Robust zero-inflated interval regression for cyber security survey data

Zero-inflated interval regression models handle the excess of zeros in an ordinal response by combining a probit model with an ordered probit model. In case of violation of the usual distributional assumptions, standard maximum likelihood estimation is biased and inefficient. We propose a robust inferential approach based on exponential tilting, which weighs each observation according to its compatibility with the assumed model. This methodology is motivated by the analysis of UK survey data on cyber attacks. Our robust results clearly outperform classical inference and reveal the importance of cyber defence investments in reducing the costs from cyber security breaches.