On the detection of population heterogeneity in causation between two variables: Finite mixture modeling of data collected from twin pairs

Causal inference is inherently complex, often dependent on key assumptions that are sometimes overlooked. One such assumption is the potential for unidirectional or bidirectional causality, while another is population homogeneity, which suggests that the causal direction between two variables remains consistent across the study sample. Discerning these processes requires meticulous data collection through an appropriate research design and the use of suitable software to define and fit alternative models. In psychiatry, the co-occurrence of different disorders is common and can stem from various origins. A patient diagnosed with two disorders might have one recognized as primary and the other as secondary, suggesting the existence of two types of comorbidity within the population. For example, in some individuals, depression might lead to substance use, while in others, substance use could lead to depression. Identifying the primary disorder is crucial for developing effective treatment plans. This article explores the use of finite mixture models to depict within-sample heterogeneity. We begin with the Direction of Causation (DoC) model for twin data and extend it to a mixture distribution model. This extension allows for the calculation of the likelihood of each individual's data for the two alternate causal directions. Given twin data, there are four possible pairwise combinations of causal direction. Through simulations, we investigate the Direction of Causation Twin Mixture (mixCLPM) model's potential to detect and model heterogeneity due to varying causal directions.