title: Extending distributed lag models to higher degrees.
abstract: 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.
authors.affiliation: Department of Statistics, Brigham Young University, 204 TMCB, Provo UT 84602, USA.
authors.forename: Matthew J
authors.initials: MJ
authors.lastname: Heaton
authors.forename: Roger D
authors.initials: RD
authors.lastname: Peng
mesh_terms: D000368:Aged; D003627:Data Interpretation, Statistical; D004781:Environmental Exposure / Q000009:adverse effects; D006358:Hot Temperature / Q000009:adverse effects; D006801:Humans; D015141:Los Angeles / Q000453:epidemiology; D015233:Models, Statistical; D009026:Mortality; D009518:New York / Q000453:epidemiology
keywords: Dimension reduction; Gaussian process; Heat exposure; Lagged interaction; NMMAPS dataset