Stochastic Environmental Research and Risk Assessment

, Volume 21, Issue 5, pp 635–646

Additive versus multiplicative models in ecologic regression

  • W. Douglas Thompson
  • Daniel Wartenberg
Original Paper

DOI: 10.1007/s00477-007-0141-2

Cite this article as:
Thompson, W.D. & Wartenberg, D. Stoch Environ Res Risk Assess (2007) 21: 635. doi:10.1007/s00477-007-0141-2


Much research in environmental epidemiology relies on aggregate-level information on exposure to potentially toxic substances and on relevant covariates. We compare the use of additive (linear) and multiplicative (log-linear) regression models for the analysis of such data. We illustrate how both additive and multiplicative models can be fit to aggregate-level data sets in which disease incidence is the dependent variable, and contrast these results with similar models fitted to individual-level data. We find (1) that for aggregate-level data, multiplicative models are more likely than additive models to introduce bias into the estimation of rates, an effect not found with individual-level data; and (2) that under many circumstances multiplicative models reduce the precision of the estimates, an effect also not found in individual-level models. For both additive and multiplicative models of aggregate-level data, we find that, in the presence of covariates, narrow confidence interval are obtained only when two or more antecedent factors are strongly related to the measured covariate and/or the exposure of primary substantive interest. We conclude that the equivalency of fitting additive versus multiplicative models in studies with individual-level binary data does not carry over to studies that analyze aggregate-level information. For aggregate data, we strongly recommend use of additive models.

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • W. Douglas Thompson
    • 1
  • Daniel Wartenberg
    • 2
  1. 1.Department of Applied Medical SciencesUniversity of Southern MainePortlandUSA
  2. 2.Department of Environmental and Occupational MedicineUMDNJ–Robert Wood Johnson Medical SchoolPiscatawayUSA