A Robust Location Model through Median-based Estimators for Handling Outliers

Abstract

The location model (LM) is a well-known statistical method for mixed variable classification problems. This method is commonly used to differentiate between the two observed groups based on classical estimation techniques. However, the presence of outliers can substantially distort classical parameter estimation, leading to inaccurate classification results, particularly a high misclassification error rate. To overcome this limitation, this paper proposes a robust LM called RLMmed, which employs the median as a robust location estimator. This median estimator is paired with a robust covariance matrix derived from the product of the median absolute deviation (MADn) and Spearman rank correlation. Simulation analyses were conducted under two sample sizes ( and ) and three binary variable conditions (  and) with a fixed number of continuous variables (). For comparative purposes, simulated datasets were tested with two mean group separations (0.5 and 1.0) and five different levels of contamination (0%, 10%, 20%, 30% and 40%). Thus, a total of 60 simulation datasets were used to assess the performance of the proposed RLMmed. The results were then validated against the classical LM using real data (heart data). The simulation results and real data result consistently demonstrated that the RLMmed outperforms the classical LM, achieving lower misclassification error rates across most contamination levels in all conditions tested. Moreover, RLMmed revealed the best achievement among the contaminated data inspected with a sample size of 400 and two measured binary variables. In conclusion, the developed RLMmed model can effectively handle mixed variable classification problems in the presence of outliers, which is crucial before conducting further classification analysis.