A mixture-based approach to multiple imputation in incomplete linear-circular datasets

Model-based methods of missing value imputation in incomplete multivariate datasets require the definition of an imputation model that specifies the predictive distribution of the missing values given the observed data. Mixture models for multivariate data provide a flexible approach to specify imputation models when variables are measured on different scales. We propose to specify the joint distribution of linear and circular data through a finite mixture of conditionally independent Gamma and von Mises distributions. The procedure is illustrated on an incomplete dataset that includes measurements of wind speed and direction and significant wave height and direction, taken by a buoy and two tide gauges of the Italian wave-metric network.