Using the Rasch Model and k-Nearest Neighbors Algorithm for Response Classification

Area of Science:

• Educational Measurement
• Machine Learning
• Psychometrics

Background:

• Traditional methods for analyzing dichotomous item responses often rely on specific statistical models.
• The k-nearest neighbors (k-NN) algorithm offers a non-parametric approach with potential for robust classification.
• Integrating machine learning with psychometric models can enhance response prediction and classification accuracy.

Purpose of the Study:

• To propose and evaluate the k-nearest neighbors (k-NN) algorithm for classifying and predicting responses to dichotomous items.
• To demonstrate the compatibility of k-NN with various Rasch model parameter estimation techniques.
• To assess the accuracy and efficacy of k-NN using real-world data.

Main Methods:

• Application of the k-nearest neighbors (k-NN) algorithm for response classification.
• Integration of k-NN with Rasch model parameter estimation methods: joint maximum likelihood (JMLE), conditional maximum likelihood estimation (CMLE), marginal maximum likelihood estimation (MMLE), and marginal Bayes modal estimation (MBME).
• Utilization of the percent correct statistic to evaluate performance.
• Analysis of the fraction subtraction data set (Tatsuoka, 1984) using R software.

Main Results:

• The k-nearest neighbors (k-NN) algorithm effectively classifies dichotomous item responses.
• k-NN demonstrates compatibility and utility with established Rasch model parameter estimation methods.
• Empirical validation using the fraction subtraction data set confirms the accuracy and efficacy of the proposed approach.
• The study illustrates the potential for predicting future assessment responses using k-NN.

Conclusions:

• The k-nearest neighbors (k-NN) algorithm presents a viable and effective tool for response classification in educational measurement.
• Combining k-NN with Rasch modeling offers a powerful approach for both current response analysis and future prediction.
• The findings highlight the potential of machine learning algorithms to enhance psychometric analyses.