Correcting for selection bias after conditioning on a sum score in the Ising model

In psychological studies, it is common practice to select a sample based on the sum score of the modeled variables (e.g., based on symptom severity when investigating the associations between those same symptoms). However, this practice introduces bias if the sum score selection imperfectly defines the population of interest. Here, we propose a correction for this type of selection bias in the Ising model, a popular network model for binary data. Possible applications of our correction are when one wants to obtain (1) full population estimates when only the sum score subset of the data is available, and (2) improved estimates of a subpopulation, if we observe a mixture of populations that differ from each other in the sum score. In a simulation study, we verify that our correction recovers the network structure of the desired population after a sum score selection using both a node-wise regression and a multivariate estimation of the Ising model. In an example, we show how our correction can be used in practice using empirical data on symptoms of major depression from the National Comorbidity Study Replication (N = 9,282). We implemented our correction in four commonly used R packages for estimating the Ising model, namely IsingFit, IsingSampler, psychonetrics, and bootnet.