In this paper, we present an extension of the Poisson Zero-Modified model with Normal and Generalized Log-Gamma random effects. The random effect induces correlation and accommodate the intrinsic variability of each individual. The Generalized Log-Gamma effect is a generalized Normal effect and can be used in atypical situations where the Normal effect is not appropriate. In particular, the mixed Zero-Modified Poisson model allows us to deal with longitudinal count data, without requiring any previous knowledge about data characteristics, mainly to the number of zero observations (zero-inflated or zero-deflated). We consider the maximum likelihood approach to estimate the model parameters. A simulation study is presented to evaluate the estimators' performance. A real data set referring to the number of notification of infant deaths in the municipalities of the state of Bahia/Brazil is analyzed. The results revealed the Generalized Log-Gamma effect seems to be more appropriate to model this longitudinal data set.

在本文中，我们提出了具有正态和广义对数伽玛随机效应的泊松零修正模型的扩展。随机效应引起相关性并适应每个人的内在可变性。Generalized Log-Gamma 效应是一种广义 Normal 效应，可用于 Normal 效应不合适的非典型情况。特别是，混合零修正泊松模型允许我们处理纵向计数数据，而不需要任何关于数据特征的先前知识，主要是零观测的数量（零膨胀或零收缩）。我们考虑最大似然法来估计模型参数。提出了一个模拟研究来评估估计器的性能。分析了涉及巴伊亚州/巴西各市的婴儿死亡通知数量的真实数据集。结果表明，广义对数伽玛效应似乎更适合对这个纵向数据集进行建模。