Predicting implementation of response to intervention in math using elastic net logistic regression

Abstract

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IntroductionThe primary objective of this study was to identify variables that significantly influence the implementation of math Response to Intervention (RTI) at the school level, utilizing the ECLS-K: 2011 dataset.MethodsDue to missing values in the original dataset, a Random Forest algorithm was employed for data imputation, generating a total of 10 imputed datasets. Elastic net logistic regression, combined with nested cross-validation, was applied to each imputed dataset, potentially resulting in 10 models with different variables. Variables for the models derived from the imputed datasets were selected using four methods, leading to four candidate models for final selection. These models were assessed based on their performance of prediction accuracy, culminating in the selection of the final model that outperformed the others.Results and discussionMethod50 and Methodcoef emerged as the most effective, achieving a balanced accuracy of 0.852. The ultimate model selected relevant variables that effectively predicted RTI. The predictive accuracy of the final model was also demonstrated by the receiver operating characteristic (ROC) plot and the corresponding area under the curve (AUC) value, indicating its ability to accurately forecast math RTI implementation in schools for the following year.

Keywords

• math achievement
• response-to-intervention
• elastic net logistic regression
• multiple imputation
• random forest algorithm
• variable selection