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Natural feeling domain-specific language for building structural equation models in R for estimation by covariance-based methods (like LISREL/Lavaan) or partial least squares (like SmartPLS)

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SEMinR allows users to easily create and modify structural equation models (SEM). It allows estimation using either covariance-based SEM (CBSEM, such as LISREL/Lavaan), or Partial Least Squares Path Modeling (PLS-PM, such as SmartPLS/semPLS).

First Look

Main features of using SEMinR:

  • A natural feeling, domain-specific language to build and estimate SEMs in R
  • High-level functions to quickly specify interactions and complicated structural models
  • Modular design of models that promotes reuse of model components
  • Encourages best practices by use of smart defaults and warnings

Take a look at the easy syntax and modular design:

# Define measurements with famliar terms: reflective, composite, multi-item constructs, etc.
measurements <- constructs(
  reflective("Image",       multi_items("IMAG", 1:5)),
  composite("Expectation", multi_items("CUEX", 1:3)),
  composite("Loyalty",     multi_items("CUSL", 1:3), weights = mode_B),
  composite("Complaints",  single_item("CUSCO"))
)

# Create four relationships (two regressions) in one line!
structure <- relationships(
  paths(from = c("Image", "Expectation"), to = c("Complaints", "Loyalty"))
)

# Estimate the model using PLS estimation scheme (Consistent PLS for reflectives)
pls_model <- estimate_pls(data = mobi, measurements, structure)
#> Generating the seminr model
#> All 250 observations are valid.

# Re-estimate the model as a purely reflective model using CBSEM
cbsem_model <- estimate_cbsem(data = mobi, as.reflective(measurements), structure)
#> Generating the seminr model for CBSEM

SEMinR can plot models using the semplot (for CBSEM models) or DiagrammeR (for PLS models) packages with a simple plot method.

plot(pls_model, title = "PLS Model")
save_plot("myfigure.pdf")

SEMinR allows various estimation methods for constructs and SEMs:

  • Covariance-based Structural Equation Modeling (CBSEM)
    • Covariance-based estimation of SEM using the popular Lavaan package
    • Currently supports mediation and moderation models with constructs
    • Easily specify interactions between constructs
    • Adds ten Berge factor score extraction to get same correlation patterns as latent factors
    • Adds VIF and other validity assessments
  • Confirmatory Factor Analysis (CFA) using Lavaan
    • Uses Lavaan package and returns results and syntax
    • Adds ten Berge factor score extraction to get same correlation patterns as latent factors
  • Partial Least Squares Path Modeling (PLS-PM)
    • Uses non-parametric variance-based estimation to construct composites and common-factors
    • Automatically estimates using Consistent PLS (PLSc) when emulating reflective common factors
    • Adjusts for known biases in interaction terms in PLS models
    • Continuously tested against leading PLS-PM software to ensure parity of outcomes: SmartPLS, ADANCO, semPLS, and matrixpls
    • High performance, multi-core bootstrapping function

Researchers can now create a SEM and estimate it using different techniques (CBSEM, PLS-PM).

Installation

You can install SEMinR from R with:

install.packages("seminr")

Usage and Examples

Load the SEMinR package:

library(seminr)

Describe measurement and structural models and then estimate them. See the various examples below for different use cases:

  1. CFA + CBSEM Example with Common Factors
  2. Consistent-PLS (PLSc) Example with Common Factors
  3. PLS-PM Example with Composites
  4. Comparing CBSEM and PLS-PM Example

CFA + CBSEM Example with Common Factors

Note that CBSEM models reflective common-factor constructs, not composites. SEMinR uses the powerful Lavaan package to estimate CBSEM models – you can even inspect the more complicated Lavaan syntax that is produced.

Describe reflective constructs and interactions:

# Distinguish and mix composite or reflective (common-factor) measurement models
# - composite measurements will have to be converted into reflective ones for CBSEM (see below)
measurements <- constructs(
  reflective("Image",       multi_items("IMAG", 1:5)),
  reflective("Expectation", multi_items("CUEX", 1:3)),
  interaction_term(iv = "Image", moderator = "Expectation", method = two_stage),
  reflective("Loyalty",     multi_items("CUSL", 1:3)),
  reflective("Complaints",  single_item("CUSCO"))
)

Describe the causal relationships between constructs and interactions:

# Quickly create multiple paths "from" and "to" sets of constructs
structure <- relationships(
  paths(from = c("Image", "Expectation", "Image*Expectation"), to = "Loyalty"),
  paths(from = "Image", to = c("Complaints"))
)

Put the above elements together to estimate the model using Lavaan:

# Evaluate only the measurement model using Confirmatory Factor Analysis (CFA)
cfa_model <- estimate_cfa(data = mobi, measurements)
summary(cfa_model)

# Dynamically compose full SEM models from individual parts
# - if measurement model includes composites, convert all constructs to reflective using:
#     as.reflective(measurements)
cbsem_model <- estimate_cbsem(data = mobi, measurements, structure)
sum_cbsem_model <- summary(cbsem_model)
sum_cbsem_model$meta$syntax # See the Lavaan syntax if you wish

Consistent-PLS (PLSc) Example with Common Factors

Models with reflective common-factor constructs can also be estimated in PLS-PM, using Consistent-PLS (PLSc). Note that the popular SmartPLS software models constructs as composites rather than common-factors (see below) but can also do PLSc as a special option.

We will reuse the measurement and structural models from earlier:

# Optionally inspect the measuremnt and structural models
measurements
structure

Estimate full model using Consistent-PLS and bootstrap it for confidence intervals:

# Models with reflective constructs are automatically estimated using PLSc
pls_model <- estimate_pls(data = mobi, measurements, structure)
summary(pls_model)

# Use multi-core parallel processing to speed up bootstraps
boot_estimates <- bootstrap_model(pls_model, nboot = 1000, cores = 2)
summary(boot_estimates)

PLS-PM Example with Composites

PLS-PM typically models composites (constructs that are weighted average of items) rather than common factors. Popular software like SmartPLS models composites either as Mode A (correlation weights) or Mode B (regression weights). We also support both modes as well as second-order composites. rather than common factors. Popular software like SmartPLS models composites by default, either as Mode A (correlation weights) or Mode B (regression weights). We also support second-order composites.

Describe measurement model for each composite, interaction, or higher order composite:

# Composites are Mode A (correlation) weighted by default
mobi_mm <- constructs(
  composite("Image",        multi_items("IMAG", 1:5)),
  composite("Value",        multi_items("PERV", 1:2)),
  higher_composite("Satisfaction", dimensions = c("Image","Value"), method = two_stage),
  composite("Expectation",  multi_items("CUEX", 1:3)),
  composite("Quality",      multi_items("PERQ", 1:7), weights = mode_B),
  composite("Complaints",   single_item("CUSCO")),
  composite("Loyalty",      multi_items("CUSL", 1:3), weights = mode_B)
)

Define a structural (inner) model for our PLS-PM:

mobi_sm <- relationships(
  paths(from = c("Expectation","Quality"),  to = "Satisfaction"),
  paths(from = "Satisfaction", to = c("Complaints", "Loyalty"))
)

Estimate full model using PLS-PM and bootstrap it for confidence intervals:

pls_model <- estimate_pls(
  data = mobi,
  measurement_model = mobi_mm,
  structural_model = mobi_sm
)

summary(pls_model)

# Use multi-core parallel processing to speed up bootstraps
boot_estimates <- bootstrap_model(pls_model, nboot = 1000, cores = 2)
summary(boot_estimates)

Plotting the model results

SEMinR can plot all supported models using the dot language and the graphViz.js widget from the DiagrammeR package.

# generate a small model for creating the plot
mobi_mm <- constructs(
  composite("Image",        multi_items("IMAG", 1:3)),
  composite("Value",        multi_items("PERV", 1:2)),
  higher_composite("Satisfaction", dimensions = c("Image","Value"), method = two_stage),
  composite("Quality",      multi_items("PERQ", 1:3), weights = mode_B),
  composite("Complaints",   single_item("CUSCO")),
  reflective("Loyalty",      multi_items("CUSL", 1:3))
)
mobi_sm <- relationships(
  paths(from = c("Quality"),  to = "Satisfaction"),
  paths(from = "Satisfaction", to = c("Complaints", "Loyalty"))
)
pls_model <- estimate_pls(
  data = mobi,
  measurement_model = mobi_mm,
  structural_model = mobi_sm
)
#> Generating the seminr model
#> Generating the seminr model
#> All 250 observations are valid.
#> All 250 observations are valid.
boot_estimates <- bootstrap_model(pls_model, nboot = 100, cores = 1)
#> Bootstrapping model using seminr...
#> SEMinR Model successfully bootstrapped

When we have a model, we can plot it and save the plot to files.

plot(boot_estimates, title = "Bootstrapped Model")
save_plot("myfigure.pdf")

Themes

We can customize the plot using an elaborate theme. Themes can be used for individual plots as a parameter or set as a default. Using the seminr_theme_create() function allows to define different themes.

# Tip: auto complete is your friend in finding all possible themeing options.
thm <- seminr_theme_create(plot.rounding = 2, plot.adj = F, 
                           sm.node.fill = "cadetblue1",
                           mm.node.fill = "lightgray")
# change new default theme - valid until R is restarted
seminr_theme_set(thm)

# the new plot
plot(boot_estimates)

Comparing CBSEM and PLS-PM Example

We can re-estimate a composite PLS-PM model as a common-factor CBSEM. Such a comparison might interest researchers seeking to evaluate how their constructs behave when modeled as composites versus common-factors.

# Define measurements with famliar terms: reflective, multi-item constructs, etc.
measurements <- constructs(
  composite("Image",       multi_items("IMAG", 1:5)),
  composite("Expectation", multi_items("CUEX", 1:3)),
  composite("Loyalty",     multi_items("CUSL", 1:3)),
  composite("Complaints",  single_item("CUSCO"))
)

# Create four relationships (two regressions) in one line!
structure <- relationships(
  paths(from = c("Image", "Expectation"), to = c("Complaints", "Loyalty"))
)

# First, estimate the model using PLS
pls_model <- estimate_pls(data = mobi, measurements, structure)

# Reusable parts of the model to estimate CBSEM results
# note: we are using the `as.reflective()` function to convert composites to common factors
cbsem_model <- estimate_cbsem(data = mobi, as.reflective(measurements), structure)

# Re-estimate the model using common factors in Consistent PLS (PLSc)
pls_model <- estimate_pls(data = mobi, as.reflective(measurements), structure)

Documentation

The vignette for Seminr can be found on CRAN or by running the vignette("SEMinR") command after installation.

Demo code for various use cases with SEMinR can be found in the seminr/demo/ folder or by running commands such as demo("seminr-contained") after installation.

Sister Projects

  • seminrstudio: A set of addins for RStudio to simplify using SEMinR.

Partner Projects

We communicate and collaborate with several other open-source projects on SEM related issues.

  • plspm package for R: an early and limited PLS path modeling package for R that inspired the development of SEMinR, among others; it is no longer maintained.
  • plspm package for Python: a well-maintained PLS modeling pakage for Python; it is tested against SEMinR and borrows some syntactic ideas from SEMinR.
  • cSEM: a well-maintained and comprehensive composite analysis project implementing PLS and GSCA for R, using Lavaan style syntax

Contact Us

Facebook Group: https://www.facebook.com/groups/seminr

You will find the developers and other users here who might also be able to help or discuss.

Issue Tracker: https://github.com/sem-in-r/seminr/issues

This is the official place to submit potential bugs or request new features for consideration.

About Us

Primary Authors:

Key Contributors:

And many thanks to the growing number of folks who have reached out with feature requests, bug reports, and encouragement. You keep us going!

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Natural feeling domain-specific language for building structural equation models in R for estimation by covariance-based methods (like LISREL/Lavaan) or partial least squares (like SmartPLS)

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