On synthetic interval data with predetermined subject partitioning, and partial control of the variables' marginal correlation structure

A standard approach for assessing the performance of partition models is to create synthetic data sets with a prespecified clustering structure, and assess how well the model reveals this structure. A common format is that subjects are assigned to different clusters, with observations simulated so that subjects within the same cluster have similar profiles, allowing for some variability. In this manuscript, we consider observations from interval variables, taking a finite number of values. Interval data are commonly observed in cohort and Genome Wide Association studies, and our focus is on Single Nucleotide Polymorphisms. Theoretical and empirical results are utilized to explore the dependence structure between the variables, in relation with the clustering structure for the subjects. A novel algorithm is proposed that allows to control the marginal stratified correlation structure of the variables, specifying exact correlation values within groups of variables. Practical examples are shown, and a synthetic dataset is compared to a real one, to demonstrate similarities and differences.