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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (5): 525-534.doi: 10.3969/j.issn.1005-3085.2019.05.004

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混合广义线性模型的统计推断

袁巧莉1,2,  吴刘仓1,  戴  琳1   

  1. 1- 昆明理工大学理学院，昆明  650093
    2- 重庆工程学院通识学院，重庆  400056
  • 收稿日期:2017-06-19 接受日期:2018-05-07 出版日期:2019-10-15 发布日期:2019-12-15
  • 基金资助:
    国家自然科学基金(11861041; 11261025)；重庆工程学院科研基金(2019XZKY03).

Statistical Inference of Mixture of Generalized Linear Models

YUAN Qiao-li1,2,  WU Liu-cang1,  DAI Lin1   

  1. 1- Faculty of Science, Kunming University of Science and Technology, Kunming 650093
    2- College of General Education, Chongqing Institute of Engineering, Chongqing 400056
  • Received:2017-06-19 Accepted:2018-05-07 Online:2019-10-15 Published:2019-12-15
  • Supported by:
    The National Natural Science Foundation of China (11861041; 11261025); the Science Foundation of Chongqing Institute of Engineering (2019XZKY03).

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摘要： 为了更好地拟合实际数据，本文提出了混合广义线性模型并进行参数估计．首先，基于异质总体的一阶矩以及二阶矩存在的条件下，运用混合广义线性模型对子总体的均值进行建模，构造扩展拟似然和伪似然函数，然后利用 EM 算法对均值参数、散度以及混合比例进行估计，并通过 Monte Carlo 模拟验证所提出的模型参数估计方法的有效性．最后，实例研究的结果表明本文的模型和方法是科学实用的．

关键词: 混合广义线性模型, 扩展拟似然, 伪似然, EM 算法

Abstract: In this paper, a mixture of generalized linear model is proposed and the parameter estimation to fit the practical data is performed. Firstly, based on the existence of the first, second order moments of a heterogeneous population, the mixture of generalized linear models is applied to establish the mean model in the subpopulation, and the extended quasi-likelihood and pseudo-likelihood functions are constructed. Moreover, by using EM algorithm, the mean parameter, dispersion and mixing ratio are estimated, and Monte Carlo simulation studies are indicated the effectiveness. Finally, a real example illustrates that the model and method is scientific and useful.

Key words: mixture of generalized linear models, extended quasi-likelihood, pseudo-likelihood, EM algorithm

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