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Using Structural Equation Modeling to Analyze Monitoring Data

Using Structural Equation Modeling to Analyze Monitoring Data. Jim Grace NWRC . 0. .26. lake, x 1. 1.00. Macrohabitat η c1. Diversity η e3. .75. .95. impound, x 2. rich, y 8. swale, x 3. .44. 0. ns. Microhabitat η c2. ns. vhit1, y 1. wlitr, y 5. .92. .80. 1.13. .59.

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Using Structural Equation Modeling to Analyze Monitoring Data

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  1. Using Structural Equation Modeling to Analyze Monitoring Data Jim Grace NWRC

  2. 0 .26 lake, x1 1.00 Macrohabitat ηc1 Diversity ηe3 .75 .95 impound, x2 rich, y8 swale, x3 .44 0 ns Microhabitat ηc2 ns vhit1, y1 wlitr, y5 .92 .80 1.13 .59 .64 vhit2, y2 Herbaceous ηe1 Litter ηe2 .77 litrd, y6 .90 herbl, y3 .98 litrc, y7 -.47 .81 herbc, y4 1.0 1.0 A framework for using statistical methods to ask complex questions of data. What is structural equation modeling?

  3. Sewell Wright 1897-1988 1st paper in: 1920 The Origin of Structural Equation Modeling

  4. X Y1 ε1i Y2 ε2i The Wright Idea Y1 = α1 + β1X + ε1i Y2 = α2 + β2X + β3Y1 + ε2i

  5. The LISREL Synthesis Karl Jöreskog 1934 - present Key Synthesis paper- 1973

  6. x = Λxξ + δ y = Λyη + ε η = α + Β η + Γξ + ζ The LISREL Equations Jöreskög 1973 LISREL: A flexible, multiequational framework y1 = α1 + β1x + ε1iy2 = α2 + β2x + β3y1 + ε2i y3 = α3 + β4y1 + β5y2 + ε3i y4 = α4 + β6y1 + β7y3 + ε4i Can include observed, latent, and composite variables.

  7. Observed Covariance Matrix Hypothesized Model { } + σ11 σ12 σ22 σ13 σ23 σ33 x1 y2 Σ = y1 estimation LS, ML, and BA compare Absolute Model Fit Parameter Estimates { } 1.3 .24.41 .01 9.7 12.3 S Implied Covariance Matrix = Estimation and Evaluation

  8. Some Properties of SEM 1. It is a “model-oriented” method, not a null-hypothesis-oriented method. 2. Highly flexible modeling toolbox. 3. Can be applied in either confirmatory (testing) or exploratory (model building) mode. 4. Variety of estimation approaches can be used, including likelihood and Bayesian.

  9. A Bit about the Bayesian Approach 1. Seeks to model uncertainty rather than probabilities. 2. Philosophically well suited for supporting decision making. 3. Popularity partly based on new algorithms that create great flexibility in modeling. 4. It's indeterminant solution procedure, contributes to some uncertainty about results for more complex models(?)

  10. Why do we need multivariate modeling?

  11. 73 variables 179 variables 129 variables

  12. All your great scientific ideas! ANOVA result you hope to get! Do the conventional methods meet your needs?

  13. How do data relate to learning? multivariate descriptive statistics multivariate data modeling realistic predictive models SEM univariate descriptive statistics univariate data modeling Data exploration, methodology and theory development abstract models more detailed theoretical models Understanding of Processes modified from Starfield and Bleloch (1991)

  14. Example #1:Theodore Roosevelt Natl. ParkWeed Problem

  15. The Use of Biocontrol Insects On Leafy Spurge spurge flea beetles Aphthona nigriscutus Aphthona lacertosa - beetles released since 1989 - data collected since 1999 Larson & Grace (2004) Biol. Ctl. 29:207-214; Larson et al. (2007) Biol. Ctl. 40:1-8.

  16. Spurge is in decline Based on the Available Data, What Have the Beetles Been Doing?

  17. Change in spurge density as a function of A. nigriscutis density Change in spurge density as a function of A. lacertosa density r = -0.21, p = 0.01 r = -0.40, p < 0.001 How Does Spurge Decline Relate to Beetle Density?

  18. Multivariate View: Hypothesized Model A. nigriscutis 2000 A. nigriscutis 2001 Number of Stems 2000 Change in Stems 2000-2001 A. lacertosa 2000 A. lacertosa 2001

  19. .57 .31 .51 .08 ns -.14 -.55 -.24 .17 .23 -.20 .66 Results for 2000 - 2001 note: raw correlation was r = -.21 R2 = 0.61 A. nigriscutis 2000 A. nigriscutis 2001 Number of Stems 2000 Change in Stems 2000-2001 R2 = 0.42 note: raw correlation was r = -.40 A. lacertosa 2000 A. lacertosa 2001 R2 = 0.54

  20. Axis 2 Axis 1 Example #2: Coastal Prairie Vegetation and Soil Properties Summary of Community Characteristics using Ordination

  21. elev .77 Ca Mg -.35 Mn Axis1 Zn K Axis2 P -.23 pH C N Results from Stepwise Regression Analysis

  22. elev ELEV .57 -.67 Ca AXIS1 .71 a1 Mg -.30 Mn MINRL R2 = .63 Zn -.23 K AXIS2 -.33 a2 P -.28 R2 = .09 pH HYDR C N SEM model results

  23. Example #3: Evaluating Theories of Diversity The Problem: A variety of theories about diversity lead to a similar set of bivariate expectations

  24. Hetero- geneity expansion of niche space facilitation of coexistence Species Richness Species Lost recruitment extinction Local Species Pool filtering mortality Abiotic Conditions Disturbance niche complementarity sampling effect competitive inhibition competitive exclusion stress damage production biomass loss Biomass Net Photosyn. Biomass Removed Suspected Underlying Processes

  25. Africa grassland Finnish meadows Indian tropical savanna Minn. prairie Miss. prairie Kansas prairie Louisiana prairie Texas grasslands Louisiana marsh1 Utah grassland Wisconsin prairie Louisiana marsh2 National Center for Ecological Analysis and Synthesis Project

  26. Interpretations recruitment Species Richness Species Lost extinction Local Species Pool mortality filtering Abiotic Conditions Disturbance niche complementarity competitive exclusion stress damage production biomass loss Biomass Net Photosyn. Biomass Removed

  27. Collaborative Applications of Multivariate Modeling • Syracuse Univ. • Rice Univ. • Univ. Houston • LSU • US Forest Service • Colorado State Univ. • Univ. California - Irving • Oregon State Univ. • Yale Univ. • Univ. Wisc. - Eau Claire • Univ. Connecticut • Univ. Newcastle - UK • Univ. Montpellier - France • USGS - Numerous units and individuals • Univ. California - Davis • Univ. Northern Arizona • Univ. North Carolina • Univ. Alabama • Univ. Minnesota • Nat. Ctr. Ecol. Analysis • Univ. New Mexico • Purdue Univ. • Univ. Texas - Arlington • Michigan State Univ. • Univ. Groenegen (The Netherlands)

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