Type: Package
Title: Complex Partial Least Squares Structural Equation Modeling
Version: 0.1.1
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
RoxygenNote: 7.3.3
Imports: stats, modsem (≥ 1.0.17), lme4, lavaan, stringr, purrr, matrixStats, Rfast, collapse, mvnfast, reformulas, parallel, FNN
Depends: R (≥ 4.1.0)
URL: https://github.com/kss2k/plssem, https://kss2k.github.io/plssem/
Suggests: knitr, rmarkdown, mice, mvtnorm
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2026-04-25 15:42:23 UTC; kss
Author: Kjell Solem Slupphaug ORCID iD [aut, cre]
Repository: CRAN
Date/Publication: 2026-04-25 16:50:02 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)

Get bootstrapped coefficients from PLS model

Description

Get bootstrapped coefficients from PLS model

Usage

boot(object)

Arguments

object

A fitted model object.

Value

Matrix with bootstrapped coefficients.

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)

Check if object is a MC-PLS model

Description

Check if object is a MC-PLS model

Usage

isMC_PLS(object)

Arguments

object

A fitted model object.

Value

TRUE/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 plssem objects

Description

Parameter estimates for plssem objects

Usage

## S3 method for class 'plssem'
parameter_estimates(object, colon.pi = TRUE, label.renamed.prod = FALSE, ...)

Arguments

object

An object of class plssem.

colon.pi

Logical; whether to replace labels for interaction terms with colon notation.

label.renamed.prod

Logical; whether renamed product labels should be retained when colon expansion occurs.

...

Additional arguments (not used).

Value

A parameter table (data frame) describing the fitted model.

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,
  probit = NULL,
  tolerance = 1e-05,
  max.iter.0_5 = 100L,
  boot.ncpus = 1L,
  boot.parallel = c("no", "multicore", "snow"),
  boot.R = 50L,
  boot.iseed = NULL,
  sample = NULL,
  mc.min.iter = 5L,
  mc.max.iter = 250L,
  mc.reps = 20000L,
  mc.tol = 0.001,
  mc.fixed.seed = FALSE,
  mc.polyak.juditsky = FALSE,
  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 = 2 * mc.tol, polyak.juditsky = 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 a Monte-Carlo consistency correction be applied?

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.ncpus

Integer: number of processes to be used in parallel operation. By default this is the number of cores (as detected by parallel::detectCores()) minus one.

boot.parallel

The type of parallel operation to be used (if any). If missing, the default is "no".

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 (non-parallel) and parallel settings. Internally, RNGkind() is set to "L'Ecuyer-CMRG" if parallel = "multicore". If parallel = "snow" (under windows), parallel::clusterSetRNGStream() is called which automatically switches to "L'Ecuyer-CMRG". When iseed is not NULL, .Random.seed (if it exists) in the global environment is left untouched.

sample

DEPRECTATED. 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.tol

Tolerance in MC-PLS algorithm.

mc.fixed.seed

Should a fixed seed be used in the MC-PLS algorithm?

mc.polyak.juditsky

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

mc.fn.args

Additional arguments to MC-PLS algorithm, mainly for controling 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).

mc.boot.control

List of control parameters passed to the MC-PLS algorithm inside each bootstrap replicate when boot.optimize = TRUE. This can be used to speed up bootstrapping by, for example, increasing the tolerance or reducing mc.reps. The element reuse.p.start controls whether to reuse the original p.start for the bootstrap replicates.

reliabilities

Optional named numeric vector of user-supplied reliabilities used for the PLSc consistency correction. Values are interpreted as construct reliabilities (i.e., squared construct quality, Q^2) for the named constructs. These override the internally computed construct qualities.

...

Internal arguments. For advanced users only.

Value

An object of class plssem containing the estimated parameters, fit measures, factor scores, and any bootstrap results. Methods such as summary(), print(), and coef() can be applied to inspect the fit.

See Also

[summary.plssem()], [print.plssem()]

Examples

# Linear Model with Continuous Data


library(plssem)
library(modsem)

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, bootstrap = TRUE)
summary(fit)

# Linear Model with Ordered Data
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, bootstrap = TRUE)
summary(fit)

# Multilevel Random Slopes Model with Continuous Data
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, bootstrap = TRUE)
summary(fit)

# Multilevel Random Slopes Model with Ordered Data
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, bootstrap = TRUE)
summary(fit)

# Multilevel Random Intercepts Model with Continuous Data
syntax <- '
  f =~ y1 + y2 + y3
  f ~ x1 + x2 + x3 + w1 + w2 + (1 | cluster)
'

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

# Multilevel Random Intercepts Model with Ordered Data
syntax <- '
  f =~ y1 + y2 + y3
  f ~ x1 + x2 + x3 + w1 + w2 + (1 | cluster)
'

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

# Interaction Model with Continuous Data
m <- '
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

  Y ~ X + Z + X:Z
'

fit <- pls(m, modsem::oneInt, bootstrap = TRUE)
summary(fit)

# Interaction Model with Ordered Data
m <- '
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

  Y ~ X + Z + X:Z
'

fit <- pls(m, oneIntOrdered, 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,
  approach = c("earliest", "direct"),
  newdata = NULL,
  std.ord.exp = FALSE,
  benchmark = "R2",
  benchmark.vars = c("endog", "exog", "all"),
  ...
)

Arguments

object

A fitted plssem model.

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.

...

Additional arguments passed to internal helpers.

Value

A PlsSemPredict object with matrices and benchmark results.

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.plssem()].

...

Additional arguments for compatibility with the generic.

Value

The input object, invisibly.

Print a plssem object

Description

Print a plssem object

Usage

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

Arguments

x

An object of class plssem.

...

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)

Summarize a fitted plssem model

Description

Summarize a fitted plssem model

Usage

## S3 method for class 'plssem'
summary(object, fit = TRUE, ...)

Arguments

object

An object of class plssem.

fit

Should fit measures be calculated?

...

Additional arguments passed to or from methods.

Value

A SummaryPlsSem object containing formatted parameter estimates.

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")