Causal model selection tests in systems genetics

We develop a novel hypothesis testing framework for causal inference among pairs of phenotypes in the context of segregating populations. Our model selection test extends Vuong’s test to the case of three misspecified models, to handle the full range of possible causal relationships among a pair of traits, namely, causal, reactive or independent models. The ability to properly address misspecified models for systems genetics is key since in general any two phenotypes may be part of a complex network that is grossly oversimplified by the pairwise models. We evaluate and compare our test against the BIC model selection criterium and to another causality inference test in simulation studies using data generated from simple and complex networks and from models affected by measurement error. While our causal model selection test is less powered than alternative approaches when one of the competing models is correctly specified, it makes mistakes at much lower rates than the other approaches under model misspecification and in the presence of measurement error. Finally, we apply and compare these three approaches using a mice intercross data set.