# Presentation: 071929

## Using Structural Equation Modeling to Analyze Monitoring Data

**Using Structural Equation Modeling to Analyze Monitoring Data**

**Jim Grace**
**NWRC **

## What is structural equation modeling?

## The Origin of Structural Equation Modeling

## The Wright Idea

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## The LISREL Synthesis

**Karl J****ö****reskog**
**1934 - present**
**Key Synthesis paper- 1973**

## LISREL: A flexible, multiequational framework

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**Can include **_**observed**_**, **_**latent**_**, and **_**composite**_** variables.**

## Estimation and Evaluation

**Estimation and Evaluation**

## 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.**

## 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(?)**

## Why do we need multivariate modeling?

## Slide 11

## Do the conventional methods meet your needs?

## How do data relate to learning?

**Understanding of Processes**

**univariate descriptive statistics**

**exploration, methodology and theory development**

**realistic predictive models**

**abstract models**

**multivariate descriptive statistics**

**more detailed theoretical models**

**univariate data modeling**

**multivariate data modeling**

**Data**

- SEM

## Example #1:Theodore Roosevelt Natl. ParkWeed Problem

- Example #1:Theodore Roosevelt Natl. ParkWeed Problem

## The Use of Biocontrol Insects On Leafy Spurge

**Larson & Grace (2004) Biol. Ctl. 29:207-214; Larson et al. (2007) Biol. Ctl. 40:1-8.**

_**spurge flea beetles**_
*Aphthona nigriscutus*
*Aphthona lacertosa*

**- beetles released**
**  ****since 1989**

**- data collected **
**  ****since 1999**

## Based on the Available Data, 

- Based on the Available Data,
- What Have the Beetles Been Doing?

## How Does Spurge Decline Relate to Beetle Density?

## Multivariate View: Hypothesized Model

***A. lacertosa***
**2001**

**Number of**
**Stems**
**2000**

***A. nigriscutis***
**2000**

***A. lacertosa***
**2000**

***A. nigriscutis***
**2001**

**Change in**
**Stems**
**2000-2001**

## Results for 2000 - 2001

**Stems**
**2000-2001**

***A. nigriscutis***
**2001**

**Number of**
**Stems**
**2000**

***A. nigriscutis***
**2000**

***A. lacertosa***
**2001**

***A. lacertosa***
**2000**

**R****2**** = 0.54**

**R****2**** = 0.61**

**R****2**** = 0.42**

**Results for 2000 - 2001**

**note: raw**
**correlation**
**was *****r***** = -.21**

**note: raw**
**correlation**
**was *****r***** = -.40**

## Example #2: Coastal Prairie Vegetation and Soil Properties

**Example #2: ****Coastal Prairie Vegetation and Soil Properties**

**Summary of Community**
**Characteristics using Ordination**

## Results from Stepwise Regression Analysis

**Results from Stepwise Regression Analysis**

## SEM model results

## Example #3:

**A variety of theories**
**about diversity**
**lead to a similar set**
**of bivariate **
**expectations**

- Evaluating
- Theories of
- Diversity

## Suspected  Underlying Processes

## National Center for Ecological Analysis and Synthesis Project

## Interpretations

**Abiotic**
**Conditions**

**stress**

**filtering**

**Disturbance**

**damage**

**mortality**

**recruitment**

**extinction**

**Species**
**Richness**

**Species**
**Lost**

**Local Species**
**Pool**

**Biomass**

**production**

**biomass loss**

**Biomass**
**Removed**

**Net**
**Photosyn.**

**niche**
**complementarity**

**competitive exclusion**

## 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**