Using Structural Equation Modeling to Analyze Monitoring Data

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Using Structural Equation Modeling to Analyze
Monitoring Data

• Jim Grace
• NWRC

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What is structural equation modeling?
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The Origin of Structural Equation Modeling
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The Wright Idea
Y1 a1 ß1X e1i
Y2 a2 ß2X ß3Y1 e2i
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The LISREL Synthesis
Karl Jöreskog 1934 - present Key Synthesis paper-
1973
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LISREL A flexible, multiequational framework
y1 a1 ß1x e1i y2 a2 ß2x ß3y1
e2i y3 a3 ß4y1 ß5y2 e3i y4 a4 ß6y1
ß7y3 e4i
Can include observed, latent, and composite
variables.
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Estimation and Evaluation
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1. It is a model-oriented method, not a
null-hypothesis-oriented method.
Some Properties of SEM
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.
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1. Seeks to model uncertainty rather than
probabilities.
A Bit about the Bayesian Approach
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(?)
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Why do we need multivariate modeling?
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(No Transcript)
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Do the conventional methods meet your needs?
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How do data relate to learning?
realistic predictive models
multivariate descriptive statistics
multivariate data modeling
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)
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Example 1Theodore Roosevelt Natl. ParkWeed
Problem
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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. 29207-214
Larson et al. (2007) Biol. Ctl. 401-8.
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Based on the Available Data, What Have the
Beetles Been Doing?
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How Does Spurge Decline Relate to Beetle Density?
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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
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Results for 2000 - 2001
note raw correlation was r -.21
R2 0.61
A. nigriscutis 2001
A. nigriscutis 2000
Change in Stems 2000-2001
Number of Stems 2000
R2 0.42
note raw correlation was r -.40
A. lacertosa 2000
A. lacertosa 2001
R2 0.54
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Example 2 Coastal Prairie Vegetation and Soil
Properties
Summary of Community Characteristics using
Ordination
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Results from Stepwise Regression Analysis
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SEM model results
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Example 3 Evaluating Theories of Diversity
The Problem A variety of theories about
diversity lead to a similar set of bivariate
expectations
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Suspected Underlying Processes
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National Center for Ecological Analysis and
Synthesis Project
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Interpretations
recruitment
Species Richness
Species Lost
extinction
Local Species Pool
mortality
filtering
Abiotic Conditions
Disturbance
niche complementarity
competitive exclusion
stress
damage
production
Biomass
biomass loss
Biomass Removed
Net Photosyn.
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Collaborative Applications of Multivariate
Modeling

• 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)

• 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