Environmental and Ecological Statistics

, Volume 18, Issue 2, pp 257–270 | Cite as

Multinomial mixture model with heterogeneous classification probabilities

  • Mark D. Holland
  • Brian R. Gray


Royle and Link (Ecology 86(9):2505–2512, 2005) proposed an analytical method that allowed estimation of multinomial distribution parameters and classification probabilities from categorical data measured with error. While useful, we demonstrate algebraically and by simulations that this method yields biased multinomial parameter estimates when the probabilities of correct category classifications vary among sampling units. We address this shortcoming by treating these probabilities as logit-normal random variables within a Bayesian framework. We use Markov chain Monte Carlo to compute Bayes estimates from a simulated sample from the posterior distribution. Based on simulations, this elaborated Royle-Link model yields nearly unbiased estimates of multinomial and correct classification probability estimates when classification probabilities are allowed to vary according to the normal distribution on the logit scale or according to the Beta distribution. The method is illustrated using categorical submersed aquatic vegetation data.


Abundance index Classification probability Detection probability Latent class model Population index Site occupancy Submersed aquatic vegetation 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of StatisticsUniversity of MinnesotaMinneapolisUSA
  2. 2.United States Geological SurveyUpper Midwest Environmental Sciences CenterLa CrosseUSA

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