﻿ 模型选择与模型平均在Meta分析中的应用研究 The Application Research of Model Selection and Model Averaging in Meta-Analysis

Open Journal of Nature Science
Vol.03 No.03(2015), Article ID:15926,8 pages
10.12677/OJNS.2015.33011

The Application Research of Model Selection and Model Averaging in Meta-Analysis

Xiaoxiao Yin

School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming Yunnan

Email: yinxiaoxiao2011@163.com

Received: Jul. 27th, 2015; accepted: Aug. 14th, 2015; published: Aug. 21st, 2015

ABSTRACT

Model selection and model averaging have been the important issues which are researched by statistics and economic circles. This paper relies on theories and methods of Meta-analysis and takes the analysis of factors influencing legumes-rhizobium mutualism cooperative systems as an example. Then, the application results of model selection and model averaging method in meta- analysis are compared. The results show that model averaging method can be applied to meta- analysis and its performance is better than model selection.

Keywords:Meta-Analysis, Model Selection, Model Averaging

Email: yinxiaoxiao2011@163.com

1. 引言

2. 研究背景

3. 研究方法介绍

3.1. 模型选择(Model Selection)

(1)

(2)

3.2. 模型平均(Model Averaging)

(4)

Mallow准则[6] 最初是在2007年由Hansen提出的，他通过极小化Mallow’准则构建了最小二乘模型平均估计。具体过程为：

(5)

(6)

3.3. Meta-Analysis

，其中为第i个研究的统计量，期望

，则随机效应Meta回归模型为

4. 模型选择与模型平均在Meta分析中的应用实例分析

4.1. 资料来源

4.2. 模型选择分析

Model1:metareglnorX3X4X1*X4 X1*X5 X3*X4,wsse (selnor);

Model2:metareglnorX3X4X5 X1*X4 X1*X5 X3*X4,wsse (selnor);

Model3:metareglnorX2 X3X4X1*X4 X3*X4,wsse (selnor);

Model4:metareglnorX3X4X1*X4 X1*X5 X3*X4,wsse (selnor);

Model5:metareglnorX3X4X5X1*X4 X3*X4,wsse (selnor);

… … …

Model51:metareglnorX3X4X5X1*X3X1*X4,wsse(selnor)。

4.3. 模型平均分析

Model2:metareglnorX3X4X5 X1*X4 X1*X5 X3*X4,wsse (selnor);

Model3:metareglnorX2 X3X4X1*X4 X3*X4,wsse (selnor);

Model4:metareglnorX3X4X1*X4 X1*X5 X3*X4,wsse (selnor);

Model5:metareglnorX3X4X5X1*X4 X3*X4,wsse (selnor);

Model9:metareglnorX3X4X1*X4 X3*X4,wsse (selnor);

Table 1. Akaike Information Criterion of every model

Table 2. The weight of Smoothed Akaike Information Criterion

4.4. 模型选择与模型平均法所得结果的比较

5. 结论

(1) 本文基于Meta分析，整合了豆科植物–根瘤菌互利共生系统的相关研究，建立了许多Meta回归模型。基于所建立的Meta回归模型，我们分别采用模型选择和模型平均方法对豆科植物–根瘤菌互利共生系统影响因素的分析模型进行确定。结果表明：模型平均方法得到的组合分析模型，详细的解释了豆科植物–根瘤菌互利共生合作系统的主要影响因素有X2、X3、X4、X5、X1*X4、X3*X4、X1*X5、X1、X1*X3、X3*X5、X4*X5等，此外，根据每个模型所占的权重，发现X4、X3、X1*X4以及X3*X4这四个因素的影响作用最大。而通过模型选择，得到X3、X4、X5、X1*X4、X1*X5以及X3*X4是该合作系统的影响因素。模型选择得到的模型中没出现的变量并不能说明其对合作系统没有影响，模型平均方法弥补了这一缺陷。

(2) 事实上，线性回归中，模型平均方法的分析效果往往优于模型选择，经本文研究发现：模型选择与模型平均方法除了应用于线性回归中之外，也均可应用于Meta分析中，而且模型平均的分析效果优于模型选择，这和线性回归的结论是一致的。因此，未来可将模型平均广泛的应用于统计学以及其他领域。

The Application Research of Model Selection and Model Averaging in Meta-Analysis[J]. 自然科学, 2015, 03(03): 81-88. http://dx.doi.org/10.12677/OJNS.2015.33011

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