Extending distributed lag models to higher degrees

Matthew J. Heaton, Roger D. Peng

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Distributed lag (DL) models relate lagged covariates to a response and are a popular statistical model used in a wide variety of disciplines to analyze exposure-response data. However, classical DL models do not account for possible interactions between lagged predictors. In the presence of interactions between lagged covariates, the total effect of a change on the response is not merely a sum of lagged effects as is typically assumed. This article proposes a new class of models, called high-degree DL models, that extend basic DL models to incorporate hypothesized interactions between lagged predictors. The modeling strategy utilizes Gaussian processes to counterbalance predictor collinearity and as a dimension reduction tool. To choose the degree and maximum lags used within the models, a computationally manageable model comparison method is proposed based on maximum a posteriori estimators. The models and methods are illustrated via simulation and application to investigating the effect of heat exposure on mortality in Los Angeles and New York.

Original languageEnglish (US)
Pages (from-to)398-412
Number of pages15
Issue number2
StatePublished - Apr 2014


  • Dimension reduction
  • Gaussian process
  • Heat exposure
  • Lagged interaction
  • NMMAPS dataset

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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