Marginal and copula modeling

  • Philip Hougaard
Part of the Statistics for Biology and Health book series (SBH)


Marginal modeling is a term used for an approach where the effect of explanatory factors is estimated based on considering the marginal distributions. The dependence is not the interesting aspect and is not considered in detail. Afterwards, the variability of the regression coefficient estimators is determined by a procedure that accounts for the dependence between the observations. For parallel data, there are in practice two versions of this general idea. The coordinate-wise (CW) approach considers each marginal separately and estimates the regression coefficients in each marginal. The covariance matrix of these estimates is estimated and used for combining the estimates from the coordinates by means of a weighted average. The estimated covariance matrix is further used to evaluate the variance of the combined estimate. The second version of the approach is the independence working model (IWM) approach, where the estimate is found under the (incorrect) assumption of independence between the coordinates. This yields directly the final estimate of the regression coefficients. The uncertainty of the regression coefficient estimate is evaluated by means of an estimator that accounts for the dependence between the coordinates. This is typically done by a ”sandwich estimator” (see below). The independence working model approach is closely related to the so-called generalized estimating equations. For recurrent events, there is an approach similar in concept to the IWM approach.


Marginal Distribution Frailty Model Isosorbide Dinitrate Marginal Modeling Combine Estimate 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Philip Hougaard
    • 1
  1. 1.Department of StatisticsNovo Nordisk A/SBagsvaerdDenmark

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