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

In this paper we propose using the k-nearest neighbors (k-NN) algorithm (Cover and Hart, 1967) for classifying and predicting the responses to dichotomous items. We show using the percent correct statistic how k-NN can be used with Rasch model parameter estimation methods such as joint maximum likelihood (JMLE), conditional maximum likelihood estimation (CMLE), marginal maximum likelihood estimation (MMLE), and marginal Bayes modal estimation (MBME). We further suggest how one can use the algorithm to predict responses on future assessments. The empirical data set that we used to illustrate this procedure was the fraction subtraction data set from Tatsuoka (1984). Using R software we show the accuracy and efficacy of k-NN for classifying responses.