Change we can believe in: Comparing longitudinal network models on consistency, interpretability and predictive power

•We compare auto-regressive and process-based network models on examples TERGM & SAOM.•The TERGM has no consistent interpretation on the tie-level and on network change.•TERGM parameters strongly depend on time between measurements.•The SAOM suffers from neither of these limitations.•Both models perform poorly in out-of-sample prediction of individual ties. While several models for analysing longitudinal network data have been proposed, their main differences, especially regarding the treatment of time, have not been discussed extensively in the literature. However, differences in treatment of time strongly impact the conclusions that can be drawn from data. In this article we compare auto-regressive network models using the example of TERGMs – a temporal extensions of ERGMs – and process-based models using SAOMs as an example. We conclude that the TERGM has, in contrast to the ERGM, no consistent interpretation on tie-level probabilities, as well as no consistent interpretation on processes of network change. Further, parameters in the TERGM are strongly dependent on the interval length between two time-points. Neither limitation is true for process-based network models such as the SAOM. Finally, both compared models perform poorly in out-of-sample prediction compared to trivial predictive models.