Ricardo Carrizo Vergara (Station Ornithologique Suisse)
We introduce the evolving categories multinomial (ECM) distribution for multivariate count data taken across time. This distribution is used to model the count of individuals following independently the same stochastic dynamics among categories, the categories themselves also evolving with time. The key parameters of this distribution are the path probabilities, which model the underlying between-categories movement. We specify the one-time and two-times marginal distributions and the first and second order moments. When the number of individuals is unknown, a Poisson assumption on it provides a new distribution (ECM-Poisson) which can be related to classical independent Poisson counts models and to the bivariate Poisson distribution. Likelihood computation is usually either intractable or impractical, so two special fitting methods are proposed for parameter estimation: replacing the likelihood by a multivariate Gaussian respecting mean and covariance, and pairwise composite likelihood. We show two application scenarios where this distribution can be used. The first, aimed for ecological applications, is the inference of movement parameters of individuals moving continuously in space-time with irregular survey regions, paying special attention on the parameters present in the space-time auto-correlation structure. The second, aimed for sociological applications, is the inference of vote transfer in two-rounds elections. We illustrate with simulation studies and with applications for inferring movement parameters of prairie-chickens and for estimating vote transfer in the 2021 Chilean presidential election.
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