Statistical distinguishability of psychopathology symptom network and common factor models in longitudinal data

Psychometric conceptualizations of psychopathology have gained popularity. Most prominent approaches are the common factor (CF) and the symptom network models. A known problem in theory development through empirical findings is the statistical indistinguishability of CF and symptom network models in cross-sectional data. However, the extent of this problem and its implications have not been inspected formally for longitudinal studies. In this study, we sought to clarify the distinguishability between CF and symptom network models in longitudinal designs. We show necessary and sufficient conditions for indistinguishability in covariance for commonly applied vector autoregressive symptom network models and CF models and suggest a procedure for assessing whether a CF model can be refuted based on an estimated symptom network model. We give easy-to-implement R -functions for conducting the comparison. Numerical and empirical examples show that potential indistinguishability is relevant when interpreting the published literature. Overall, this study promotes comparative analysis of symptom network and CF models.