Is following method of testing SEM and Moderation Suitable in Lavaan?

[Harmanjit Singh]

Dear all,

If following approach for testing SEM and Moderation Suitable?

The main doubt is, should moderator variable be added in the structural model part, considering it is being tested in Parts 3 and 4 of the code?
If yes why, if not why?

# ==============================================================================
# PART 1: SETUP & LIBRARIES
# ==============================================================================
library(lavaan)
library(semTools)
library(readxl)

# Load Data
Fulldata <- read_excel("your_data_path.xlsx")

# --- DATA CLEANING ---
Fulldata <- na.omit(Fulldata)

# Convert Demographics to Numeric (Generic Labels)
Fulldata$C1 <- as.numeric(as.factor(Fulldata$Gender)) - 1
Fulldata$C2 <- as.numeric(as.factor(Fulldata$Occupation))
Fulldata$C3 <- as.numeric(as.factor(Fulldata$Education))
Fulldata$C4 <- as.numeric(as.factor(Fulldata$Income))
Fulldata$C5 <- as.numeric(Fulldata$Age)

# ==============================================================================
# PART 2: THE MAIN EFFECTS MODEL
# ==============================================================================
Model_Main <- '
  # Measurement Model
  IV_1           =~ AB1 + AB2 + AB3 
  IV_2           =~ CD1 + CD2 + CD3 
  IV_3           =~ EF1 + EF2 + EF3 
  IV_4           =~ GH1 + GH2 + GH3
  IV_5           =~ IJ1 + IJ2 + IJ3 
  IV_6           =~ KL1 + KL2 + KL3 
  Moderator      =~ MN1 + MN2 + MN3 
  Dependent_Var  =~ OP1 + OP2 + OP3 
 
  # Structural Model
  Dependent_Var ~ IV_1 + IV_2 + IV_3 + IV_4 +
                  IV_5 + IV_6 + Moderator +
                  C1 + C2 + C3 + C4 + C5
'

# Using MLM for robust estimation
fit_main <- sem(Model_Main, estimator="MLM", data=Fulldata, meanstructure=TRUE)

print("--- MAIN EFFECTS MODEL RESULTS ---")
summary(fit_main, fit.measures=TRUE, standardized=TRUE, rsquare=TRUE)
print(fitmeasures(fit_main, c("chisq.scaled","df.scaled","pvalue.scaled","tli.robust","cfi.robust","rmsea.robust","srmr")))

# ==============================================================================
# PART 3: AUTOMATED MODERATION ANALYSIS
# ==============================================================================

# 1. VARIABLE DICTIONARY
item_dict <- list(
  IV_1          = paste0("AB", 1:3),
  IV_2          = paste0("CD", 1:3),
  IV_3          = paste0("EF", 1:3),
  IV_4          = paste0("GH", 1:3),
  IV_5          = paste0("IJ", 1:3),
  IV_6          = paste0("KL", 1:3),
  Moderator     = paste0("MN", 1:3),
  Dependent_Var = paste0("OP", 1:3)
)

control_vars <- "C1 + C2 + C3 + C4 + C5"

# 2. MODERATION FUNCTION
run_moderation_robust <- function(df, iv_name, mod_name, dv_name) {
 
  iv_items  <- item_dict[[iv_name]]
  mod_items <- item_dict[[mod_name]]
  dv_items  <- item_dict[[dv_name]]
 
  # Calculate Mean Scores and Center for Interaction
  iv_score      <- rowMeans(df[, iv_items], na.rm = TRUE)
  mod_score     <- rowMeans(df[, mod_items], na.rm = TRUE)
  iv_centered   <- scale(iv_score, center=TRUE, scale=FALSE)
  mod_centered  <- scale(mod_score, center=TRUE, scale=FALSE)
 
  # Add Interaction Term to df
  df$Interaction_Observed <- as.numeric(iv_centered * mod_centered)
 
  model_syntax <- paste0("
    # Measurement Models
    ", iv_name, "  =~ ", paste(iv_items, collapse=" + "), "
    ", mod_name, " =~ ", paste(mod_items, collapse=" + "), "
    ", dv_name, "  =~ ", paste(dv_items, collapse=" + "), "
   
    # Structural Regression
    ", dv_name, " ~ ", iv_name, " + ", mod_name, " + Interaction_Observed + ", control_vars, "
   
    # Covariances
    Interaction_Observed ~~ ", iv_name, "
    Interaction_Observed ~~ ", mod_name, "
  ")
 
  fit <- sem(model_syntax, data = df, std.lv = TRUE, estimator="MLM")
  return(fit)
}

# ==============================================================================
# PART 4: EXECUTION LOOP
# ==============================================================================
IV_List  <- c("IV_1", "IV_2", "IV_3", "IV_4", "IV_5", "IV_6")
Mod_List <- c("Moderator")
DV_List  <- c("Dependent_Var")

results_table <- data.frame()

for (mod in Mod_List) {
  for (dv in DV_List) {
    for (iv in IV_List) {
     
      tryCatch({
        fit <- run_moderation_robust(Fulldata, iv, mod, dv)
       
        if (inspect(fit, "converged")) {
          params <- parameterEstimates(fit, standardized = TRUE)
          interaction_row <- subset(params, op == "~" & rhs == "Interaction_Observed")
         
          if(nrow(interaction_row) > 0) {
            new_row <- data.frame(
              Independent_Var = iv,
              Moderator = mod,
              Dependent_Var = dv,
              Interaction_Est = round(interaction_row$est, 3),
              P_Value = round(interaction_row$pvalue, 3),
              Std_Beta = round(interaction_row$std.all, 3),
              Significant = ifelse(interaction_row$pvalue < 0.05, "YES", "NO")
            )
            results_table <- rbind(results_table, new_row)
          }
        }
      }, error = function(e) {
        cat(paste("Error in model for IV:", iv, "\n"))
      })
     
    }
  }
}

# ==============================================================================
# PART 5: VIEW RESULTS
# ==============================================================================
print("--- FINAL MODERATION RESULTS ---")
print(results_table)

[Rönkkö, Mikko]

Harmanjit,

 

Are you using an LLM to generate R code and then ask other people to validate it for you? (The code looks a lot like R code that LLMs generate)

 

The answer to your question is: No, this would not work. The code takes a latent variable model and then calculates the interaction term using scale scores. This approach produces biased estimates of the interaction effect. It also probably does not make sense to treat occupation as a continuous variable in the model.

 

This paper explains how you can estimate interaction models using semTools:

 

Schoemann, A. M., & Jorgensen, T. D. (2021). Testing and Interpreting Latent Variable Interactions Using the semTools Package. Psych, 3(3), Article 3. https://doi.org/10.3390/psych3030024

 

 

Best regards,

 

Mikko

 

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[Harmanjit Singh]

Dear Mikko,

Thanks for your reply.

I understand IndProd() method of testing moderation in Lavaan and have used it in the past. Thanks for pointing out flaws in this code. Yes, this has been generated via LLM. I was doing some experimentation with it and this is a part of that. My main concern at this stage is that even if I use IndProd() method, should I include moderator in the structural model or not (for instance as a control variables)? The idea is, if it is added as a control in structural model, and its affect is insignificant, latter on when we check moderation using IndProd() and its moderating affects are significant, we can claim that it is a true moderation effect, i.e., no direct affect from it is playing part, only its interaction with the independent variable is modifying the impact on dependent variable.

Looking forward to hearing from you.

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