Package {plssem}

Type: Package
Title: Complex Partial Least Squares Structural Equation Modeling
Version: 0.1.2
Maintainer: Kjell Solem Slupphaug <slupphaugkjell@gmail.com>
Description: Estimate complex Structural Equation Models (SEMs) by fitting Partial Least Squares Structural Equation Modeling (PLS-SEM) and Partial Least Squares consistent Structural Equation Modeling (PLSc-SEM) specifications that handle categorical data, non-linear relations, and multilevel structures. The implementation follows Lohmöller (1989) for the classic PLS-SEM algorithm, Dijkstra and Henseler (2015) for consistent PLSc-SEM, Dijkstra et al., (2014) for nonlinear PLSc-SEM, and Schuberth, Henseler, Dijkstra (2018) for ordinal PLS-SEM and PLSc-SEM. Additional extensions are under development. The MC-OrdPLSc algorithm, used to handle ordinal interaction models is detailed in Slupphaug et al., (2026). References: Lohmöller, J.-B. (1989, ISBN:9783790803002). "Latent Variable Path Modeling with Partial Least Squares." Dijkstra, T. K., & Henseler, J. (2015). <doi:10.1016/j.jmva.2015.06.002>. "Consistent partial least squares path modeling." Dijkstra, T. K., & Schermelleh-Engel, K. (2014). <doi:10.1016/j.csda.2014.07.008>. "Consistent partial least squares for nonlinear structural equation models." Schuberth, F., Henseler, J., & Dijkstra, T. K. (2018). <doi:10.1007/s11135-018-0767-9>. "Partial least squares path modeling using ordinal categorical indicators." Slupphaug, K. Mehmetoglu, M. & Mittner, M. (2026). <doi:10.31234/osf.io/fwzj6_v1>. "Consistent Estimates from Biased Estimators: Monte-Carlo Consistent Partial Least Squares for Latent Interaction Models with Ordinal Indicators."
License: GPL-3
Encoding: UTF-8
LazyData: true
Imports: methods, stats, modsem (≥ 1.0.20), lme4, lavaan, stringr, purrr, matrixStats, Rfast, collapse, mvnfast, reformulas, future, future.apply, progressr, FNN, MASS
Depends: R (≥ 4.1.0)
URL: https://github.com/kss2k/plssem, https://kss2k.github.io/plssem/
Suggests: knitr, rmarkdown, ggplot2, mice, mvtnorm, pkgload
VignetteBuilder: knitr
Config/roxygen2/version: 8.0.0
NeedsCompilation: yes
Packaged: 2026-06-01 17:38:16 UTC; kss
Author: Kjell Solem Slupphaug ORCID iD [aut, cre]
Repository: CRAN
Date/Publication: 2026-06-01 19:20:02 UTC

TPB_Ordered

Description

A simulated dataset.

Examples


tpb <- '
# Outer Model (Based on Hagger et al., 2007)
  ATT =~ att1 + att2 + att3 + att4 + att5
  SN =~ sn1 + sn2
  PBC =~ pbc1 + pbc2 + pbc3
  INT =~ int1 + int2 + int3
  BEH =~ b1 + b2

# Inner Model (Based on Steinmetz et al., 2011)
  INT ~ ATT + SN + PBC
  BEH ~ INT + PBC
'

fit <- pls(tpb, TPB_Ordered)
summary(fit)

Retrieve bootstrap coefficient matrix

Description

Retrieve bootstrap coefficient matrix

Usage

boot(object)

## S4 method for signature 'PlsModel'
boot(object)

Arguments

object

A fitted model object.

Value

A PlsSemMatrix of bootstrap replicate parameter vectors (rows = replicates, cols = parameters).

Examples

library(modsem)
library(plssem)

m <- "
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3
  Y ~ X + Z + X:Z
"

fit <- pls(m, oneInt, bootstrap = TRUE, boot.R = 50)
boot(fit)

Extract coefficients from a PlsModel model

Description

Extract coefficients from a PlsModel model

Usage

## S4 method for signature 'PlsModel'
coef(object, ...)

## S4 method for signature 'PlsModel'
coefficients(object, ...)

Arguments

object

A PlsModel object.

...

Currently unused.

Value

A named PlsSemVector of parameter estimates.

Fit Measures

Description

Computes global fit measures (e.g., chi-square, SRMR, RMSEA) for a fitted model.

Usage

fit_measures(object, saturated = FALSE, mc.reps = 1e+06, ...)

## S4 method for signature 'PlsModel'
fit_measures(object, saturated = FALSE, mc.reps = 1e+06, ...)

Arguments

object

A fitted [PlsModel] object.

saturated

Logical; if 'TRUE', compute the saturated fit.

mc.reps

Integer; number of Monte Carlo resamples used for MC-PLSc fit.

...

Reserved for future extensions.

Value

A named list with fit statistics.

Implied Construct Correlation Matrix

Description

Returns the implied construct correlation matrix for a fitted model.

Usage

implied_construct_corr(object, saturated = FALSE, mc.reps = 1e+06, ...)

## S4 method for signature 'PlsModel'
implied_construct_corr(object, saturated = FALSE, mc.reps = 1e+06, ...)

Arguments

object

A fitted [PlsModel] object.

saturated

Logical; if 'TRUE', return the saturated implied matrix.

mc.reps

Integer; number of Monte Carlo resamples used for MC-PLSc.

...

Reserved for future extensions.

Details

For higher-order models, this is computed for the combined model returned by [combinedModel()].

Value

A [PlsSemMatrix].

Implied Indicator Correlation Matrix

Description

Returns the implied indicator correlation matrix for a fitted model.

Usage

implied_indicator_corr(object, saturated = FALSE, mc.reps = 1e+06, ...)

## S4 method for signature 'PlsModel'
implied_indicator_corr(object, saturated = FALSE, mc.reps = 1e+06, ...)

Arguments

object

A fitted [PlsModel] object.

saturated

Logical; if 'TRUE', return the saturated implied matrix.

mc.reps

Integer; number of Monte Carlo resamples used for MC-PLSc.

...

Reserved for future extensions.

Details

For higher-order models, this is computed for the combined model returned by [combinedModel()].

Value

A numeric matrix.

Check whether a fitted model has admissible parameter estimates

Description

Check whether a fitted model has admissible parameter estimates

Usage

is_admissible(object)

## S4 method for signature 'PlsModel'
is_admissible(object)

Arguments

object

A fitted PlsModel object.

Value

A single logical value.

Check whether an object uses the MC-OrdPLSc estimator

Description

Check whether an object uses the MC-OrdPLSc estimator

Usage

is_mcpls(object)

## S4 method for signature 'PlsModel'
is_mcpls(object)

Arguments

object

A fitted model object.

Value

TRUE or FALSE.

oneIntOrdered

Description

A simulated dataset.

Examples


m <- '
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

  Y ~ X + Z + X:Z
'

fit <- pls(m, oneIntOrdered)
summary(fit)

Generic accessor for model parameter estimates

Description

Generic accessor for model parameter estimates

Usage

parameter_estimates(object, ...)

Arguments

object

A fitted model object.

...

Additional arguments passed to methods.

Value

A parameter table describing the fitted model.

Parameter estimates for PlsModel objects

Description

Parameter estimates for PlsModel objects

Usage

## S4 method for signature 'PlsModel'
parameter_estimates(object, colon.pi = TRUE, label.renamed.prod = FALSE, ...)

Arguments

object

A PlsModel object.

colon.pi

Logical; replace product-indicator labels with colon notation (X:Z).

label.renamed.prod

Logical; retain renamed product labels when colon expansion occurs.

...

Currently unused.

Value

A PlsSemParTable data frame.

Fit Partial Least Squares Structural Equation Models

Description

pls() estimates Partial Least Squares Structural Equation Models (PLS-SEM) and their consistent (PLSc) variants. The function accepts lavaan-style syntax, handles ordered indicators through polychoric correlations and probit factor scores, and supports multilevel specifications expressed with lme4-style random effects terms inside the structural model.

Usage

pls(
  syntax,
  data,
  standardize = TRUE,
  consistent = TRUE,
  bootstrap = FALSE,
  ordered = NULL,
  missing = c("listwise", "mean", "kNN"),
  knn.k = 5,
  mcpls = NULL,
  mc.fast.lmer = mcpls,
  probit = NULL,
  tolerance = 1e-05,
  max.iter.0_5 = 100L,
  boot.ncores = 1L,
  boot.ncpus = NULL,
  boot.parallel = c("no", "multicore", "multisession", "snow"),
  boot.R = 50L,
  boot.iseed = NULL,
  sample = NULL,
  mc.min.iter = 50L,
  mc.max.iter = 500L,
  mc.reps = 20000L,
  mc.fixed.seed = FALSE,
  mc.polyak.juditsky = TRUE,
  mc.pj.extrapolate = TRUE,
  mc.tol = if (mc.polyak.juditsky) 1e-04 else 0.001,
  mc.delta.se = TRUE,
  mc.delta.jacobian.k = max(floor(boot.R/100L), 1),
  mc.fn.args = list(),
  verbose = interactive(),
  boot.optimize = TRUE,
  mc.boot.control = list(min.iter = mc.min.iter, max.iter = mc.max.iter, mc.reps =
    floor(0.5 * mc.reps), tol = mc.tol, polyak.juditsky = mc.polyak.juditsky,
    pj.extrapolate = FALSE, verbose = FALSE, fixed.seed = TRUE, reuse.p.start = TRUE),
  reliabilities = NULL,
  ...
)

Arguments

syntax

Character string with lavaan-style model syntax describing both measurement (=~) and structural (~) relations. Random effects are specified with (term | cluster) statements.

data

A data.frame or coercible object containing the manifest indicators referenced in syntax. Ordered factors are automatically detected, but can also be supplied explicitly through ordered.

standardize

Logical; if TRUE, indicators are standardized before estimation so that factor scores have comparable scales.

consistent

Logical; TRUE requests PLSc corrections, whereas FALSE fits the traditional PLS model.

bootstrap

Logical; if TRUE, nonparametric bootstrap standard errors are computed with boot.R resamples.

ordered

Optional character vector naming manifest indicators that should be treated as ordered when computing polychoric correlations.

missing

Character string specifying how to handle missing indicator data. "listwise" removes rows with missing values (listwise deletion). "mean" imputes missing indicator values using simple univariate imputation: the mean for continuous variables, the median for ordered variables with more than two categories, and the mode for binary ordered variables (two categories) or nominal variables. "kNN" (or "knn") imputes missing indicator values using k-nearest neighbors imputation (kNN). When missing = "kNN", rows with all indicators missing are removed prior to imputation, and rows with missing cluster values are removed for multilevel models.

knn.k

Integer specifying the number of neighbors (k) used when missing = "kNN".

mcpls

Should the model be estimated using the Monte-Carlo Consistent Partial Least Squares (MC-PLSc) algorithm?

mc.fast.lmer

Should a faster (biased) GLS based estimator of the Mixed-Effects model be used in conjunction with the MC-PLS algorithm?

probit

Logical; overrides the automatic choice of probit factor scores that is based on whether ordered indicators are present.

tolerance

Numeric; Convergence criteria/tolerance.

max.iter.0_5

Maximum number of PLS iterations performed when estimating the measurement and structural models.

boot.ncores

Integer: number of workers to be used for parallel bootstrapping. Parallel bootstrapping is enabled when boot.ncores > 1.

boot.ncpus

Deprecated alias for boot.ncores.

boot.parallel

The type of parallel operation to be used (if any). The default is "no". "multisession" runs the bootstrap using multiple background R sessions (works on all platforms), while "multicore" uses forked processes (not available on Windows). "snow" is kept for backwards compatibility and is treated as an alias for "multisession". Internally this is implemented using the future package

boot.R

Integer giving the number of bootstrap resamples drawn when bootstrap = TRUE.

boot.iseed

An integer to set the bootstrap seed. Or NULL if no reproducible results are needed. This works for both serial and parallel settings. When boot.iseed is not NULL, .Random.seed (if it exists) in the global environment is left untouched.

sample

DEPRECATED. Integer giving the number of bootstrap resamples drawn when bootstrap = TRUE.

mc.min.iter

Minimum number of iterations in MC-PLS algorithm.

mc.max.iter

Maximum number of iterations in MC-PLS algorithm.

mc.reps

Monte-Carlo sample size in MC-PLS algorithm.

mc.fixed.seed

Should a fixed seed be used in the MC-PLS algorithm? Setting a fixed seed will likely yield less accurate estimates, but can substantially improve the stability and computational efficiency of the algorithm.

mc.polyak.juditsky

Should the polyak.juditsky running average method be applied in the MC-PLS algorithm?

mc.pj.extrapolate

Logical; if TRUE (the default), the Polyak-Juditsky convergence point is estimated via NLS exponential extrapolation (with Aitken \delta^2 as a fallback). If FALSE a warm start is performed instead, and the plain Polyak-Juditsky average is used. Only relevant when mc.polyak.juditsky = TRUE.

mc.tol

Tolerance in MC-PLS algorithm.

mc.delta.se

Should delta-method standard errors be computed for MC-PLS estimates?

mc.delta.jacobian.k

Integer number of Monte-Carlo Jacobians to average when computing delta-method standard errors. Defaults to one per 100 bootstrap resamples, with a minimum of 1.

mc.fn.args

Additional arguments to MC-PLS algorithm, mainly for controlling the step size.

verbose

Should verbose output be printed?

boot.optimize

Logical; if TRUE and bootstrap = TRUE, applies the settings in mc.boot.control inside each bootstrap replicate (MC-PLS only). In general it will lead to slightly larger and less accurate standard errors.

mc.boot.control

List of control parameters passed to the MC-PLS algorithm inside each bootstrap replicate when boot.optimize = TRUE.

reliabilities

Optional named numeric vector of user-supplied reliabilities used for the PLSc consistency correction.

...

Internal arguments. For advanced users only.

Value

A Plssem object containing the estimated parameters, fit measures, factor scores, and any bootstrap results. Methods such as summary(), coef(), and parameter_estimates() can be applied to inspect the fit.

See Also

summary, show

Examples


library(plssem)
library(modsem)

tpb <- '
  ATT =~ att1 + att2 + att3 + att4 + att5
  SN =~ sn1 + sn2
  PBC =~ pbc1 + pbc2 + pbc3
  INT =~ int1 + int2 + int3
  BEH =~ b1 + b2
  INT ~ ATT + SN + PBC
  BEH ~ INT + PBC
'

fit <- pls(tpb, TPB, bootstrap = TRUE)
summary(fit)

Construct latent variable scores

Description

Convenience wrapper around [pls_predict()] returning only the predicted latent scores matrix.

Usage

pls_construct_scores(object, ...)

Arguments

object

A fitted Plssem model.

...

Passed to [pls_predict()].

Value

A PlsSemMatrix of predicted latent scores.

Predict from a fitted PLS-SEM model

Description

Predict from a fitted PLS-SEM model

Usage

pls_predict(object, ...)

## S4 method for signature 'PlsModel'
pls_predict(
  object,
  approach = c("earliest", "direct"),
  newdata = NULL,
  std.ord.exp = FALSE,
  benchmark = "R2",
  benchmark.vars = c("endog", "exog", "all"),
  ...
)

Arguments

object

A fitted PlsModel object.

...

Additional arguments passed to internal helpers.

approach

Prediction approach. If approach = "earliest" (default), then only indicators of exogenous benchmark.vars are used for prediction. If approach = "direct", then all indicators are used.

newdata

Optional new data matrix/data frame.

std.ord.exp

Logical; standardize ordinal expectation scores.

benchmark

Benchmark type(s). Either length 1 (recycled) or one entry per indicator (optionally named). Supported: "r2", "rmse", "mae", "q2_predict", "acc", "ord_mae".

benchmark.vars

What predictions should be benchmarked? If benchmark.vars = "endog" (default), preidction benchmarks are applied to indicators of endogenous benchmark.vars. If benchmark.vars = "exog", preidction benchmarks are applied to indicators of exogenous benchmark.vars. If benchmark.vars = "all", preidction benchmarks are applied to all of the indicators in the model.

Value

A PlsSemPredict object with matrices and benchmark results.

Predict from a fitted PlsModel (alias for pls_predict)

Description

Predict from a fitted PlsModel (alias for pls_predict)

Usage

## S4 method for signature 'PlsModel'
predict(object, newdata = NULL, ...)

Arguments

object

A fitted PlsModel object.

newdata

Optional new data matrix/data frame.

...

Further arguments passed to pls_predict.

Value

A PlsSemPredict object.

Print a PlsSemPredict object

Description

Print a PlsSemPredict object

Usage

## S3 method for class 'PlsSemPredict'
print(x, ...)

Arguments

x

A PlsSemPredict object.

...

Additional arguments for compatibility with the generic.

Value

The input object, invisibly.

Print a SummaryPlsSem object

Description

Print a SummaryPlsSem object

Usage

## S3 method for class 'SummaryPlsSem'
print(x, ...)

Arguments

x

A SummaryPlsSem object as returned by summary().

...

Additional arguments for compatibility with the generic.

Value

The input object, invisibly.

randomIntercepts

Description

A simulated dataset.

Examples


syntax <- '
  f =~ y1 + y2 + y3
  f ~ x1 + x2 + x3 + w1 + w2 + (1 | cluster)
'

fit <- pls(syntax, data = randomIntercepts)
summary(fit)

randomInterceptsOrdered

Description

A simulated dataset.

Examples


syntax <- '
  f =~ y1 + y2 + y3
  f ~ x1 + x2 + x3 + w1 + w2 + (1 | cluster)
'

fit <- pls(syntax, data = randomInterceptsOrdered)
summary(fit)

randomSlopes

Description

A simulated dataset. syntax <- " X =~ x1 + x2 + x3 Z =~ z1 + z2 + z3 Y =~ y1 + y2 + y3 W =~ w1 + w2 + w3 Y ~ X + Z + (1 + X + Z | cluster) W ~ X + Z + (1 + X + Z | cluster) "

fit <- pls(syntax, data = randomSlopes) fit

randomSlopesOrdered

Description

A simulated dataset.

Examples


syntax <- "
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3
  W =~ w1 + w2 + w3
  Y ~ X + Z + (1 + X + Z | cluster)
  W ~ X + Z + (1 + X + Z | cluster)
"

fit <- pls(syntax, data = randomSlopesOrdered)
fit
summary(fit)

Show a PlsModel object

Description

Called automatically when an object is printed at the prompt. Displays the package version, iteration count, and the parameter table.

Usage

## S4 method for signature 'PlsModel'
show(object)

Arguments

object

A PlsModel object.

Value

object, invisibly.

Summarize a fitted PlsModel model

Description

Summarize a fitted PlsModel model

Usage

## S4 method for signature 'PlsModel'
summary(object, fit = TRUE, ...)

Arguments

object

A PlsModel object.

fit

Logical; whether to compute fit measures.

...

Currently unused.

Value

A SummaryPlsSem list with formatted results.

Titanic Passenger Survival Data Set.

Description

This dataset has been re-packaged for convenience from https://github.com/paulhendricks/titanic

PassengerId

Passenger ID

Survived

Passenger Survival Indicator

Pclass

Passenger Class

Name

Name

Sex

Sex

Age

Age

SibSp

Number of Siblings/Spouses Aboard

Parch

Number of Parents/Children Aboard

Ticket

Ticket Number

Fare

Passenger Fare

Cabin

Cabin

Embarked

Port of Embarkation

Female

Dummy variable for Sex="female"

Format

A data frame with 1309 rows and 12 variables:

Source

https://www.kaggle.com/c/titanic/data

Examples


fit <- pls("Survived ~ Age + Female + Age:Female",
           data = titanic, ordered = "Survived")
pls_predict(fit, benchmark = "acc")

Extract the variance-covariance matrix from a PlsModel model

Description

Extract the variance-covariance matrix from a PlsModel model

Usage

## S4 method for signature 'PlsModel'
vcov(object, ...)

Arguments

object

A PlsModel object.

...

Currently unused.

Value

A PlsSemMatrix (bootstrap-based vcov, or NULL).