# How to Simulate Data for a SEM Model with Moderation Effect Using R?

I'm working on a project where I need to simulate data for a Structural Equation Model (SEM) that includes a moderation effect. Specifically, I have three latent variables: an independent variable (IV), a moderator (MOD), and a dependent variable (DV). I need to model the interaction between IV and MOD and assess its effect on DV.

I plan to use the lavaan package in R for fitting the model but need guidance on how to properly generate the data including the moderation effect. I have some familiarity with using the simsem package for data simulation but am unsure of the best approach to correctly specify the model and generate the interaction terms.

I added a sample model. simulateData creates new variable like iva1:mod1 which is not the product of iva1 and mod1:

model_test <- "
# Measurement model for independent variable A (IVA)
iva =~ iva1 + iva2 + iva3

# Measurement model for independent variable B (IVB)
ivb =~ ivb1 + ivb2 + ivb3

# Measurement model for the moderator (MOD)
mod =~ mod1 + mod2 + mod3

# Interaction terms between IVA and MOD
mod_iva =~ iva1:mod1 + iva2:mod1 + iva3:mod1 +
iva1:mod2 + iva2:mod2 + iva3:mod2 +
iva1:mod3 + iva2:mod3 + iva3:mod3

# Interaction terms between IVB and MOD
mod_ivb =~ ivb1:mod1 + ivb2:mod1 + ivb3:mod1 +
ivb1:mod2 + ivb2:mod2 + ivb3:mod2 +
ivb1:mod3 + ivb2:mod3 + ivb3:mod3

# Measurement model for dependent variable (DV)
dv =~ dv1 + dv2 + dv3 + dv4

# Structural model: regression equations
dv ~ 0.5*iva + 0.4*ivb + -0.3*mod + -0.12*mod_iva + -0.17*mod_ivb

# Covariance between IVA and IVB
iva ~~ 0.54*ivb
"

result = simulateData(model_test, sample.nobs=300L)
$$$$

• How will you analyze the data? There are different approaches within lavaan. Commented May 29 at 21:16
• @JeremyMiles I added a sample model
– Iman
Commented May 29 at 21:38

That being said, if you want to use structural equation modeling it is safe to say that your envisioned data generation mechanism can be described using a directed acyclic graph of some sort. You can simulate arbitrarily complex data from such graphs using the simDAG R package. Full disclosure, I am the developer of that package. An alternative would be the simCausal R package.
The simulateData() function just calls MASS::mvrnorm() with the population model's implied covariance matrix. That treats each product term as a separate variable (which is nonsense) rather than a function of other variables. When you simulate any nonlinearity, you have to simulate from the data model, one component at a time (starting with the set of exogenous variables. @Denzo mentioned simDAG and simCausal packages. If you'd like to stick with the lavaan` ecosystem, I posted an example over 10 years ago on the lavaan forum: