  We 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. To specify the joint covariance matrix for the
multivariate response vector the generalized Kronecker product is employed. The
count nature of the data is taken into account 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 dataset consisting of prey animals (the
main hunted species, the blue duiker \textit{Philantomba monticola} and other
taxa) shot or snared for bushmeat by $52$ commercial hunters over a $33$-month
period in Pico Basil\'e, 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.
