Title: On synthetic data with predetermined subject partitioning and cluster profiling, and pre-specified categorical variable marginal dependence structure,
Abstract: A standard approach for assessing the performance of partition or mixture
models is to create synthetic data sets with a pre-specified clustering
structure, and assess how well the model reveals this structure. A common
format is that subjects are assigned to different clusters, with variable
observations simulated so that subjects within the same cluster have similar
profiles, allowing for some variability. In this manuscript, we consider
observations from nominal, ordinal and interval categorical variables.
Theoretical and empirical results are utilized to explore the dependence
structure between the variables, in relation to the clustering structure for
the subjects. A novel approach is proposed that allows to control the marginal
association or correlation structure of the variables, and to specify exact
correlation values. Practical examples are shown and additional theoretical
results are derived for interval data, commonly observed in cohort studies,
including observations that emulate Single Nucleotide Polymorphisms. We compare
a synthetic dataset to a real one, to demonstrate similarities and differences.