How to Perform Structural Equation Modeling (SEM) in Exploratory

Structural Equation Modeling (SEM) is a powerful statistical method that introduces “latent variables” that cannot be directly measured and allows you to visualize and verify complex causal relationships between variables as path diagrams.

Currently, Exploratory’s standard UI (Analytics View) does not have a menu for structural equation modeling, but you can perform SEM using the R package lavaan through Exploratory’s “Note” feature.

Installing Required Packages

First, install the packages needed to run SEM.

Select “Manage R Packages” from the Project menu.

When the R Package Management dialog appears, click “Install Package” and install the “lavaan” and “semPlot” packages.

Sample Data

We will use customer satisfaction survey data as sample data. You can download the data from here.

Creating a Note and Running Structural Equation Modeling

Click the plus button in Reports and select “Create Note”.

Once the Note window opens, click the plus button in the upper left and then click the “R Code” button.

A code block for writing R scripts has been added.

Running Structural Equation Modeling

In the lavaan package, models are defined in text format. The key is to use these three symbols appropriately:

• =~ : Defining latent variables (composed of observed variables on the right side)

• ~ : Regression (causal relationship)

• ~~ : Covariance (correlation)

Use the following R script:

library(lavaan)
library(semPlot)

# Create variable names for SEM model
customer_satisfaction_survey$y1 <- customer_satisfaction_survey$Product_Quality_Satisfaction
customer_satisfaction_survey$y2 <- customer_satisfaction_survey$Service_Satisfaction
customer_satisfaction_survey$y3 <- customer_satisfaction_survey$Price_Satisfaction
customer_satisfaction_survey$y4 <- customer_satisfaction_survey$Would_Use_Again
customer_satisfaction_survey$y5 <- customer_satisfaction_survey$Would_Recommend
customer_satisfaction_survey$x1 <- customer_satisfaction_survey$Purchase_Count
customer_satisfaction_survey$x2 <- customer_satisfaction_survey$Usage_Period_Months
customer_satisfaction_survey$x3 <- customer_satisfaction_survey$Age

# Define SEM model
model <- '
  # Measurement model
  f1 =~ y1 + y2 + y3
  f2 =~ y4 + y5
  
  # Structural model
  f2 ~ f1 + x1 + x2
  f1 ~ x3
'

# Fit SEM model
fit <- sem(model, data = customer_satisfaction_survey)

# Summary of results
summary(fit, fit.measures = TRUE, standardized = TRUE)

# Visualize the model
if(requireNamespace("semPlot", quietly = TRUE)) {
  semPaths(fit, 
           whatLabels = "est", 
           layout = "tree", 
           rotation = 2,
           edge.label.cex = 0.7,        # Make labels slightly smaller
           sizeMan = 8,
           sizeLat = 10,
           curve = 1.5,                  # Bend arrows slightly
           edge.label.position = 0.55,  # Adjust label position
           mar = c(3, 3, 3, 3),         # Increase margins
           nodeLabels = c("Age", "Price Sat", "Service Sat", 
                          "Quality Sat", "Purchase Count", "Usage Period",
                          "Use Again", "Recommend",
                          "Customer Satisfaction", "Repurchase Intention"))
}

The results of executing this R script are as follows:

# Example: When the data frame name is "customer_satisfaction_survey"

fit <- sem(model, data = customer_satisfaction_survey)

# Example: When the data frame name is "survey_results"

fit <- sem(model, data = survey_results)

# Change according to your data's column names

dataframe_name$y1 <- dataframe_name$actual_column_name1

dataframe_name$y2 <- dataframe_name$actual_column_name2

dataframe_name$y3 <- dataframe_name$actual_column_name3

dataframe_name$y4 <- dataframe_name$actual_column_name4

dataframe_name$y5 <- dataframe_name$actual_column_name5

dataframe_name$x1 <- dataframe_name$actual_column_name6

dataframe_name$x2 <- dataframe_name$actual_column_name7

dataframe_name$x3 <- dataframe_name$actual_column_name8

# You can use the basic model structure as is

model <- '

# Measurement model

f1 =~ y1 + y2 + y3    # Latent variable f1 is measured by y1, y2, y3

f2 =~ y4 + y5          # Latent variable f2 is measured by y4, y5

# Structural model

f2 ~ f1 + x1 + x2      # f2 is influenced by f1, x1, x2

f1 ~ x3                # f1 is influenced by x3

'

nodeLabels = c("Age", "Price Sat", "Service Sat",

"Quality Sat", "Purchase Count", "Usage Period",

"Use Again", "Recommend",

"Customer Satisfaction", "Repurchase Intention")

Common Errors and Solutions

Summary

Structural Equation Modeling (SEM) is a statistical method that uses latent variables that cannot be directly measured to visualize and verify complex causal relationships between variables. It can extract underlying concepts (such as customer satisfaction and repurchase intention) from multiple survey questions and express their relationships as path diagrams, making it useful for clarifying the basis for business decision-making.

In Exploratory, while the standard UI does not have a menu for structural equation modeling, you can perform SEM by using the R lavaan package in the Note feature. This method allows you to consistently perform data analysis and result visualization within Exploratory.