结构方程模型及其在生态学中的应用

doi:10.3724/SP.J.1258.2011.00337

摘要/Abstract

摘要：

基于多变量统计方法同时研究自然系统内多个因子之间的相互关系, 是阐释复杂的自然系统的一个重要手段。相比传统的多变量统计法, 结构方程模型基于研究者的先验知识预先设定系统内因子间的依赖关系, 不仅能够判别各因子之间的关系强度(路径系数), 还能对整体模型进行拟合和判断, 从而能更全面地了解自然系统。由于结构方程模型只在近年才被应用到生态学的数据分析中, 因此该文试图对其作一简略介绍, 包括结构方程模型的定义和变量类型, 结合事例研究展现结构方程模型分析的一般步骤、在生态学中的应用以及相关软件的介绍等。望能为相关研究人员提供直观的认识, 加强结构方程模型在生态学数据分析中的应用。

关键词: 生物复杂性, 因子分析, 多变量统计, 路径分析, 结构方程模型

Abstract:

Natural systems are essentially complex. In most cases, fully understanding natural systems requires the capacity to examine simultaneous influences and responses among multiple interacting factors. Compared with traditional multivariate methods, structural equation model (SEM) could specify the causal or dependent relationships among variables using the prior knowledge of researchers before conducting relevant experiments, i.e. initial models. SEM could not only identify the individual path coefficient for each relationship, but also estimate the whole model fit to determine whether to revise the initial models. We attempt to introduce SEM from the following aspects: definition and types of variables in SEM, detailed procedures for how to analyze data through SEM, some applications of SEM in ecology and recommended software. We encourage more researchers to apply SEM in ecological data analyses in order to improve understanding of natural systems and advance the field of ecology.

Key words: biocomplexity, factor analysis, multivariate statistics, path analysis, structural equation model

王酉石, 储诚进. 结构方程模型及其在生态学中的应用. 植物生态学报, 2011, 35(3): 337-344. DOI: 10.3724/SP.J.1258.2011.00337

WANG You-Shi, CHU Cheng-Jin. A brief introduction of structural equation model and its application in ecology. Chinese Journal of Plant Ecology, 2011, 35(3): 337-344. DOI: 10.3724/SP.J.1258.2011.00337

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链接本文: https://www.plant-ecology.com/CN/10.3724/SP.J.1258.2011.00337

https://www.plant-ecology.com/CN/Y2011/V35/I3/337

图/表 5

图1 结构方程模型的图形表示形式, 涉及1个自变量(x1)和3个因变量(y1, y2和y3)。其中γ (γ11, γ21和γ31)表示的是变量x对变量y的影响, β (β21和β32)表示的是变量y之间的影响, ξ表示响应变量的残差(改自Grace, 2006)。

Fig. 1 The generic graph demonstration of structural equation model, which involves one independent variable (x1) and three dependent variables (y1, y2 and y3). γ (γ11, γ21 and γ31) represent the effects of x variable on y variables, and β (β21 and β32) represent the effects among y variables. The residual variances are denoted by ξ (Modified from Grace, 2006).

表1 结构方程模型与其他多变量统计方法的比较(改自Grace, 2006)

Table 1 Attribute comparisons of SEM with other multivariate methods (Modified from Grace, 2006)

	SEM	DA	RT	PCA	MR
包含判断模型拟合程度的测量 Includes measures of absolute model fit	√
预先假定变量间因果关系 User can specify majority of relationships	√
包含隐变量 Includes latent variables	√			√
处理测量误差 Address measurement error	√
进行模型整体评价 Allows evaluation of alternative models	√				√
探讨系统内多个变量间关系 Examines networks of relationships	√
模型构建 Model building	√	√	√	√	√

图2 结构方程模型中不同箭头类型和不同变量类型图示。a-g, 观察变量; I-L, 隐变量; M, 综合变量。ξ项表示隐变量上无法明确来源的效应, 而δ和ε表示观察变量上无法明确来源的效应。(改自Grace, 2006)

Fig. 2 The generic demonstration for the types of arrows and variables used in structural equation model. a-g: observed variables; I-L: latent variables; M: composite variable. The ξ terms refer to variables that represent unspecified effects on dependent latent variables, while δ and ε are variables that represent unspecified effects on observed variables. (Modified from Grace, 2006)

图3 隐变量a与综合变量b的区别。(改自Grace, 2006)

Fig. 3 The difference between latent variable (a) and composite variable (b). (Modified from Grace, 2006)

图4 两种跳甲防治乳浆大戟入侵的事例研究。上图为初始模型, 下图为修正后的模型。(改自Larson & Grace, 2004)

Fig. 4 The bio-control of two flea beetle species (Aphthona lacertosa and A. nigriscutis) on invasive species leafy spurge (Euphorbia esula). The upper panel is for the initial model and the lower for the revised model. (Modified from Larson & Grace, 2004)

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