How to get standardized coefficients of Monte Carlo method for indirect effects in lavaan/semTools?

Question

I've run a path analysis using semTools. I'm interested to test indirect effects. I would like to report the results based on Monte Carlo confidence interval. However, the code monteCarloCI(output, standardized = TRUE) is not able to generate standardized estimates of the coefficients because standardized = TRUE is only applicable to class lavaan, not lavaan.mi according to the semTools manual. I used the runMi function because I had multiply imputed datasets so I had lavaan.mi object.

I read this post How to use probe2WayMC() with fully standardized solution with semTools / Lavaan R packages?. The suggested solution was to standardize all variables to have SD = 1, and run the analysis again. The standardized estimates would then merely be effect sizes to report along side unstandardized estimates and their tests.

All variables in my model are observed (without latent variables), and continuous.

My question is - is this method applicable to getting standardized estimates of indirect effects using the Monte Carlo method as well? I'm only interested in getting the standardized estimates of indirect effects' coefficients, but it would be great if this method can be used to generate the standardized Monte Carlo confidence interval as well.

Updates: I've included a link to reproducible data and codes below. I got an error message even though I called library(semTools) before library(lavaan.mi). The error message is "Error in monteCarloCI(output, standardized = TRUE) : argument "expr" is missing, with no default".

Link to RDS imputed datasets: https://2ly.link/1yd2r

Codes (shortened version, I included more indirect effects in my codes but they are not the focus of the question so I left them out).

## load packages
library(semTools)
library(lavaan.mi)

## load imputed data
data3t.mi.1 <- readRDS("data3t.RDS")

## make the output of mice for the lavaan.mi function to work 
data3t.mi.1 <- NULL
for(i in 1:50) data3t.mi.1[[i]] <- mice::complete(data3t.mi, action=i, inc=FALSE)

## specify my model
model <- '
MRC_Ego_total ~ a1a * ECR_anxiety_average + a2a * ECR_avoidance_average
MRC_Altru_total ~ a1b * ECR_anxiety_average + a2b * ECR_avoidance_average
MRC_provide_total ~ a1c * ECR_anxiety_average + a2c * ECR_avoidance_average
MRC_recog_total ~ a1d * ECR_anxiety_average + a2d * ECR_avoidance_average
MRC_worthy_total ~ a1e * ECR_anxiety_average + a2e * ECR_avoidance_average

TABS_self_total_T ~ d1 * MRC_Ego_total + d3 * MRC_provide_total + d4 * MRC_recog_total
TABS_other_total_T ~ d2 * MRC_Altru_total + d5 * MRC_worthy_total

TABS_self_total_T ~ e1 * ECR_anxiety_average + e3 * ECR_avoidance_average
TABS_other_total_T ~ e2 * ECR_anxiety_average + e4 * ECR_avoidance_average

# outcomes
CBI_total ~ b1 * TABS_self_total_T + b3 * TABS_other_total_T + c1 * ECR_anxiety_average + c3 * ECR_avoidance_average
STSS_total ~ b2 * TABS_self_total_T + b4 * TABS_other_total_T + c2 * ECR_anxiety_average + c4 * ECR_avoidance_average

# variances of exogenous variables
ECR_anxiety_average ~~ v1 * ECR_anxiety_average
ECR_avoidance_average ~~ v2 * ECR_avoidance_average

# covariance of exogenous variables
ECR_anxiety_average ~~ cov1 * ECR_avoidance_average

# variances for endogenous variables (mediators & outcome variables)
MRC_Ego_total ~~ v3 * MRC_Ego_total
MRC_Altru_total ~~ v4 * MRC_Altru_total
MRC_provide_total ~~ v5 * MRC_provide_total
MRC_recog_total ~~ v6 * MRC_recog_total
MRC_worthy_total ~~ v7 * MRC_worthy_total
TABS_self_total_T ~~ v8 * TABS_self_total_T
TABS_other_total_T ~~ v9 * TABS_other_total_T
CBI_total ~~ v10 * CBI_total
STSS_total ~~ v11 * STSS_total

# covariance for endogenous variables (mediators & outcome variables)
MRC_Ego_total ~~ cov2 * MRC_Altru_total + cov3 * MRC_provide_total + cov4 * MRC_recog_total + cov5 * MRC_worthy_total
MRC_Altru_total ~~ cov6 * MRC_provide_total + cov7 * MRC_recog_total + cov8 * MRC_worthy_total
MRC_provide_total ~~ cov9 *MRC_recog_total + cov10 * MRC_worthy_total
MRC_recog_total ~~ cov11 * MRC_worthy_total
TABS_self_total_T ~~ cov12 * TABS_other_total_T
CBI_total ~~ cov13 * STSS_total

# indirect effects
indirect1 := a1a*d1*b1
indirect2 := a1a*d1*b2
indirect3 := a1b*d2*b3

# defined parameters
ECR_an_an := v1
ECR_av_av := v2
'

## the analysis ====
output <- lavaan.mi(model, data=data3t.mi.1, estimator = "MLM", se = "robust.huber.white")

## Monte Carlo CI
monteCarloCI(output, standardized = TRUE)

## the error message is:
Error in monteCarloCI(output2T, standardized = TRUE) : 
  argument "expr" is missing, with no default

## including "ECR_an_an := v1" and "ECR_av_av := v2" gives an error message. The error message is:
Error in chol.default(varcov) : 
  the leading minor of order 1 is not positive

Answer 1

The feature monteCarloCI(output, standardized = TRUE) is now available for lavaan.mi-class objects, but at the time of this post (24 June 2024), you need to install the development versions because the feature is not yet on CRAN. For future readers, the following CRAN versions will be sufficient:

• lavaan version $\ge$ 0.6-19
• lavaan.mi version $\ge$ 0.1, which is where I moved all multiple-imputation features. The runMI() function is now deprecated in semTools, so use the lavaan.mi() function in the new package instead.
• semTools version $\ge$ 0.6, for the monteCarloCI() function. Even though runMI() is deprecated, many of the same semTools functions still work with lavaan.mi-class objects from the new package, including compRelSEM(), fmi(), compareFit()

If those versions are not on CRAN when you read this, then you can install the development versions from GitHub:

remotes::install_github("yrosseel/lavaan")
remotes::install_github("TDJorgensen/lavaan.mi")
remotes::install_github("simsem/semTools/semTools")

Here is an arbitrary reprex to illustrate:

library(semTools)  # load semTools FIRST to prevent it
library(lavaan.mi) # from masking lavaan.mi functions

data(HS20imps) # import a list of 20 imputed data sets

## specify CFA model from lavaan's ?cfa help page
## with some labels to define an arbitrary parameter
HS.model <- '
  visual  =~ x1 + a*x2 + x3
  textual =~ x4 + b*x5 + x6
  speed   =~ x7 + c*x8 + x9

  # arbitrary, for illustration:
  abc := a*b*c
'
## fit model to 20 imputed data sets
fit <- cfa.mi(HS.model, data = HS20imps) 
monteCarloCI(fit)