Presented by Grace Charles to the Davis R Users' Group on May 15, 2015

1. An introduction to Structural
equation models using Lavaan
Grace Charles

2. Jim Grace at USGS has a great website that goes
through basics of SEMs
http://www.nwrc.usgs.gov/SEM/
Other tutorials
http://lavaan.ugent.be/tutorial/tutorial.pdf
http://jarrettbyrnes.info/ubc_sem/

3. Why SEMs?
• Good for testing complex hypotheses and
alternative hypotheses
– Typically involve multiple equations and represent
“network” hypotheses
• Can test direct and indirect interactions
between variables
• Variables can be both exogenous (predictors)
and endogenous (response)

4. Sample size (taken from Jim Grace)
• First, there are problems with any guidance on sample size.
• Second, simulations show we would really like to have huge
• sample sizes (see Model Evaluation module)
• People often talk about absolute sample sizes (e.g., 200
best, 100 OK, 50 minimal). But, it depends on model
complexity (and signal-to-noise ratios)
• (1) We would love to have 20 samples per parameter
(2) It would be helpful to have 10 samples per parameter
(3) We hope to have a minimum of at least 5 samples per
estimated parameter
(4) It is claimed that Bayesian estimates are stable with as
few as 2.5 samples per parameter.

5. Latent variables

6. Latent variables

7. What can you specify?
• Direct and indirect pathways
• “Latent” variables
• Covariance between variables (assumed for
regressions, have to specify otherwise)
• Other things not covered today: composite
variables, non-linear relationships, time series,
etc.

8. What does summary output actually
mean???
• This is actually a poor fit
• P-value represents the probability you will reject your null
hypothesis, but in this case the null hypothesis is that your
model is the right fit for your data. I would use
modindices(fit) to look for possible missing links.

9. What does summary output actually
mean???

10. Other possibilities
• Nonlinearities in data
• “Composite” variables
• Time Series
• Bayesian approaches
• Spatial autocorrelation