On Hinde–Demétrio regression models for overdispersed count data

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• 作者：Cé ; lestin C. Kokonendji ; Clarice G.B. Demé ; trio ; Silvio S. Zocchi
• 关键词：Additive exponential dispersion model ; Compound Poisson ; Generalized linear model ; Model selection ; Unit variance function ; Zero-inflation
• 刊名：Statistical Methodology
• 出版年：2007
• 出版时间：July 2007
• 年：2007
• 卷：4
• 期：3
• 页码：277-291
• 全文大小：396 K

文摘

We introduce the Hinde–Demétrio (HD) regression models in order to analyze overdispersed count data. We mainly investigate the effect of the dispersion parameter. The HD distributions are discrete additive exponential dispersion models (depending on canonical and dispersion parameters) with a third real index parameter coration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B7CRS-4MHPBWD-2&_mathId=mml43&_user=3986987&_cdi=18002&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=c7d82a7f13ba52fd52c524e5c1a167e1"" title=""Click to view the MathML source"">p. They have been characterized by the unit variance function coration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B7CRS-4MHPBWD-2&_mathId=mml44&_user=3986987&_cdi=18002&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=bdbb1e709406a46e3faac247d2bef756"" title=""Click to view the MathML source"">;c;+;c;^p. For coration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B7CRS-4MHPBWD-2&_mathId=mml45&_user=3986987&_cdi=18002&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=9db2a8618cdfe3a839caae5a17922605"" title=""Click to view the MathML source"">p equal to 2, 3, …, the corresponding distributions are concentrated on non-negative integers, overdispersed and zero-inflated with respect to a Poisson distribution having the same mean. The negative binomial (coration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B7CRS-4MHPBWD-2&_mathId=mml46&_user=3986987&_cdi=18002&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=269d62593a0e53a9f7cc61c4434cbf0f"" title=""Click to view the MathML source"">p=2), strict arcsine (coration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B7CRS-4MHPBWD-2&_mathId=mml47&_user=3986987&_cdi=18002&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=2975005f9a884e278fe805d338acf415"" title=""Click to view the MathML source"">p=3) and Poisson (coration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B7CRS-4MHPBWD-2&_mathId=mml48&_user=3986987&_cdi=18002&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=8316f8347bedbfa7b1310d475977d530"" title=""Click to view the MathML source"">p→∞) distributions are particular count HD families. In a generalized linear modelling framework, the effect of the dispersion parameter in the HD regression models is, among other things, pointed out through the two parametrizations for the mean: unit and standard means. In this particular additive model, this effect must be negligible within an adequate HD model for fixed coration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B7CRS-4MHPBWD-2&_mathId=mml49&_user=3986987&_cdi=18002&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=3a42d1e5e8781ba9f2ccc5eb09fc18c2"" title=""Click to view the MathML source"">p. The estimation of the integer coration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B7CRS-4MHPBWD-2&_mathId=mml50&_user=3986987&_cdi=18002&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=6bb04a207c89768218952a1bc3d6d714"" title=""Click to view the MathML source"">p is also examined separately. The results are illustrated and discussed on a horticultural data set.