Introduction to ESEM

#> Loading required package: GPArotation

Exploratory Structural Equiation Modeling ESEM with esem package


Install packages if required

remotes::install_github("maria-pro/esem", build_vignettes = TRUE)



#the package with the dataset to be used
remotes::install_github("maria-pro/esem", build_vignettes = FALSE)

Load the data into the R: sdq_lsac is in-built dataset that is also available at …….


To review the dimensions of the data (i.e. observations and variables), use dim() function


describe() function provides the statistics about the dataset. Other functions are available to explore the variables and relationships between them which is not part of this tutorial.


The current tutorial skips the preprocessing and data exploration steps and goes straight to the steps to complete the ESEM.

We follow the classical approach in treating SDQ data which is a 5-factor model. The allocation of variables to factors are set up using the named list data structure using list() function where factors are specified using the left-hand side of = and the constituent sdq_lsac items are provided as a vector using c(). Five factors are specified below: pp, cp, es, ha and ps.

main_loadings_list <- list(
                          pp = c("s6_1", "s11_1R", "s14_1R", "s19_1", "s23_1"),
                          cp = c("s5_1", "s7_1R", "s12_1", "s18_1", "s22_1"),
                          es = c("s3_1", "s8_1", "s13_1", "s16_1", "s24_1"),
                          ha = c("s2_1","s10_1","s15_1","s21_1R","s25_1R"),
                          ps = c("s1_1","s4_1","s9_1","s17_1","s20_1")

ESEM based on EFA derived loading thresholds

The esem_efa() function estimates and reports EFA. The results are saved in esem_efa_results object.

The following arguments are used:

For more options on running the esem_efa() function please see here. Please ignore the “Loading required namespace: GPArotation” message received, as such functions are already addressed by the packages retrieved.

esem_efa_results <- esem_efa(data=sdq_lsac, 
                      nfactors =5,
                      fm = 'ML',


The alternative solution is to run EFA with Target rotation. This option is explained in Step 1a below

Conduct EFA to calculate EFA derived cross-loadings with Target rotation

For target rotation, there needs to be a target supplied to the EFA.

To make a target, a list of main loadings (main_loading_list) is created using the list() function and supplied to make_target() function.

The following arguments are used:

The esem_efa() function is used with rotate= “TargetQ" and target matrix provided as Target. All other arguments remain the same

main_loadings_list <- list(
  pp = c("s6_1", "s11_1R", "s14_1R", "s19_1", "s23_1"),
  cp = c("s5_1", "s7_1R", "s12_1", "s18_1", "s22_1"),
  es = c("s3_1", "s8_1", "s13_1", "s16_1", "s24_1"),
  ha = c("s2_1","s10_1","s15_1","s21_1R","s25_1R"),
  ps = c("s1_1","s4_1","s9_1","s17_1","s20_1")


     nfactors = 5,
    Target= target)

Reviewing the generated loadings and creating a referent items per factor, list

esem_model <- esem_syntax(esem_efa_results, referent_list)


To address this step an ESEM model is required. This can be automatically produced using the esem _syntax() function available from the esem code developed for this tutorial. The function uses the step 1 EFA results and the step 2 referent item(s) per factor list.

Providing the referent_list object is optional. If no referent list is provided, it is created by the function itself and is used in model syntax generation. This allows all primary and non-primary loadings to be considered at their EFA varying levels.

Step 3 also automatically produces the esem_model syntax as one structural unit/object to be tested at step 4.

writeLines(model_syntax) allows to review the model syntax before it is used further. If required the model can be adjusted manually by the researcher.

Review the generated syntax carefully. This may be required for model identification purposes. For example, in case the variance-covariance matrix of the estimated parameters (vcov) does not appear to be positive definite, further adjustments to the model are required.

If adjustments are required the model can be rewritten manually

Testing the ESEM model

esem_fit <- esem_cfa(model=esem_model, 
               ordered = TRUE)
summary(esem_fit, fit.measures = TRUE, standardized = TRUE, ci = TRUE)

The esem_cfa() function fits a CFA model, where:

To review the results the summary()function is used with:

-fit.measures = TRUE. This calculates the goodness of fit parameters to assess model fit

The argument Standardized = TRUE provides two columns reporting (i) standardized parameters when only the latent variable is standardized (, and (ii) standardized parameters when both observed and latent variables are standardized (std.all).

For more options on running esem_cfa() function please see here

Visualizing ESEM Model

semPaths(esem_fit,whatLabels = "std",layout = "tree")

The semPaths () function plots the model and allows to customise its visualization with the following arguments:
- esem_fit as the fitted model, created in step 4 - whatLabels=”std” to produce standardized path coefficients - layout=”tree” to produce a tree-like disposition of elements in the plot