization iterations and tune the model with multiple hyperparameters. In addition, a ten-fold CV method was applied to mitigate the overfitting. The final prediction ability of each model was verified by aggregating the prediction results of all CV groups.