Causality on longitudinal data: Stable specification search in constrained structural equation modeling

Stat Methods Med Res. 2018 Dec;27(12):3814-3834. doi: 10.1177/0962280217713347. Epub 2017 Jun 28.


A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for longitudinal data, that is robust for finite samples based on recent advances in stability selection using subsampling and selection algorithms. Our approach uses exploratory search but allows incorporation of prior knowledge, e.g., the absence of a particular causal relationship between two specific variables. We represent causal relationships using structural equation models. Models are scored along two objectives: the model fit and the model complexity. Since both objectives are often conflicting, we apply a multi-objective evolutionary algorithm to search for Pareto optimal models. To handle the instability of small finite data samples, we repeatedly subsample the data and select those substructures (from the optimal models) that are both stable and parsimonious. These substructures can be visualized through a causal graph. Our more exploratory approach achieves at least comparable performance as, but often a significant improvement over state-of-the-art alternative approaches on a simulated data set with a known ground truth. We also present the results of our method on three real-world longitudinal data sets on chronic fatigue syndrome, Alzheimer disease, and chronic kidney disease. The findings obtained with our approach are generally in line with results from more hypothesis-driven analyses in earlier studies and suggest some novel relationships that deserve further research.

Keywords: Alzheimer’s disease; Longitudinal data; causal modeling; chronic fatigue syndrome; chronic kidney disease; multi-objective evolutionary algorithm; stability selection; structural equation model.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Algorithms
  • Alzheimer Disease / diagnostic imaging
  • Causality*
  • Cognitive Behavioral Therapy
  • Disease Progression
  • Fatigue Syndrome, Chronic / therapy
  • Humans
  • Kidney Failure, Chronic / nursing
  • Latent Class Analysis*
  • Longitudinal Studies
  • Treatment Outcome