Package 'plssem'

Title: Complex Partial Least Squares Structural Equation Modeling
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."
Authors: Kjell Solem Slupphaug [aut, cre] (ORCID: <https://orcid.org/0009-0005-8324-2834>)
Maintainer: Kjell Solem Slupphaug <[email protected]>
License: GPL-3
Version: 0.2.0
Built: 2026-10-12 16:26:05 UTC
Source: https://github.com/kss2k/plssem

Help Index

Retrieve bootstrap coefficient matrix

Description

Retrieve bootstrap coefficient matrix

Usage

boot(object)

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

## S4 method for signature 'PlsModel'
pls_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, use.labels = TRUE, ...)

## S4 method for signature 'PlsModel'
coefficients(object, use.labels = TRUE, ...)

Arguments

object

A PlsModel object.
use.labels

Logical; Should parameter labels be used as names?
...

Currently unused.

Value

A named PlsSemVector of parameter estimates.

Extract coefficients from a PlsMultilevelModel model

Description

Parameters at the between level (level 2) are suffixed with .l2.

Usage

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

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

Arguments

object

A PlsMultilevelModel 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.

Fit measures for PlsMultilevelModel objects

Description

Computes the fit measures (chi-square, SRMR, RMSEA) for each level. The observed (auxiliary) correlation matrices of the levels are compared with the ones implied by the model.

Usage

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

Arguments

object

A PlsMultilevelModel object.
saturated

Logical; if TRUE, compute the saturated fit.
mc.reps

Integer; number of observations in the simulated data.
...

Currently unused.

Value

A list with the fit measures of each level (level.1 and level.2).

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)

## S4 method for signature 'PlsMultilevelModel'
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.

Loglikelihood of MC-PLS parameters

Description

Compute Loglikelihood statistics for an MC-PLS model.

Usage

mcpls_loglik(object, boot.R = 500, verbose = interactive(), ...)

## S4 method for signature 'PlsModel'
mcpls_loglik(object, boot.R = 500, verbose = interactive(), ...)

Arguments

object

A fitted [PlsModel] object, using MC-PLS.
boot.R

Integer; Number of bootstrap replicates.
verbose

Logical; Should a progressbar be displayed?
...

Reserved for future extensions.

Value

List with loglikelihood value, expected and observed auxiliary parameters, and variance covariance matrix of the expected auxiliary parameters.

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.

Parameter estimates for PlsMultilevelModel objects

Description

Parameter estimates for PlsMultilevelModel objects

Usage

## S4 method for signature 'PlsMultilevelModel'
parameter_estimates(object, ...)

Arguments

object

A PlsMultilevelModel object.
...

Currently unused.

Value

A PlsSemParTable data frame, with a level column.

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 estimates two-level (multilevel) models, with separate models for the within (level: 1) and between (level: 2) levels.

Usage

pls(
  syntax,
  data,
  standardize = TRUE,
  consistent = NULL,
  bootstrap = FALSE,
  ordered = NULL,
  missing = c("listwise", "mean", "kNN"),
  knn.k = 5,
  mcpls = NULL,
  probit = NULL,
  tolerance = 1e-05,
  max.iter.0_5 = 500L,
  boot.ncores = 1L,
  boot.ncpus = NULL,
  boot.parallel = c("no", "multicore", "multisession", "snow"),
  boot.R = 500L,
  boot.iseed = NULL,
  sample = NULL,
  mc.min.iter = 50L,
  mc.max.iter = 1000L,
  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(),
  mc.rescov = c("auto", "reduced", "full"),
  mc.diag.secant = FALSE,
  mc.small.sample = FALSE,
  mc.small.sample.max.k = 100L,
  mc.small.sample.point.estimate = c("median", "mean"),
  verbose = interactive(),
  boot.optimize = TRUE,
  boot.drop.inadmissible = FALSE,
  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,
  default.path.estimator = c("ols", "gls", "lmer"),
  cluster = NULL,
  inner.weights = c("path", "centroid", "factorial"),
  approach.weights = c("pls", "pca"),
  mlm = NULL,
  level2.cov = c("muml", "means"),
  level2.approach.weights = c("pca", "pls"),
  ...
)

Arguments

syntax

Character string with lavaan-style model syntax describing both measurement (=~) and structural (~) relations. Two-level models are specified with level: 1 and level: 2 blocks (see mlm), where random slopes are specified with rv() modifiers at level 1 (e.g., fw ~ rv(s1)*x1). The random slopes (e.g., s1) are variables at level 2.
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. If NULL (default), FALSE is used for MC-PLS (including two-level models) and for models using lmer as the path estimator, and TRUE otherwise.
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. Rows with missing cluster values are always removed.
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?
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 δ2\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.
mc.rescov

How residual covariances are treated in MC-PLS. One of "auto" (the default), "reduced", or "full". In "reduced" mode residual covariances are not treated as free parameters; they are identified from the rest of the structural model and the disturbances are simulated independently. In "full" mode the endogenous residual covariances (eta ~~ eta and xi ~~ eta) are free parameters, explicitly simulated. "auto" uses "full" when the structural model is estimated by GLS (i.e. the model contains residual covariances) and "reduced" otherwise.
mc.diag.secant

Logical; if TRUE, the MC-PLS root-finding algorithm uses a per-coordinate diagonal-secant step (estimating each coordinate's local slope from consecutive iterates), instead of the standard Robbins-Monro step. This might be usefull if the binding funtion is non-monotone.
mc.small.sample

Logical; if TRUE, average MC-PLS estimating equations over simulated samples of the observed sample size. If FALSE (default), fit one sample using all simulated observations. This assumes that the auxiliary estimator (i.e., traditional PLS) has negligible finite sample bias. I.e., that the bias of the estimator is not affected by the sample size.
mc.small.sample.max.k

Maximum number of simulated samples to average when mc.small.sample = TRUE. Defaults to 100. The number of samples is also limited by mc.reps, rounded down to a multiple of the observed sample size, with at least one sample.
mc.small.sample.point.estimate

Which point estimate of the simulated auxiliary parameters the root equation matches to the observed ones, when mc.small.sample = TRUE? "mean" solves E[θ∗∣θ]=θ^∗E[\theta^{*}|\theta] = \hat{\theta}^{*}. "median" (the default) solves median[θ∗∣θ]=θ^∗median[\theta^{*}|\theta] = \hat{\theta}^{*}.

The median commutes with the (monotone) binding function where the mean does not, so median-matching targets a median-unbiased estimator. This removes the finite-sample bias. which can be introduced by the curvature size models, and when the indicators are uninformative (small loadings, few categories, strongly assymetric thresholds). It makes the estimating function somewhat noisier for a given number of simulated samples. Ignored when mc.small.sample = FALSE.
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.
boot.drop.inadmissible

Logical; if TRUE and bootstrap = TRUE, bootstrap replicates that yield an inadmissible solution (e.g. a Heywood case) are discarded before computing standard errors, just like replicates where the estimation procedure fails outright. Defaults to FALSE, which keeps inadmissible replicates. In either case the number of inadmissible replicates is reported. Note that dropping inadmissible solutions conditions the bootstrap distribution on well-behaved resamples and may bias the standard errors downward.
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.
default.path.estimator

Character string selecting the estimator used for the structural (path) model when the model does not require Generalized Least Squares (GLS), or Linear Mixed-Effects Regression (LMER). The default "ols" uses Ordinary Least Squares whenever possible, falling back to GLS automatically when the model contains residual covariances. Setting default.path.estimator = "gls" forces GLS estimation of the structural model even when OLS would otherwise be used.
cluster

Optional character vector naming the cluster variable(s) in data. The cluster variables are stored alongside the (standardized) indicators, and bootstrapping resamples whole clusters instead of rows. Required for two-level models (a single cluster variable).
inner.weights

Character string selecting the inner weighting scheme used with approach.weights = "pls". One of: "centroid", "factorial", or "path". Defaults to "path".
approach.weights

Character string selecting the approach used to estimate the outer weights. "pls" (default) uses the PLS algorithm, with the inner weighting scheme given by inner.weights. "pca" forms the weights from each construct's own indicators only, ignoring the structural.
mlm

Should the model be estimated as a two-level (multilevel) model? If NULL (default), this is detected from syntax, i.e., whether it has level: 1 and level: 2 blocks. Two-level models are estimated using an extension of the MC-PLSc estimator. The mc.* arguments (e.g., mc.max.iter, mc.reps) are used when they are specified, whereas arguments like standardize are (currently) not supported. Standard errors (bootstrap = TRUE) are computed using the delta method.
level2.cov

Two-level models only. How the (co-)variances of the variables at level 2 are computed. "means" uses the covariances of the cluster means. "muml" (default) uses Muthen's (1994) estimator of the between-cluster covariance matrix, which corrects for the within-cluster variation in the cluster means.
level2.approach.weights

Two-level models only. The approach used to estimate the outer weights of the level 2 model (approach.weights applies to the level 1 model). Defaults to "pca".
...

Internal arguments. For advanced users only.

Value

A PlsModel object containing the estimated parameters, fit measures, factor scores, and any bootstrap results (a PlsMultilevelModel object for two-level models). 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)

Retrieve bootstrap coefficient matrix

Description

Retrieve bootstrap coefficient matrix

Usage

pls_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)
pls_boot(fit)

Chi-Square

Description

Compute Chi-Square value for a PLS model.

Usage

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

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

## S4 method for signature 'PlsModel'
pls_chisq_df(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

Chi-Square value

Chi-Square Degrees of Freedom

Description

Compute Chi-Square degrees of freedom for a PLS model.

Usage

pls_chisq_df(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

Chi-Square degrees of freedom

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.

Implied Construct Correlation Matrix

Description

Returns the implied construct correlation matrix for a fitted model.

Usage

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

## S4 method for signature 'PlsModel'
pls_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

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

## S4 method for signature 'PlsModel'
pls_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.

Implied Joint Correlation Matrix

Description

Returns the joint implied correlation matrix of the observed and latent variables for a fitted model.

Usage

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

## S4 method for signature 'PlsModel'
pls_implied_joint_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].

Inspect a fitted PLS-SEM model

Description

Extract important information from a fitted PlsModel. The interface is modelled after lavaan::lavInspect(): a single what argument selects which piece of information to return.

Usage

pls_inspect(object, what = "estimates", ...)

## S4 method for signature 'PlsModel'
pls_inspect(object, what = "estimates", ...)

Arguments

object

A fitted PlsModel object.
what

A single string selecting what to extract (case-insensitive); defaults to "estimates". Several values accept aliases, given in parentheses. One of:

"estimates" (aliases "est", "x", "matrices")

A list of the estimated model matrices in lavaan-style representation (lambda, wmat, theta, psi, C, gamma).

"lambda", "wmat", "theta", "psi", "C", "gamma"

The corresponding single matrix from the "estimates" list.

"coef" (alias "coefficients")

The model coefficients.

"par" (alias "partable")

The parameter table.

"fit"

Fit measures.

"mcpls.history" (alias "history")

The history of the MC-PLS estimates.

"chisq"

The model chi-square statistic.

"chisq.df" (alias "df")

The chi-square degrees of freedom.

"srmr"

The standardized root mean square residual.

"rmsea"

The root mean square error of approximation.

"se"

The standard errors of the estimates.

"vcov"

The variance-covariance matrix of the estimates.

"boot"

The bootstrap results.

"info"

A list with the number of observations (nobs), the number of latent variables (nlv), the number of observed variables (nov), and the estimation modes ("A"/"B") for each latent variable.

"status"

A list with the number of iterations, whether the algorithm converged, and whether the solution is admissible.

"qualities"

The construct qualities (Q2Q^2).

"reliabilities" (alias "rel")

The construct reliabilities.

"cov.lv"

The model-implied covariance matrix of the latent variables.

"cov.ov"

The model-implied covariance matrix of the observed variables.

"cov.all"

The joint model-implied covariance matrix of the observed and latent variables.

"r2.lv", "r2.ov", "r2.all"

The model-implied R2R^2 for the latent variables, the observed variables, or both.

"data"

The (standardized) data matrix used for estimation.
...

Currently ignored.

Value

The requested information; the type depends on what (see above).

Examples

## Not run: 
  fit <- pls(model, data = data)
  pls_inspect(fit, "info")
  pls_inspect(fit, "cov.lv")

## End(Not run)

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", prediction benchmarks are applied to all of the indicators in the model.

Value

A PlsSemPredict object with matrices and benchmark results.

RMSEA

Description

Compute RMSEA for a PLS model.

Usage

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

## S4 method for signature 'PlsModel'
pls_rmsea(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

RMSEA value

SRMR

Description

Compute SRMR for a PLS model.

Usage

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

## S4 method for signature 'PlsModel'
pls_srmr(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

SRMR value

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 SummaryPlsMultilevel object

Description

Print a SummaryPlsMultilevel object

Usage

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

Arguments

x

A SummaryPlsMultilevel object as returned by summary().
...

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.

randomSlopes

Description

A simulated dataset.

Examples

syntax <- '
  f =~ y1 + y2 + y3
  f ~ rv(s1)*x1 + rv(s2)*x2 + x3
'

fit <- pls(syntax, data = randomSlopes, cluster = "cluster")
summary(fit)

randomSlopesOrdered

Description

A simulated dataset.

Examples

syntax <- '
  f =~ y1 + y2 + y3
  f ~ rv(s1)*x1 + rv(s2)*x2 + x3
'

fit <- pls(syntax, data = randomSlopesOrdered, cluster = "cluster")
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.

Show a PlsMultilevelModel object

Description

Show a PlsMultilevelModel object

Usage

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

Arguments

object

A PlsMultilevelModel 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, unstandardized = FALSE, ci = FALSE, ...)

Arguments

object

A PlsModel object.
fit

Logical; Whether to compute fit measures.
unstandardized

Logical; Should unstandardized estiamtes be included?
ci

Logical; Should confidence intervals for parameter estimates be included?
...

Arguments passes to unstandardized_estimates.

Value

A SummaryPlsSem list with formatted results.

Summarize a fitted PlsMultilevelModel model

Description

Summarize a fitted PlsMultilevelModel model

Usage

## S4 method for signature 'PlsMultilevelModel'
summary(object, fit = TRUE, unstandardized = FALSE, ci = FALSE, ...)

Arguments

object

A PlsMultilevelModel object.
fit

Logical; Whether to compute fit measures (for each level).
unstandardized

Logical; Should unstandardized estimates be included?
ci

Logical; Should confidence intervals for parameter estimates be included?
...

Arguments passed to unstandardized_estimates.

Value

A SummaryPlsMultilevel 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")

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)

Unstandardized Parameter Estimates

Description

Transform parameter estimates from a fitted PLS-SEM model to observed- and latent-variable scales. Variables not selected through unstandardized remain on their standardized scales.

Usage

unstandardized_estimates(
  model,
  unstandardized = "all",
  se = c("delta", "none"),
  scale.uncertainty = FALSE,
  eps = 1e-04,
  zero.tol = 1e-10,
  rm.tmp.ov = TRUE,
  clean.tmp.ind = TRUE,
  clean.tmp.mimic = TRUE
)

## S4 method for signature 'PlsModel'
unstandardized_estimates(
  model,
  unstandardized = "all",
  se = c("delta", "none"),
  scale.uncertainty = FALSE,
  eps = 1e-04,
  zero.tol = 1e-10,
  rm.tmp.ov = TRUE,
  clean.tmp.ind = TRUE,
  clean.tmp.mimic = TRUE
)

Arguments

model

A fitted PlsModel object.
unstandardized

Character vector naming variables to unstandardize, or one of "all", "ov", or "lv".
se

Character string selecting delta-method standard errors ("delta") or no standard errors ("none").
scale.uncertainty

Should scale uncertainty be included? defaults to FALSE.
eps

Positive numeric finite-difference step used for the delta-method Jacobian.
zero.tol

Non-negative numeric tolerance below which standard errors are returned as missing.
rm.tmp.ov

Logical; whether rows involving temporary observed variables should be removed from the returned parameter table.
clean.tmp.ind

Logical; whether rows involving temporary indicators should be cleaned from the returned parameter table.
clean.tmp.mimic

Logical; whether rows involving temporary mimic indicators should be cleaned from the returned parameter table.

Value

A PlsSemParTable containing transformed estimates and (when requested) delta-method standard errors. The transformed covariance matrix is stored in the "vcov" attribute.

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 + INT:PBC
'

fit <- pls(tpb, modsem::TPB, bootstrap = TRUE, boot.R = 50)
unstandardized_estimates(fit)

Unstandardized estimates for PlsMultilevelModel objects

Description

Computes the unstandardized estimates of each level of a two-level model.

Usage

## S4 method for signature 'PlsMultilevelModel'
unstandardized_estimates(
  model,
  unstandardized = "all",
  se = c("delta", "none"),
  scale.uncertainty = FALSE,
  eps = 1e-04,
  zero.tol = 1e-10,
  rm.tmp.ov = TRUE,
  clean.tmp.ind = TRUE,
  clean.tmp.mimic = TRUE
)

Arguments

model

A fitted PlsModel object.
unstandardized

Character vector naming variables to unstandardize, or one of "all", "ov", or "lv".
se

Character string selecting delta-method standard errors ("delta") or no standard errors ("none").
scale.uncertainty

Should scale uncertainty be included? defaults to FALSE.
eps

Positive numeric finite-difference step used for the delta-method Jacobian.
zero.tol

Non-negative numeric tolerance below which standard errors are returned as missing.
rm.tmp.ov

Logical; whether rows involving temporary observed variables should be removed from the returned parameter table.
clean.tmp.ind

Logical; whether rows involving temporary indicators should be cleaned from the returned parameter table.
clean.tmp.mimic

Logical; whether rows involving temporary mimic indicators should be cleaned from the returned parameter table.

Details

The levels are unstandardized separately, using the (decomposed) scales of the variables at each level, i.e., sqrt(1 - icc) * sd at level 1, and sqrt(icc) * sd at level 2 for variables at both levels. The latent variables are scaled by their first indicators. The scales of the random slopes (y ~ rv(s) * x) are rsd * sd(y) / sd(x), where sd(y) and sd(x) are the scales of y and x at level 1. For ordered variables, the latent responses are scaled such that their (total) residual variances are 1, i.e., (1 - icc) * theta_W + icc * theta_B = 1, where theta_W and theta_B are the standardized residual variances at each level. The thresholds are rescaled accordingly.

Value

A PlsSemParTable data frame, with a level column.

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, use.labels = TRUE, ...)

Arguments

object

A PlsModel object.
use.labels

Logical; Should parameter labels be used as names?
...

Currently unused.

Value

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

Extract the variance-covariance matrix from a PlsMultilevelModel model

Description

Delta-method (co-)variances, see the bootstrap argument of mpls(). Parameters at the between level (level 2) are suffixed with .l2.

Usage

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

Arguments

object

A PlsMultilevelModel object.
...

Currently unused.

Value

A PlsSemMatrix, or NULL if no standard errors were computed.