I want to estimate a structural equation model using lavaan in R with a categorical mediator. A wrinkle is that three of the exogenous variables are linearly dependent. However, this shouldn't be a problem since I'm using the categorical mediator to achieve identification a la Judea Pearl's front-door criterion. That is, mathematically each particular equation is identified (see the R code below).
With lavaan in R I can obtain estimates when the mediator is numeric, but not when it is categorical. With a categorical mediator I obtain the following error:
Error in lav_samplestats_step1(Y = Data, ov.names = ov.names, ov.types = ov.types,
: lavaan ERROR: linear regression failed for y; X may not be of full rank in group 1
Any advice on how to obtain estimates with a categorical mediator using lavaan?
Code:
# simulating the dataset
set.seed(1234) # seed for replication
x1 <- rep(seq(1:4), 100) # variable 1
x2 <- rep(1:4, each=100) # variable 2
x3 <- x2 - x1 + 4 # linear dependence
m <- sample(0:1, size = 400, replace = TRUE) # mediator
df <- data.frame(cbind(x1,x2,x3,m)) # dataframe
df$y <- 6.5 + x1*(0.5) + x2*(0.2) + m*(-0.4) + x3*(-1) + rnorm(400, 0, 1) # outcome
# structural equation model using pearl's front-door criterion
sem.formula <- 'y ~ 1 + x1 + x2 + m
m ~ 1 + x3'
# continuous mediator: works!
fit <- lavaan::sem(sem.formula, data=df, estimator="WLSMV",
se="none", control=list(iter.max=500))
# categorical mediator: doesn't work
fit <- lavaan::sem(sem.formula, data=df, estimator="WLSMV",
se="none", control=list(iter.max=500),
ordered = "m")
