Comparing mixture estimates by parametric bootstrapping likelihood ratios

Editor’s Invited Article

DOI: 10.1198/1085711043145

Cite this article as:
Reynolds, J.H. & Templin, W.D. JABES (2004) 9: 57. doi:10.1198/1085711043145


Wildlife managers and researchers often need to estimate the relative contributions of distinct populations in a miture of organisms. Increasingly, there is interest in comparing these mixture contributions across space or time. Comparisons usually just check for overlap in the interval estimates for each population contribution from each mixture. This method inflates Type I error rates, has limited power due to its focus on marginal comparisons, and employs a fundamentally inappropriate measure of mixture difference. Given the difficulty of defining an appropriate measure of mixture difference, a powerful alternative is to compare mixtures using a likelihood ratio test. In applications where the standard asymptotic theory does not hold, the null reference distribution can be obtained through parametric bootstrapping. In addition to testing simple hypotheses, a likelihood ratio framework encourages modeling the change in mixture contributions as a function of covariates. The method is demonstrated with an analysis of potential sampling bias in the estimation of population contributions to the commercial sockeye, salmon (Oncorhynchus nerka) fishery in Upper Cook Inlet, Alaska.

Key Words

Compositional data Compositional difference discrete mixture analysis Genetic stock identification Mixed stock analysis Mixture homogeneity 

Copyright information

© International Biometric Society 2004

Authors and Affiliations

  1. 1.U. S. Fish and Wildlife ServiceDivision of Natural ResourcesAnchorage
  2. 2.Gene Conservation Laboratory of the Commericial Fisheries DivisionAlaska Department of Fish and GameUSA

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