Modelling the Covariance Structure in Marginal Multivariate Count Models: Hunting in Bioko Island

  • W. H. BonatEmail author
  • J. Olivero
  • M. Grande-Vega
  • M. A. Farfán
  • J. E. Fa


The main goal of this article is to present a flexible statistical modelling framework to deal with multivariate count data along with longitudinal and repeated measures structures. The covariance structure for each response variable is defined in terms of a covariance link function combined with a matrix linear predictor involving known matrices. In order to specify the joint covariance matrix for the multivariate response vector, the generalized Kronecker product is employed. We take into account the count nature of the data by means of the power dispersion function associated with the Poisson–Tweedie distribution. Furthermore, the score information criterion is extended for selecting the components of the matrix linear predictor. We analyse a data set consisting of prey animals (the main hunted species, the blue duiker Philantomba monticola and other taxa) shot or snared for bushmeat by 52 commercial hunters over a 33-month period in Pico Basilé, Bioko Island, Equatorial Guinea. By taking into account the severely unbalanced repeated measures and longitudinal structures induced by the hunters and a set of potential covariates (which in turn affect the mean and covariance structures), our method can be used to indicate whether there was statistical evidence of a decline in blue duikers and other species hunted during the study period. Determining whether observed drops in the number of animals hunted are indeed true is crucial to assess whether species depletion effects are taking place in exploited areas anywhere in the world. We suggest that our method can be used to more accurately understand the trajectories of animals hunted for commercial or subsistence purposes and establish clear policies to ensure sustainable hunting practices.

Supplementary materials accompanying this paper appear online.


Multivariate models Estimating functions Hunting Longitudinal data 



The authors thank Professors Elias Teixeira Krainski, Walmes Marques Zeviani, Fernando Poul Mayer and Paulo Justianiano Ribeiro Jr for their comments and suggestions that substantially improved the article. The first author is supported by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior)-Brazil.

Supplementary material

13253_2017_284_MOESM1_ESM.pdf (621 kb)
Supplementary material 1 (pdf 621 KB)
13253_2017_284_MOESM2_ESM.r (1 kb)
Supplementary material 2 (R 1 KB)
13253_2017_284_MOESM3_ESM.txt (64 kb)
Supplementary material 3 (txt 63 KB)
13253_2017_284_MOESM4_ESM.r (36 kb)
Supplementary material 4 (R 36 KB)


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Copyright information

© International Biometric Society 2017

Authors and Affiliations

  • W. H. Bonat
    • 1
    • 2
    Email author
  • J. Olivero
    • 3
  • M. Grande-Vega
    • 4
    • 5
  • M. A. Farfán
    • 3
    • 6
  • J. E. Fa
    • 7
    • 8
  1. 1. Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark
  2. 2. Department of Statistics, Centro PolitécnicoParaná Federal UniversityCuritibaBrazil
  3. 3. Grupo de Biogeografía, Diversidad Y Conservación, Departamento de Biologia Animal, Facultad de CienciasUniversidad de MálagaMálagaSpain
  4. 4. Research Group for Sustainable Management Silvanet, Faculty of ForestryTechnical University of Madrid, Ciudad UniversitariaMadridSpain
  5. 5. Asociación EcotonoMadridSpain
  6. 6. BioGea ConsultoresMálagaSpain
  7. 7. Division of Biology and Conservation Ecology, School of Science and the EnvironmentManchester Metropolitan UniversityManchesterUK
  8. 8. Center for International Forestry Research (CIFOR), CIFOR HeadquartersBogorIndonesia

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