Ayala-Godoy, Jairo A.

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    Modelos lineales generalizados mixtos con distribución binomial negativa
    (2011-08) Ayala-Godoy, Jairo A.; Macchiavelli, Raúl E.; College of Arts and Sciences - Sciences; Acuña Fernández, Edgar; Lorenzo González, Edgardo; Department of Mathematics; Santiago, Wilma
    The generalized linear mixed model (MLGM) is a widely used model with random effects. It is a good alternative to traditional linear mixed models if the Normal distribution assumption is not satisfied. In this work we study some properties of generalized linear mixed models when the conditional distribution of observations is Negative Binomial and the random effects distribution is normal. We compare these properties with those of generalized linear mixed models with conditional Poisson distribution. The Negative Binomial distribution has been widely used to model counts, and it is the standard alternative for overdispersed Poisson counts. For repeated measurements and other correlated data, GLMMs using negative binomial distribution can be very useful to model counts, accounting for possible correlations and for overdispersion. We study some properties of this model, such as the induced marginal distribution, its moments, and the relationship between the conditional distributions defining the model and the induced marginal distribution. Many of these properties are studied using simulations in R and SAS, since they are analytically intractable. Finally, we apply these models to a real problem based on the findings in a study of counts of seeds collected in traps in the dry forest of Guanica (Puerto Rico) between 2006 and 2008 under different treatments.