On estimation of the Poisson parameter in zero-modified Poisson models
On estimation of the Poisson parameter in zero-modified Poisson models
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DOI：
10.1016/s0167-9473(99)00111-5
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发表时间：
2000-10-28
影响因子：
1.8
通讯作者：
Böhning, D
中科院分区：
文献类型：
--
作者：
Dietz, E;Böhning, D
对于计数数据，通常假设泊松模型。然而，在各种应用中已经观察到该模型不适合，因为数据中的零太少或太多。对于后者的情况下，零膨胀泊松（回归）模型已被提出。在某些情况下，由于某些原因，根本没有零可以观察到，零截断泊松（回归）模型是适当的。本文提供了一个EM算法的ML估计后一个模型的标准软件泊松回归。它示出，该算法也可以用来估计零膨胀，零收缩，和标准泊松模型的泊松参数，当零观测值被忽略。如果对零修正的种类一无所知，则相应的估计是完全有效的。描述的情况下，其中的效率损失是小的，虽然知识的零修改的种类是可用的。在第二步骤中，可以使用泊松参数的相应估计来分析零修改的种类并估计零修改参数。(C)2000 Elsevier Science B.V.保留所有权利。
For count data, typically, a Poisson model is assumed. However, it has been observed in various applications that this model does not fit, because of too few or too many zeros in the data. For the latter case the zero-inflated Poisson (regression) model has been proposed. In situations where, for certain reasons, no zeros at all can be observed, the zero-truncated Poisson (regression) model is appropriate. This paper provides an EM algorithm for ML estimation of the latter model by standard software for Poisson regression. It is shown, that this algorithm can be used also to estimate the Poisson parameters of zero-inflated, zero-deflated, and standard Poisson models, when the zero observations are ignored. If nothing is known about the kind of zero modification, the respective estimates are fully efficient. Situations are described, in which the loss of efficiency is small although knowledge of the kind of zero modification is available. In a second step, the respective estimates of the Poisson parameter can be used to analyze the kind of zero modification and to estimate the zero modification parameter. (C) 2000 Elsevier Science B.V. All rights reserved.