Using observed sequence to orient causal networks.

In learning causal networks, typically cross-sectional data are used and the sequence among the network nodes is learned through conditional independence. Sequence is inherently a longitudinal concept. We propose to learn sequence of events in longitudinal data and use it to orient arc directions in a network learned from cross-sectional data. The network is learned from cross-sectional data using various established algorithms, with one modification. Arc directions that do not agree with the longitudinal sequence were prohibited. We established longitudinal sequence through two methods: Probabilistic Contrast, and Goodman and Kruskal error reduction methods. In simulated data, the error reduction method was used to learn the sequence in the data. The procedure reduced the number of arc direction errors and larger improvements were observed with increasing number of events in the network. In real data, different algorithms were used to learn the network from cross-sectional data, while prohibiting arc directions not supported by longitudinal information. The agreement among learned networks increased significantly. It is possible to combine sequence information learned from longitudinal data with algorithms organized for learning network models from cross-sectional data. Such models may have additional causal interpretation as they more explicitly take into account observed sequence of events.