customizing interaction terms

library(modsem)
#> This is modsem (1.0.11). Please report any bugs!

By default, modsem() creates product indicators for you based on the interaction specified in your model. Behind the scenes, modsem() generates a total of 9 variables (product indicators) that are used as the indicators for your latent product.

m1 <- '
# Outer Model
X =~ x1 + x2 + x3
Y =~ y1 + y2 + y3
Z =~ z1 + z2 + z3

# Inner model
Y ~ X + Z + X:Z 
'

est1 <- modsem(m1, oneInt)
cat(est1$syntax)

While this is often sufficient, you might want more control over how these indicators are created. In general, modsem() offers two mechanisms for controlling the creation of product indicators: 1. By specifying the measurement model for your latent product yourself. 2. By using the mean() and sum() functions, collectively known as parceling operations.

Specifying the Measurement Model

By default, modsem() creates all possible combinations of product indicators. However, another common approach is to match the indicators by order. For example, let’s say you have an interaction between the latent variables X and Z: X =~ x1 + x2 and Z =~ z1 + z2. By default, you would get XZ =~ x1z1 + x1z2 + x2z1 + x2z2. If you prefer to use the matching approach, you would expect XZ =~ x1z1 + x2z2 instead. To achieve this, you can use the match = TRUE argument.

m2 <- '
# Outer Model
X =~ x1 + x2
Y =~ y1 + y2
Z =~ z1 + z2

# Inner model
Y ~ X + Z + X:Z 
'

est2 <- modsem(m2, oneInt, match = TRUE)
summary(est2)

More Complicated Models

If you want even more control, you can use the get_pi_syntax() and get_pi_data() functions to extract the modified syntax and data from modsem(), allowing you to modify them as needed. This can be particularly useful in cases where you want to estimate a model using a feature in lavaan that isn’t available in modsem().

For example, the syntax for ordered and multigroup models (as of now) isn’t as flexible in modsem() as it is in lavaan. You can modify the auto-generated syntax (along with the altered dataset) from modsem() to suit your needs.

m3 <- '
# Outer Model
X =~ x1 + x2 + x3
Y =~ y1 + y2 + y3
Z =~ z1 + z2 + z3

# Inner model
Y ~ X + Z + X:Z 
'
syntax <- get_pi_syntax(m3)
cat(syntax)
data <- get_pi_data(m3, oneInt)
head(data)

The generated syntax and data can then be used to estimate a model using lavaan, giving the user more control over arguments passed onto lavaan::sem(), and potentially the ability to modify the the generated syntax and data.

library(lavaan)
fit <- sem(syntax, data = data, fixed.x = FALSE, 
           std.lv = TRUE, auto.fix.first = TRUE, 
           auto.var = TRUE, auto.cov.lv.x = TRUE)
summary(fit)