Regularized Cross-Sectional Network Modeling with Missing Data: A Comparison of Methods

Many applications of network modeling involve cross-sectional data of psychological variables (e.g., symptoms for psychological disorders), and analyses are often conducted using a regularized Gaussian graphical model (GGM) employing a lasso, also known as the graphical lasso or glasso. Appropriate methodology for handling missing data is underdeveloped while using glasso, precluding the use of planned missing data designs to reduce participant fatigue. In this research, we compare three approaches to handling missing data with glasso. The first resembles a two-stage estimation approach-borrowed from the covariance structure modeling literature-whereby a saturated covariance matrix among the items is estimated prior to using glasso. The second and third approaches use glasso and the expectation-maximization (EM) algorithm in a single stage and either use EBIC or cross-validation for tuning parameter selection. We compared these approaches in a simulation study with a variety of sample sizes, proportions of missing data, and network saturation. An example with data from the Patient Reported Outcomes Measurement Information System is also provided. The EM algorithm with cross-validation performed best, but all methods appeared to be viable strategies under larger samples and with less missing data.