A brief introduction of structural equation model and its application in ecology

doi:10.3724/SP.J.1258.2011.00337

Abstract

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

WANG You-Shi, CHU Cheng-Jin. A brief introduction of structural equation model and its application in ecology[J]. Chin J Plant Ecol, 2011, 35(3): 337-344.

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URL: https://www.plant-ecology.com/EN/10.3724/SP.J.1258.2011.00337

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

Figures/Tables 5

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).

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	√	√	√	√	√

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)

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

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)

References 35

[1]	Akaike H (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control AC, 19, 716-723. DOI URL
[2]	Blalock HM (1964). Causal Inferences in Nonexperimental Research. University of North Carolina Press, Chapel Hill, NC, USA.
[3]	Bollen KA (1984). Multiple indicators: internal consistency or no necessary relationship. Quality and Quantity, 18, 377-385.
[4]	Bollen KA (1989). Structural Equations with Latent Variables. John Wiley & Sons, New York).
[5]	Byrne BM (2001). Structural Equation Modeling with AMOS. Lawrence Erlbaum Associates, Mahway, NJ.
[6]	Cherry JA, MeKee KL, Grace JB (2009). Elevated CO₂ enhances biological contributions to elevation change in coastal wetlands by offsetting stressors associated with sea-level rise. Journal of Ecology, 97, 67-77. DOI URL
[7]	Clark JS (2007). Models for Ecological Data: An Introduction. Princeton University Press, Princeton, NJ, USA.
[8]	Dietze MC, Wolosin MS, Clark JS (2008). Capturing diversity and interspecific variability in allometries: a hierarchical approach. Forest Ecology and Management, 256, 1939-1948. DOI URL
[9]	Fornell C (1982). A Second Generation of Multivariate Analyses: Volumes I. and II. Praeger Publishers, New York, USA.
[10]	Fox J (2006). Structural equation modeling with the sem package in R. Structural Equation Modeling, 13, 465-486. DOI URL
[11]	Grace JB (1999). The factors controlling species density in herbaceous plant communities: an assessment. Perspec- tives in Plant Ecology, Evolution and Systematics, 2, 1-28.
[12]	Grace JB (2001). The roles of community biomass and species pools in the regulation of plant diversity. Oikos, 92, 191-207.
[13]	Grace JB (2006). Structural Equation Modeling and Natural Systems. Cambridge University Press, Cambridge, UK.
[14]	Grace JB, Allain LK, Allen C (2000). Factors associated with plant species richness in a coastal tall-grass prairie. Journal of Vegetation Science, 11, 443-452. DOI URL
[15]	Grace JB, Anderson TM, Smith MD, Seabloom E, Andelman SJ, Meche G, Weiher E, Allain LK, Jutila H, Sankaran M, Knops J, Ritchie M, Willig MR (2007). Does species diversity limit productivity in natural grassland communities? Ecology Letters, 10, 680-689. DOI URL PMID
[16]	Heise DR (1972). Employing nominal variables, induced variables, and block variables in path analysis. Sociological Methods and Research, 1, 147-173. DOI URL
[17]	Iriondo JM, Albert MJ, Escudero A (2003). Structural equation modelling: an alternative for assessing causal relationships in threatened plant populations. Biological Conservation, 113, 367-377. DOI URL
[18]	Jöreskog KG (1973). A general method for estimating a linear structural equation system. In: Goldberger AS, Duncan OD eds. Structural Equation Models in the Social Sciences. Seminar Press New York.
[19]	Jonsson M, Wardle DA (2010). Structural equation modelling reveals plant-community drivers of carbon storage in boreal forest ecosystems. Biology Letters, 6, 116-119. DOI URL PMID
[20]	Lamb EG, Cahill JF (2008). When competition does not matter: grassland diversity and community composition. The American Naturalist, 171, 777-787. DOI URL PMID
[21]	Lamb EG, Kembel SW, Cahill JF (2009). Shoot, but not root, competition reduces community diversity in experimental mesocosms. Journal of Ecology, 97, 155-163. DOI URL
[22]	Larson DL, Grace JB (2004). Temporal dynamics of leafy spurge (Euphorbia esula) and two species of flea beetles (Aphthona spp.) used as biological control agents. Biological Control, 29, 207-214. DOI URL
[23]	Laughlin DC, Abella SR, Covington WW, Grace JB (2007). Species richness and soil properties in Pinus ponderosa forests: a structural equation modelling analysis. Journal of Vegetation Science, 18, 231-242. DOI URL
[24]	Lee SY (2007). Structural Equation Modeling: A Bayesian Approach. John Wiley & Sons, New York, USA.
[25]	Miao SL, Carstenn S, Nungesser M (2009). Real World Ecology: Large-scale and Long-term Case Studies and Methods. Springer, New York, USA.
[26]	Muthén LK, Muthén BO (2004). Mplus User’s Guide 3rd edn. Muthén and Muthén, Los Angeles, CA.
[27]	Raftery AE (1993). Bayesian model selection in structural equation models. In: Bollen KA, Long JS eds. Testing Structural Equation Models. Sage Publishers Newbury park, CA.
[28]	Saura-Mas S, Shipley B, Lloret F (2009). Relationship between post-fire regeneration and leaf economics spectrum in Mediterranean woody species. Functional Ecology, 23, 103-110. DOI URL
[29]	Shipley B (2000). Cause and Correlation in Biology. Cambridge University Press, Cambridge, UK.
[30]	Shipley B, Lechowicz MJ, Wright I, Reich P (2006). Fundamental trade-offs generating the worldwide leaf economics spectrum. Ecology, 87, 535-541. DOI URL PMID
[31]	Spitale D, Petraglia A, Tomaselli M (2009). Structural equation modelling detects unexpected differences between bryophyte and vascular plant richness along multiple environmental gradients. Journal of Biogeography, 36, 745-755. DOI URL
[32]	Weiher E, Forbes S, Schauwecker T, Grace JB (2004). Multivariate control of plant species richness in a blackland prairie. Oikos, 106, 151-157. DOI URL
[33]	Wright S (1918). On the nature of size factors. Genetics, 3, 367-374. URL PMID
[34]	Wright S (1920). The relative importance of heredity and environment in determining the piebald pattern of guinea pigs. Proceedings of the National Academy of Sciences of the United States of America, 6, 320-332. DOI URL PMID
[35]	Wright S (1921). Correlation and causation. Journal of Agricultural Research, 10, 557-585.