Type:	Package
Title:	Partial Least Squares Path Modeling (PLS-PM)
Version:	0.6.0
Date:	2025-09-25
Author:	Gaston Sanchez [aut], Laura Trinchera [aut], Giorgio Russolillo [aut], Frederic Bertrand [cre]
Maintainer:	Frederic Bertrand <frederic.bertrand@lecnam.net>
Description:	Partial Least Squares Path Modeling (PLS-PM), Tenenhaus, Esposito Vinzi, Chatelin, Lauro (2005) <doi:10.1016/j.csda.2004.03.005>, analysis for both metric and non-metric data, as well as REBUS analysis, Esposito Vinzi, Trinchera, Squillacciotti, and Tenenhaus (2008) <doi:10.1002/asmb.728>.
Depends:	R (≥ 3.0.1)
Imports:	tester, turner, diagram, shape, amap, methods
Suggests:	FactoMineR, ggplot2, reshape, knitr, testthat (≥ 3.0.0)
URL:	https://github.com/gastonstat/plspm
BugReports:	https://github.com/gastonstat/plspm/issues
VignetteBuilder:	knitr
License:	GPL-3
LazyLoad:	yes
NeedsCompilation:	no
Repository:	CRAN
Encoding:	UTF-8
Collate:	'plspm.R' 'auxiliar.R' 'check_arguments.R' 'check_specifications.R' 'get_alpha.R' 'get_ave.R' 'get_boots.R' 'get_dummies.R' 'get_effects.R' 'get_generals.R' 'get_gof.R' 'get_inner_summary.R' 'get_manifests.R' 'get_metric.R' 'get_nom_scale.R' 'get_num_scale.R' 'get_ord_scale.R' 'get_path_scheme.R' 'get_paths.R' 'get_plsr1.R' 'get_PLSRdoubleQ.R' 'get_rank.R' 'get_rho.R' 'get_scores.R' 'get_treated_data.R' 'get_unidim.R' 'get_weights.R' 'get_weights_nonmetric.R' 'innerplot.R' 'outerplot.R' 'plot.plspm.R' 'rescale.R' 'summary_plspm.R' 'test_manifest_scaling.R' 'test_null_weights.R' 'unidimensionality.R' 'test_factors.R' 'russett-data.R' 'plspm.fit.R' 'plspm.groups.R' 'test_dataset.R' 'get_GQI.R' 'get_locals_test.R' 'get_scaled_data.R' 'it.reb.R' 'local.models.R' 'print.rebus.R' 'rebus.pls.R' 'rebus.test.R' 'res.clus.R' 'get_PLSR.R' 'get_PLSR_NA.R' 'quantiplot.R' 'plspm-package.R'
RoxygenNote:	7.3.3
Config/testthat/edition:	3
Packaged:	2025-09-25 23:35:32 UTC; bertran7
Date/Publication:	2025-09-26 23:00:11 UTC

plspm: Partial Least Squares Path Modeling (PLS-PM)

Description

Partial Least Squares Path Modeling (PLS-PM), Tenenhaus, Esposito Vinzi, Chatelin, Lauro (2005) doi:10.1016/j.csda.2004.03.005, analysis for both metric and non-metric data, as well as REBUS analysis, Esposito Vinzi, Trinchera, Squillacciotti, and Tenenhaus (2008) doi:10.1002/asmb.728.

Author(s)

This package was written by Gaston Sanchez. Maintainer: Frederic Bertrand <frederic.bertrand@lecnam.net>

See Also

Useful links:

• https://github.com/gastonstat/plspm

• Report bugs at https://github.com/gastonstat/plspm/issues

Cronbach's alpha

Description

Cronbach's alpha of a single block of variables

Usage

  alpha(X)

Arguments

Value

Cronbach's alpha

Author(s)

Gaston Sanchez

See Also

rho, unidim

Examples

## Not run: 
 # load dataset satisfaction
 data(satisfaction)

 # block Image (first 5 columns of satisfaction)
 Image = satisfaction[,1:5]

 # compute Cronbach's alpha for Image block
 alpha(Image)
 
## End(Not run)

Arizona vegetation dataset

Description

This dataset gives the measurements of 16 vegetation communitites in the Santa Catalina Mountains, Arizona. The measurements were taken along different elevations from fir forest at high elevations, through pine forest, woodlands, and desert grassland.

Format

A data frame with 16 observations and 8 variables. The variables refer to three latent concepts: 1) ENV=environment, 2) SOIL=soil, and 3) DIV=diversity.

The complete name of the rows are: 1) Abies lasiocarpa, 2) Abies concolor, 3) Pseudotsuga menziesii-Abies Concolor, 4) Pseudotsuga menziesii, 5) Pinus ponderosa-Pinus strobiformis, 6) Pinus ponderosa, 7) Pinus ponderosa-Quercus, 8) Pinus chihuahuana, 9) Pygmy conifer-oak scrub, 10) Open oak woodland, 11) Bouteloua curtipendula, 12) Spinose-suffrutescent, 13) Cercidium microphyllum, 14) Larrea divaricata, 15) Cercocarpus breviflorus, 16) Populus tremuloides.

Source

Mixed data from Whittaker et al (1968), and Whittaker and Niering (1975). See References below.

References

Whittaker, R. H., Buol, S. W., Niering, W. A., and Havens, Y. H. (1968) A Soil and Vegetation Pattern in the Santa Catalina Mountains, Arizona. Soil Science, 105, pp. 440-450.

Whittaker, R. H., and Niering, W. A. (1975) Vegetation of the Santa Catalina Mountains, Arizona. V. Biomass, Production, and Diversity Along the Elevation Gradient. Ecology, 56, pp. 771-790.

Examples

  data(arizona)
  arizona

Cereals datset

Description

Data with several variables of different brands of cereal

Usage

data(cereals)

Format

A data frame with 77 observations on the following 15 variables.

mfr

Manufacturer of cereal

type

type: cold or hot

calories

calories per serving

protein

grams of protein

fat

grams of fat

sodium

milligrams of sodium

fiber

grams of dietary fiber

carbo

grams of complex carbohydrates

sugars

grams of sugars

potass

milligrams of potassium

vitamins

vitamins and minerals - 0, 25, or 100, indicating the typical percentage of FDA recommended

shelf

display shelf (1, 2, or 3, counting from the floor)

weight

weight in ounces of one serving

cups

number of cups in one serving

rating

a rating of the cereals

Source

https://dasl.datadescription.com/datafile/cereals/

Examples

# load data
data(cereals)

# take a peek
head(cereals)

Check arguments for plspm and plspm.fit

Description

Internal function not to be called by the user

Usage

  check_args(Data, path_matrix, blocks, scaling, modes,
    scheme, scaled, tol, maxiter, plscomp, boot.val, br,
    dataset)

Arguments

Details

Internal function. check_args is called by plspm.

Value

list of validated arguments

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Check well defined blocks

Description

Internal function not to be called by the user

Usage

  check_blocks(blocks, Data)

Arguments

Details

Internal function. check_blocks is called by check_args.

Value

validated blocks (output in numeric format)

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Check bootstrap options

Description

Internal function not to be called by the user

Usage

  check_boot(boot.val, br)

Arguments

Details

Internal function. check_boot is called by check_args.

Value

validated bootstrap options

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Check Data

Description

Internal function not to be called by the user

Usage

  check_data(Data)

Arguments

Details

Internal function. check_data is called by check_args.

Value

validated Data

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Check maximum number of iterations

Description

Internal function not to be called by the user

Usage

  check_maxiter(maxiter)

Arguments

Details

Internal function. check_maxiter is called by check_specs.

Value

validated maxiter

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Check congruence between inner and outer models

Description

Internal function not to be called by the user

Usage

  check_model(path_matrix, blocks)

Arguments

Details

Internal function. check_model is called by check_args.

Value

an error if there is something wrong

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Check modes

Description

Internal function not to be called by the user

Usage

  check_modes(modes, blocks)

Arguments

Details

Internal function. check_modes is called by check_specs.

Value

validated modes

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Check path matrix

Description

Internal function not to be called by the user

Usage

  check_path(path_matrix)

Arguments

Details

Internal function. check_path is called by check_args.

Value

validated path matrix

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Check vector of PLS components (for non-metric plspm)

Description

Internal function not to be called by the user

Usage

  check_plscomp(plscomp, scaling, modes)

Arguments

Details

Internal function. check_plscomp is called by check_specs.

Value

validated plscomp

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Check types of measurement scales and metric

Description

Internal function not to be called by the user

Usage

  check_scaling(scaling, scaled, blocks)

Arguments

Details

Internal function. check_scaling is called by check_specs.

Value

list with validated scaling and scaled

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Check scheme

Description

Internal function not to be called by the user

Usage

  check_scheme(scheme)

Arguments

Details

Internal function. check_scheme is called by check_specs.

Value

validated scheme

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Check specifications of PLS-PM algorithm

Description

Internal function not to be called by the user

Usage

  check_specs(blocks, scaling, modes, scheme, scaled, tol,
    maxiter, plscomp)

Arguments

Details

Internal function. check_specs is called by check_args.

Value

validated specifications

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

if scaling is specified, it overrides scaled

Check tolerance threshold

Description

Internal function not to be called by the user

Usage

  check_tol(tol)

Arguments

Details

Internal function. check_tol is called by check_specs.

Value

validated tol

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

College datasets

Description

Dataset with different scores (high school, undergrad basic, undergrad intermediate, and GPA) of graduated college student in life sciences majors

Usage

data(college)

Format

A data frame with 352 students on the following 13 variables. The variables may be used to construct four suggested latent concepts: 1) HighSchool=High School related scores, 2) Basic=scores of basic courses, 3) InterCourse=Scores of intermediate courses, 4) GPA=Final GPA (Graduate Point Average)

Examples

# load data
data(college)

# take a peek
head(college)

Dummy by Giorgio

Description

Internal function not to be called by the user

Usage

  dummy.G(Y, X)

Arguments

Details

Internal function. dummy.G is called by get_PLSRdoubleQ.

Value

list with Xdummy, Quant, eta2

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Futbol dataset from Spain-England-Italy

Description

This data set contains the results of the teams in the Spanish, English, and Italian football leagues 2009-2010 season.

Usage

data(futbol)

Format

A data frame with 60 observations on the following 12 variables. The variables may be used to construct three latent concepts: 1) ATTACK=Attack, 2) DEFENSE=Defense, 3) SUCCESS=Success.

Source

League Day.

Examples

  data(futbol)
  futbol

Group Quality Index

Description

Calculate Group Quality Index for REBUS-PLS

Usage

  get_GQI(pls, part, DM)

Arguments

Internal PLS regression (full data)

Description

Internal function not to be called by the user

Usage

  get_PLSR(Y, X, ncomp)

Arguments

Details

Internal function. get_PLSR

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Internal PLS regression with missing values

Description

Internal function not to be called by the user

Usage

  get_PLSR_NA(Y, X, ncomp)

Arguments

Details

Internal function. get_PLSR_NA

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

get_PLSRdoubleQ

Description

Internal function not to be called by the user

Usage

  get_PLSRdoubleQ(Y = NULL, Yc = NULL, X = NULL, Xc = NULL,
    ncomp)

Arguments

Details

Internal function. get_PLSRdoubleQ

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Calculate Cronbach's alpha

Description

Internal function not to be called by the user

Usage

  get_alpha(Block)

Arguments

Details

Internal function. get_alpha is called by get_unidim and alpha.

Value

Cronbach's alpha

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Calculate AVE (Average Variance Extracted)

Description

Internal function not to be called by the user

Usage

  get_ave(communality)

Arguments

Details

Internal function. get_ave is called by plspm.

Value

vector of average variance extracted for each block

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Get data frame with bootstrap statistics

Description

Internal function not to be called by the user

Usage

  get_boot_stats(MATRIX, original)

Arguments

Details

Internal function. get_boot_stats is called by get_boots.

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Performs bootstrap validation in plspm

Description

Internal function not to be called by the user

Usage

  get_boots(DM, path_matrix, blocks, specs, br)

Arguments

Details

Internal function. get_boots is called by plspm.

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Scaling data outside plspm

Description

Internal function not to be called by the user

Usage

  get_data_scaled(DM, scaled)

Arguments

Details

Internal function. get_scaled_data is called by plspm.groups and others.

Value

matrix or data frame of (un)scaled MVs

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

In non-metric case, all mvs are starndardized, and those ordinal or nominal are rankified

Dummy matrices for categorical manifest variables

Description

Internal function not to be called by the user

Usage

  get_dummies(MV, specs)

Arguments

Details

Internal function. get_dummies is called by plspm.

Value

dummies list with dummy matrices for categorical manifest variables

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

If there are no categorical variables specified in specs, get_dummies returns NULL

Non-Metric Dummy

Description

Internal function. get_dummy is called by get_dummies. Transforms a vector of natural numbers from 1 to p into the corresponding p x p dummy matrix

Usage

  get_dummy(x)

Arguments

Value

the dummy matrix

Path coefficient effects for plspm

Description

Internal function not to be called by the user

Usage

  get_effects(Path)

Arguments

Details

Internal function. get_effects is called by plspm.

Value

data frame with relationships, direct, indirect, and total effects

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Get general parameters

Description

Internal function not to be called by the user

Usage

  get_generals(MV, path_matrix)

Arguments

Details

Internal function. get_generals is called by plspm. This function gets the number and names of: observations, manifest variables, and latent variables

Value

list with number and names of observations, MVs and LVs

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Goodness-of-fit for plspm

Description

Internal function not to be called by the user

Usage

  get_gof(comu, R2, blocks, path_matrix)

Arguments

Details

Internal function. get_gof is called by plspm

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Inner summary assessment

Description

Internal function not to be called by the user

Usage

  get_inner_summary(path_matrix, blocks, modes,
    communality, redundancy, R2)

Arguments

Details

Internal function. get_inner_summary is called by plspm.

Value

A data frame with the following columns:

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Local groups comparison test

Description

Calculate Group Quality Index for REBUS-PLS Internal function.

Usage

  get_locals_test(X, pls, g)

Arguments

Value

list with path coefficients, loadings, and gof

Building data matrix with manifest variables

Description

Internal function not to be called by the user

Usage

  get_manifests(Data, blocks)

Arguments

Details

Internal function. get_manifests is called by plspm.

Value

matrix or data frame of selected manifest variables

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Type of metric based on scaling measurement

Description

Internal function not to be called by the user

Usage

  get_metric(scaling)

Arguments

Details

Internal function. get_metric is called by plspm. It is used to decide what function apply for the iterative process of the PLS-PM algorithm.

Value

metric type of metric (metric data = TRUE / non-metric data = FALSE)

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

If scaling is NULL, apply get_weights(), otherwise apply get_weights_nonmetric()

Non-Metric Nominal Scale

Description

Internal function not to be called by the user

Usage

  get_nom_scale(y, x, Xdummy)

Arguments

Details

Internal function. get_nom_scale is called by plspm.

Value

scaled matrix

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

This function replaces the elements of x by the the means of y conditioned to the levels of x

Non-Metric Numerical Scale

Description

Internal function not to be called by the user

Usage

  get_num_scale(X)

Arguments

Details

Internal function. get_num_scale is called by plspm.

Value

scaled matrix

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

scales a matrix X in such a way that mean(X[,j])=0 and varpop(X[,j])=1 this means that sum(X[,j]^2) = n if MD, sum(X[,j]^2, na.rm=T) = number of available elements

Transform factors in MV into numeric

Description

Internal function not to be called by the user

Usage

  get_numerics(MV)

Arguments

Details

Internal function. get_numerics is called by get_treated_data.

Value

list with transformed MV and categories of factors

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

This function is used when there are categorical variables defined as 'factors'. The idea is to convert those factors into numeric vectors while keeping the levels (ie categories) in a separate list

Non-Metric Ordinal Scale

Description

Internal function not to be called by the user

Usage

  get_ord_scale(y, x, Xdummy)

Arguments

Details

Internal function. get_ord_scale is called by plspm.

Value

scaled matrix

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

This function replaces the elements of x by the the means of y conditioned to the levels of x

Calculate inner weighting path scheme

Description

Internal function not to be called by the user

Usage

  get_path_scheme(path_matrix, LV)

Arguments

Details

Internal function. get_path_scheme is called by get_weights

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Calculate path coefficients for plspm

Description

Internal function not to be called by the user

Usage

  get_paths(path_matrix, Y_lvs, full = TRUE)

Arguments

Details

Internal function. get_paths is called by plspm.

Value

list with inner results, path coefs matrix, R2, and residuals

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

PLS regression for plspm

Description

Internal function not to be called by the user

Usage

  get_plsr1(predictors, response, nc = NULL, scaled = TRUE)

Arguments

Details

Internal function. get_plsr1 performs PLS-R1.

Value

A list with pls regression results

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Rank of a non-metric variable

Description

Internal function not to be called by the user

Usage

  get_rank(X)

Arguments

Details

Internal function. get_rank is called by get_treated_data and get_weights.

Value

vector with the corresponding rank for each category

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Calculate Dillon-Goldstein's rho

Description

Internal function not to be called by the user

Usage

  get_rho(Block, score)

Arguments

Details

Internal function. get_rho is called by get_unidim and rho.

Value

Dillon-Goldstein's rho

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Calculate Latent Variable Scores

Description

Internal function not to be called by the user

Usage

  get_scores(X, W)

Arguments

Details

Internal function. get_scores is called by plspm.

Value

Scores matrix of latent variables scores

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Apply corresponding treatment to MV

Description

Internal function not to be called by the user

Usage

  get_treated_data(MV, specs)

Arguments

Details

Internal function. get_treated_data is called by plspm.

Value

matrix or data frame of treated MVs (scaling)

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

In non-metric case, all mvs are starndardized, and those ordinal or nominal are rankified

Unidimensionality of reflective blocks

Description

Internal function not to be called by the user

Usage

  get_unidim(DM, blocks, modes)

Arguments

Details

Internal function. get_unidim is called by plspm.

Value

A data frame with the following columns:

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Outer Weights

Description

Internal function not to be called by the user

Usage

  get_weights(X, path_matrix, blocks, specs)

Arguments

Details

Internal function. get_weights is called by plspm

Value

list of outer weights, ODM, iter

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

Calculate outer weights (under Lohmoller's algorithm)

Outer Weights Non-Metric Data

Description

Internal function not to be called by the user

Usage

  get_weights_nonmetric(X, path_matrix, blocks, specs)

Arguments

Details

Internal function. get_weights is called by plspm

Value

list of outer weights, ODM, scores, QQ, iter

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

Calculate outer weights for non-metric data (under Lohmoller's algorithm)

Plot inner model

Description

Plot the inner (structural) model for objects of class "plspm", as well as path matrices

Usage

  innerplot(x, colpos = "#6890c4BB", colneg = "#f9675dBB",
    box.prop = 0.55, box.size = 0.08, box.cex = 1,
    box.col = "gray95", lcol = "gray95", box.lwd = 2,
    txt.col = "gray50", shadow.size = 0, curve = 0,
    lwd = 3, arr.pos = 0.5, arr.width = 0.2, arr.lwd = 3,
    cex.txt = 0.9, show.values = FALSE, ...)

Arguments

Note

innerplot uses the function plotmat in package diagram.
https://cran.r-project.org/package=diagram/vignettes/diagram.pdf

See Also

plot.plspm, outerplot

Presence of missing values

Description

Internal function not to be called by the user

Usage

  is_missing(x)

Arguments

Details

Internal function. is_missing is called by get_weights_nonmetric

Value

vector indicating whether each element in x contains NAs

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Iterative steps of Response-Based Unit Segmentation (REBUS)

Description

REBUS-PLS is an iterative algorithm for performing response based clustering in a PLS-PM framework. it.reb allows to perform the iterative steps of the REBUS-PLS Algorithm. It provides summarized results for final local models and the final partition of the units. Before running this function, it is necessary to run the res.clus function to choose the number of classes to take into account.

Usage

  it.reb(pls, hclus.res, nk, Y = NULL, stop.crit = 0.005,
    iter.max = 100)

Arguments

Value

an object of class "rebus"

Author(s)

Laura Trinchera, Gaston Sanchez

References

Esposito Vinzi, V., Trinchera, L., Squillacciotti, S., and Tenenhaus, M. (2008) REBUS-PLS: A Response-Based Procedure for detecting Unit Segments in PLS Path Modeling. Applied Stochastic Models in Business and Industry (ASMBI), 24, pp. 439-458.

Trinchera, L. (2007) Unobserved Heterogeneity in Structural Equation Models: a new approach to latent class detection in PLS Path Modeling. Ph.D. Thesis, University of Naples "Federico II", Naples, Italy.

See Also

plspm, rebus.pls, res.clus

Examples

## Not run: 
## Example of REBUS PLS with simulated data

# load simdata
data("simdata", package='plspm')

# Calculate global plspm
sim_inner = matrix(c(0,0,0,0,0,0,1,1,0), 3, 3, byrow=TRUE)
dimnames(sim_inner) = list(c("Price", "Quality", "Satisfaction"),
                           c("Price", "Quality", "Satisfaction"))
sim_outer = list(c(1,2,3,4,5), c(6,7,8,9,10), c(11,12,13))
sim_mod = c("A", "A", "A")  # reflective indicators
sim_global = plspm(simdata, sim_inner,
                   sim_outer, modes=sim_mod)
sim_global

## Then compute cluster analysis on residuals of global model
sim_clus = res.clus(sim_global)

## To complete REBUS, run iterative algorithm
rebus_sim = it.reb(sim_global, sim_clus, nk=2,
                   stop.crit=0.005, iter.max=100)

## You can also compute complete outputs
## for local models by running:
local_rebus = local.models(sim_global, rebus_sim)

# Display plspm summary for first local model
summary(local_rebus$loc.model.1)

## End(Not run)

PLS-PM for global and local models

Description

Calculates PLS-PM for global and local models from a given partition

Usage

  local.models(pls, y, Y = NULL)

Arguments

Details

local.models calculates PLS-PM for the global model (i.e. over all observations) as well as PLS-PM for local models (i.e. observations of different partitions).

When y is an object of class "rebus", local.models is applied to the classes obtained from the REBUS algorithm.

When y is an integer vector or a factor, the values or levels are assumed to represent the group to which each observation belongs. In this case, the function local.models calculates PLS-PM for the global model, as well as PLS-PM for each group (local models).

When the object pls does not contain a data matrix (i.e. pls$data=NULL), the user must provide the data matrix or data frame in Y.

The original parameters modes, scheme, scaled, tol, and iter from the object pls are taken.

Value

An object of class "local.models", basically a list of length k+1, where k is the number of classes.

Note

Each element of the list is an object of class "plspm". Thus, in order to examine the results for each local model, it is necessary to use the summary function.

Author(s)

Laura Trinchera, Gaston Sanchez

See Also

rebus.pls

Examples

## Not run: 
## Example of REBUS PLS with simulated data

# load simdata
data("simdata", package='plspm')

# Calculate global plspm
sim_inner = matrix(c(0,0,0,0,0,0,1,1,0), 3, 3, byrow=TRUE)
dimnames(sim_inner) = list(c("Price", "Quality", "Satisfaction"),
                           c("Price", "Quality", "Satisfaction"))
sim_outer = list(c(1,2,3,4,5), c(6,7,8,9,10), c(11,12,13))
sim_mod = c("A", "A", "A")  # reflective indicators
sim_global = plspm(simdata, sim_inner,
                   sim_outer, modes=sim_mod)
sim_global

## Then compute cluster analysis on residuals of global model
sim_clus = res.clus(sim_global)

## To complete REBUS, run iterative algorithm
rebus_sim = it.reb(sim_global, sim_clus, nk=2,
                   stop.crit=0.005, iter.max=100)

## You can also compute complete outputs
## for local models by running:
local_rebus = local.models(sim_global, rebus_sim)

# Display plspm summary for first local model
summary(local_rebus$loc.model.1)

## End(Not run)

ECSI Mobile Phone Provider dataset

Description

This table contains data from the article by Tenenhaus et al. (2005), see reference below.

Usage

data(mobile)

Format

A data frame with 250 observations on 24 variables on a scale from 0 to 100. The variables refer to seven latent concepts: 1) IMAG=Image, 2) EXPE=Expectations, 3) QUAL=Quality, 4) VAL=Value, 5) SAT=Satisfaction, 6) COM=Complaints, and 7) LOY=Loyalty.

IMAG: Includes variables such as reputation, trustworthiness, seriousness, and caring about customer's needs.
EXPE: Includes variables such as products and services provided and expectations for the overall quality.
QUAL: Includes variables such as reliable products and services, range of products and services, and overall perceived quality.
VAL: Includes variables such as quality relative to price, and price relative to quality.
SAT: Includes variables such as overall rating of satisfaction, fulfillment of expectations, satisfaction relative to other phone providers.
COM: Includes one variable defining how well or poorly custmer's complaints were handled.
LOY: Includes variables such as propensity to choose the same phone provider again, propensity to switch to other phone provider, intention to recommend the phone provider to friends.

ima1

First MV of the block Image

ima2

Second MV of the block Image

ima3

Third MV of the block Image

ima4

Fourth MV of the block Image

ima5

Fifth MV of the block Image

exp1

First MV of the block Expectations

exp2

Second MV of the block Expectations

exp3

Third MV of the block Expectations

qua1

First MV of the block Quality

qua2

Second MV of the block Quality

qua3

Third MV of the block Quality

qua4

Fourth MV of the block Quality

qua5

Fifth MV of the block Quality

qua6

Sixth MV of the block Quality

qua7

Seventh MV of the block Quality

val1

First MV of the block Value

val2

Second MV of the block Value

sat1

First MV of the block Satisfaction

sat2

Second MV of the block Satisfaction

sat3

Third MV of the block Satisfaction

comp

First MV of the block Complaints

loy1

First MV of the block Loyalty

loy2

Second MV of the block Loyalty

loy3

Third MV of the block Loyalty

References

Tenenhaus, M., Esposito Vinzi, V., Chatelin Y.M., and Lauro, C. (2005) PLS path modeling. Computational Statistics & Data Analysis, 48, pp. 159-205.

Examples

data(mobile)

Normalize a vector

Description

Internal function not to be called by the user

Usage

  normalize(x)

Arguments

Details

Internal function. normalize is called internally

Value

normalized vector

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Offense dataset

Description

Dataset with offense statistics of American football teams from the NFL (2010-2011 season).

Usage

data(offense)

Format

A data frame with 32 teams on the following 17 variables. The variables may be used to construct five suggested latent concepts: 1) RUSH=Rushing Quality, 2) PASS=Passing Quality, 3) SPEC=Special Teams and Other, 4) SCORING=Scoring Success, 5)OFFENSE=Offense Performance

Source

https://www.teamrankings.com/nfl/stats/

Examples

# load data
data(offense)

# take a peek
head(offense)

Orange Juice dataset

Description

This data set contains the physico-chemical, sensory and hedonic measurements of 6 orange juices.

Format

A data frame with 6 observations and 112 variables. The variables refer to three latent concepts: 1) PHYCHEM=Physico-Chemical, 2) SENSORY=Sensory, and 3) HEDONIC=Hedonic.

Source

Laboratoire de Mathematiques Appliques, Agrocampus, Rennes.

References

Tenenhaus, M., Pages, J., Ambroisine, L., and Guinot, C. (2005) PLS methodology to study relationships between hedonic jedgements and product characteristics. Food Quality and Preference, 16(4), pp. 315-325.

Pages, J., and Tenenhaus, M. (2001) Multiple factor analysis combined with PLS path modelling. Application to the analysis of relationships between physicochemical, sensory profiles and hedonic judgements. Chemometrics and Intelligent Laboratory Systems, 58, pp. 261-273.

Pages, J. (2004) Multiple Factor Analysis: Main Features and Application to Sensory Data. Revista Colombiana de Estadistica, 27, pp. 1-26.

Examples

  data(orange)
  orange

Plot outer model

Description

Plot either outer weights or loadings in the outer model for objects of class "plspm"

Usage

  outerplot(x, what = "loadings", colpos = "#6890c4BB",
    colneg = "#f9675dBB", box.prop = 0.55, box.size = 0.08,
    box.cex = 1, box.col = "gray95", lcol = "gray95",
    box.lwd = 2, txt.col = "gray40", shadow.size = 0,
    curve = 0, lwd = 2, arr.pos = 0.5, arr.width = 0.15,
    cex.txt = 0.9, ...)

Arguments

Note

outerplot uses the function plotmat of package diagram.
https://cran.r-project.org/package=diagram/vignettes/diagram.pdf

See Also

innerplot, plot.plspm, plspm

Plots for PLS Path Models

Description

Plot method for objects of class "plspm". This function plots either the inner (i.e. structural) model with the estimated path coefficients, or the outer (i.e. measurement) model with loadings or weights.

Usage

  ## S3 method for class 'plspm'
 plot(x, what = "inner",
    colpos = "#6890c4BB", colneg = "#f9675dBB",
    box.prop = 0.55, box.size = 0.08, box.cex = 1,
    box.col = "gray95", lcol = "gray95",
    txt.col = "gray40", arr.pos = 0.5, cex.txt = 0.9, ...)

Arguments

Details

plot.plspm is just a wraper of innerplot and outerplot.

Note

Function plot.plspm is based on the function plotmat of package diagram.
https://cran.r-project.org/package=diagram/vignettes/diagram.pdf

See Also

innerplot, outerplot, plspm

Examples

## Not run: 
 ## typical example of PLS-PM in customer satisfaction analysis
 ## model with six LVs and reflective indicators
 # load data satisfaction
 data(satisfaction)

 # define inner model matrix
 IMAG = c(0,0,0,0,0,0)
 EXPE = c(1,0,0,0,0,0)
 QUAL = c(0,1,0,0,0,0)
 VAL = c(0,1,1,0,0,0)
 SAT = c(1,1,1,1,0,0)
 LOY = c(1,0,0,0,1,0)
 sat.inner = rbind(IMAG, EXPE, QUAL, VAL, SAT, LOY)

 # define outer model list
 sat.outer = list(1:5, 6:10, 11:15, 16:19, 20:23, 24:27)

 # define vector of reflective modes
 sat.mod = rep("A", 6)

 # apply plspm
 satpls = plspm(satisfaction, sat.inner, sat.outer, sat.mod, scheme="centroid",
               scaled=FALSE)

 # plot path coefficients
 plot(satpls, what="inner")

 # plot loadings
 plot(satpls, what="loadings")

 # plot outer weights
 plot(satpls, what="weights")
 
## End(Not run)

PLS-PM: Partial Least Squares Path Modeling

Description

Estimate path models with latent variables by partial least squares approach (for both metric and non-metric data)

Estimate path models with latent variables by partial least squares approach (for both metric and non-metric data)

Usage

  plspm(Data, path_matrix, blocks, modes = NULL,
    scaling = NULL, scheme = "centroid", scaled = TRUE,
    tol = 1e-06, maxiter = 100, plscomp = NULL,
    boot.val = FALSE, br = NULL, dataset = TRUE)

Arguments

Details

The function plspm estimates a path model by partial least squares approach providing the full set of results.

The argument path_matrix is a matrix of zeros and ones that indicates the structural relationships between latent variables. path_matrix must be a lower triangular matrix; it contains a 1 when column j affects row i, 0 otherwise.

• plspm: Partial Least Squares Path Modeling

• plspm.fit: Simple version for PLS-PM

• plspm.groups: Two Groups Comparison in PLS-PM

• rebus.pls: Response Based Unit Segmentation (REBUS)

Value

An object of class "plspm".

Author(s)

Gaston Sanchez, Giorgio Russolillo

References

Tenenhaus M., Esposito Vinzi V., Chatelin Y.M., and Lauro C. (2005) PLS path modeling. Computational Statistics & Data Analysis, 48, pp. 159-205.

Lohmoller J.-B. (1989) Latent variables path modeling with partial least squares. Heidelberg: Physica-Verlag.

Wold H. (1985) Partial Least Squares. In: Kotz, S., Johnson, N.L. (Eds.), Encyclopedia of Statistical Sciences, Vol. 6. Wiley, New York, pp. 581-591.

Wold H. (1982) Soft modeling: the basic design and some extensions. In: K.G. Joreskog & H. Wold (Eds.), Systems under indirect observations: Causality, structure, prediction, Part 2, pp. 1-54. Amsterdam: Holland.

Russolillo, G. (2012) Non-Metric Partial Least Squares. Electronic Journal of Statistics, 6, pp. 1641-1669. https://projecteuclid.org/euclid.ejs/1348665231

See Also

innerplot, outerplot,

Examples

## Not run: 
## typical example of PLS-PM in customer satisfaction analysis
## model with six LVs and reflective indicators

# load dataset satisfaction
data(satisfaction)

# path matrix
IMAG = c(0,0,0,0,0,0)
EXPE = c(1,0,0,0,0,0)
QUAL = c(0,1,0,0,0,0)
VAL = c(0,1,1,0,0,0)
SAT = c(1,1,1,1,0,0)
LOY = c(1,0,0,0,1,0)
sat_path = rbind(IMAG, EXPE, QUAL, VAL, SAT, LOY)

# plot diagram of path matrix
innerplot(sat_path)

# blocks of outer model
sat_blocks = list(1:5, 6:10, 11:15, 16:19, 20:23, 24:27)

# vector of modes (reflective indicators)
sat_mod = rep("A", 6)

# apply plspm
satpls = plspm(satisfaction, sat_path, sat_blocks, modes = sat_mod,
   scaled = FALSE)

# plot diagram of the inner model
innerplot(satpls)

# plot loadings
outerplot(satpls, what = "loadings")

# plot outer weights
outerplot(satpls, what = "weights")

## End(Not run)

Basic results for Partial Least Squares Path Modeling

Description

Estimate path models with latent variables by partial least squares approach without providing the full list of results as plspm(). This might be helpful when doing simulations, intensive computations, or when you don't want the whole enchilada.

Usage

  plspm.fit(Data, path_matrix, blocks, modes = NULL,
    scaling = NULL, scheme = "centroid", scaled = TRUE,
    tol = 1e-06, maxiter = 100, plscomp = NULL)

Arguments

Details

plspm.fit performs the basic PLS algorithm and provides limited results (e.g. outer model, inner model, scores, and path coefficients).

The argument path_matrix is a matrix of zeros and ones that indicates the structural relationships between latent variables. path_matrix must be a lower triangular matrix; it contains a 1 when column j affects row i, 0 otherwise.

Value

An object of class "plspm".

Author(s)

Gaston Sanchez, Giorgio Russolillo

References

Tenenhaus M., Esposito Vinzi V., Chatelin Y.M., and Lauro C. (2005) PLS path modeling. Computational Statistics & Data Analysis, 48, pp. 159-205.

Lohmoller J.-B. (1989) Latent variables path modeling with partial least squares. Heidelberg: Physica-Verlag.

Wold H. (1985) Partial Least Squares. In: Kotz, S., Johnson, N.L. (Eds.), Encyclopedia of Statistical Sciences, Vol. 6. Wiley, New York, pp. 581-591.

Wold H. (1982) Soft modeling: the basic design and some extensions. In: K.G. Joreskog & H. Wold (Eds.), Systems under indirect observations: Causality, structure, prediction, Part 2, pp. 1-54. Amsterdam: Holland.

See Also

innerplot, plot.plspm,

Examples

## Not run: 
 ## typical example of PLS-PM in customer satisfaction analysis
 ## model with six LVs and reflective indicators

 # load dataset satisfaction
 data(satisfaction)

 # inner model matrix
 IMAG = c(0,0,0,0,0,0)
 EXPE = c(1,0,0,0,0,0)
 QUAL = c(0,1,0,0,0,0)
 VAL = c(0,1,1,0,0,0)
 SAT = c(1,1,1,1,0,0)
 LOY = c(1,0,0,0,1,0)
 sat_path = rbind(IMAG, EXPE, QUAL, VAL, SAT, LOY)

 # outer model list
 sat_blocks = list(1:5, 6:10, 11:15, 16:19, 20:23, 24:27)

 # vector of reflective modes
 sat_modes = rep("A", 6)

 # apply plspm.fit
 satpls = plspm.fit(satisfaction, sat_path, sat_blocks, sat_modes,
     scaled=FALSE)

 # summary of results
 summary(satpls)

 # default plot (inner model)
 plot(satpls)
 
## End(Not run)

Two Groups Comparison in PLS-PM

Description

Performs a group comparison test for comparing path coefficients between two groups. The null and alternative hypotheses to be tested are: H0: path coefficients are not significantly different; H1: path coefficients are significantly different

Usage

  plspm.groups(pls, group, Y = NULL, method = "bootstrap",
    reps = NULL)

Arguments

Details

plspm.groups performs a two groups comparison test in PLS-PM for comparing path coefficients between two groups. Only two methods are available: 1) bootstrap, and 2) permutation. The bootstrap test is an adapted t-test based on bootstrap standard errors. The permutation test is a randomization test which provides a non-parametric option.

When the object pls does not contain a data matrix (i.e. pls$data=NULL), the user must provide the data matrix or data frame in Y.

Value

An object of class "plspm.groups"

Author(s)

Gaston Sanchez

References

Chin, W.W. (2003) A permutation procedure for multi-group comparison of PLS models. In: Vilares M., Tenenhaus M., Coelho P., Esposito Vinzi V., Morineau A. (Eds.) PLS and Related Methods - Proceedings of the International Symposium PLS03. Decisia, pp. 33-43.

Chin, W.W. (2000) Frequently Asked Questions, Partial Least Squares PLS-Graph.

See Also

plspm

Examples

## Not run: 
 ## example with customer satisfaction analysis
 ## group comparison based on the segmentation variable "gender"

 # load data satisfaction
 data(satisfaction)

 # define inner model matrix
 IMAG = c(0,0,0,0,0,0)
 EXPE = c(1,0,0,0,0,0)
 QUAL = c(0,1,0,0,0,0)
 VAL = c(0,1,1,0,0,0)
 SAT = c(1,1,1,1,0,0)
 LOY = c(1,0,0,0,1,0)
 sat_path = rbind(IMAG, EXPE, QUAL, VAL, SAT, LOY)

 # define outer model list
 sat_blocks = list(1:5, 6:10, 11:15, 16:19, 20:23, 24:27)

 # define vector of reflective modes
 sat_mod = rep("A", 6)

 # apply plspm
 satpls = plspm(satisfaction, sat_path, sat_blocks,
                modes = sat_mod, scaled = FALSE)

 # permutation test with 100 permutations
 group_perm = plspm.groups(satpls, satisfaction$gender,
                           method="permutation", reps=100)
 group_perm
 
## End(Not run)

Quantification Plot

Description

Quantification Plots for Non-Metric PLS-PM

Usage

  quantiplot(pls, lv = NULL, mv = NULL, pch = 16,
    col = "darkblue", lty = 2, ...)

Arguments

Details

If both lv and mv are specified, only the value of lv will be taken into account.
If the given lv have more than 15 variables, only the first 15 are plotted.

Response Based Unit Segmentation (REBUS)

Description

Performs all the steps of the REBUS-PLS algorithm. Starting from the global model, REBUS allows us to detect local models with better performance.

Usage

  rebus.pls(pls, Y = NULL, stop.crit = 0.005,
    iter.max = 100)

Arguments

Value

An object of class "rebus", basically a list with:

Author(s)

Laura Trinchera, Gaston Sanchez

References

Esposito Vinzi V., Trinchera L., Squillacciotti S., and Tenenhaus M. (2008) REBUS-PLS: A Response-Based Procedure for detecting Unit Segments in PLS Path Modeling. Applied Stochastic Models in Business and Industry (ASMBI), 24, pp. 439-458.

Trinchera, L. (2007) Unobserved Heterogeneity in Structural Equation Models: a new approach to latent class detection in PLS Path Modeling. Ph.D. Thesis, University of Naples "Federico II", Naples, Italy.

See Also

plspm, res.clus, it.reb, rebus.test, local.models

Examples

## Not run: 
 ## typical example of PLS-PM in customer satisfaction analysis
 ## model with six LVs and reflective indicators
 ## example of rebus analysis with simulated data

 # load data
 data(simdata)

 # Calculate plspm
 sim_inner = matrix(c(0,0,0,0,0,0,1,1,0), 3, 3, byrow=TRUE)
 dimnames(sim_inner) = list(c("Price", "Quality", "Satisfaction"),
                            c("Price", "Quality", "Satisfaction"))
 sim_outer = list(c(1,2,3,4,5), c(6,7,8,9,10), c(11,12,13))
 sim_mod = c("A", "A", "A")  # reflective indicators
 sim_global = plspm(simdata, sim_inner,
                    sim_outer, modes=sim_mod)
 sim_global

 # run rebus.pls and choose the number of classes
 # to be taken into account according to the displayed dendrogram.
 rebus_sim = rebus.pls(sim_global, stop.crit = 0.005, iter.max = 100)

 # You can also compute complete outputs for local models by running:
 local_rebus = local.models(sim_global, rebus_sim)
 
## End(Not run)

Permutation Test for REBUS Multi-Group Comparison

Description

Performs permutation tests for comparing pairs of groups from a REBUS object.

Usage

  rebus.test(pls, reb, Y = NULL)

Arguments

Details

A permutation test on path coefficients, loadings, and GoF index is applied to the classes obtained from REBUS, by comparing two classes at a time. That is to say, a permutation test is applied on pair of classes. The number of permutations in each test is 100. In turn, the number of classes handled by rebus.test is limited to 6.

When pls$data=NULL (there is no data matrix), the user must provide the data matrix or data frame in Y.

Value

An object of class "rebus.test", basically a list containing the results of each pair of compared classes. In turn, each element of the list is also a list with the results for the path coefficients, loadings, and GoF index.

Author(s)

Laura Trinchera, Gaston Sanchez

References

Chin, W.W. (2003) A permutation procedure for multi-group comparison of PLS models. In: Vilares M., Tenenhaus M., Coelho P., Esposito Vinzi V., Morineau A. (Eds.) PLS and Related Methods - Proceedings of the International Symposium PLS03. Decisia, pp. 33-43.

See Also

rebus.pls, local.models

Examples

## Not run: 
 ## typical example of PLS-PM in customer satisfaction analysis
 ## model with six LVs and reflective indicators
 ## example of rebus analysis with simulated data

 # load data
 data(simdata)

 # Calculate plspm
 sim_path = matrix(c(0,0,0,0,0,0,1,1,0), 3, 3, byrow=TRUE)
 dimnames(sim_path) = list(c("Price", "Quality", "Satisfaction"),
                            c("Price", "Quality", "Satisfaction"))
 sim_blocks = list(c(1,2,3,4,5), c(6,7,8,9,10), c(11,12,13))
 sim_mod = c("A", "A", "A")  # reflective indicators
 sim_global = plspm(simdata, sim_path,
                    sim_blocks, modes=sim_mod)
 sim_global

 # Cluster analysis on residuals of global model
 sim_clus = res.clus(sim_global)

 # Iterative steps of REBUS algorithm on 2 classes
 rebus_sim = it.reb(sim_global, sim_clus, nk=2,
                    stop.crit=0.005, iter.max=100)

 # apply rebus.test
 sim_permu = rebus.test(sim_global, rebus_sim)

 # inspect sim.rebus
 sim_permu
 sim_permu$test_1_2

 # or equivalently
 sim_permu[[1]]
 
## End(Not run)

Clustering on communality and structural residuals

Description

Computes communality and structural residuals from a global PLS-PM model and performs a Hierarchical Cluster Analysis on these residuals according to the REBUS algorithm.

Usage

  res.clus(pls, Y = NULL)

Arguments

Details

res.clus() comprises the second and third steps of the REBUS-PLS Algorithm. It computes communality and structural residuals. Then it performs a Hierarchical Cluster Analysis on these residuals (step three of REBUS-PLS Algorithm). As a result, this function directly provides a dendrogram obtained from a Hierarchical Cluster Analysis.

Value

An Object of class "hclust" containing the results of the Hierarchical Cluster Analysis on the communality and structural residuals.

Author(s)

Laura Trinchera, Gaston Sanchez

References

Esposito Vinzi V., Trinchera L., Squillacciotti S., and Tenenhaus M. (2008) REBUS-PLS: A Response-Based Procedure for detecting Unit Segments in PLS Path Modeling. Applied Stochastic Models in Business and Industry (ASMBI), 24, pp. 439-458.

Trinchera, L. (2007) Unobserved Heterogeneity in Structural Equation Models: a new approach to latent class detection in PLS Path Modeling. Ph.D. Thesis, University of Naples "Federico II", Naples, Italy.

See Also

it.reb, plspm

Examples

## Not run: 
 ## example of rebus analysis with simulated data

 # load data
 data(simdata)

 # Calculate plspm
 sim_path = matrix(c(0,0,0,0,0,0,1,1,0), 3, 3, byrow=TRUE)
 dimnames(sim_path) = list(c("Price", "Quality", "Satisfaction"),
                            c("Price", "Quality", "Satisfaction"))
 sim_blocks = list(c(1,2,3,4,5), c(6,7,8,9,10), c(11,12,13))
 sim_modes = c("A", "A", "A")
 sim_global = plspm(simdata, sim_path,
                    sim_blocks, modes=sim_modes)
 sim_global

 # Then compute cluster analysis on the residuals of global model
 sim_clus = res.clus(sim_global)
 
## End(Not run)

Rescale Latent Variable Scores

Description

Rescale standardized latent variable scores to original scale of manifest variables

Usage

  rescale(pls, data = NULL)

Arguments

Details

rescale requires all outer weights to be positive

Value

A data frame with the rescaled latent variable scores

Author(s)

Gaston Sanchez

See Also

plspm

Examples

## Not run: 
 ## example with customer satisfaction analysis

 # load data satisfaction
 data(satisfaction)

 # define inner model matrix
 IMAG = c(0,0,0,0,0,0)
 EXPE = c(1,0,0,0,0,0)
 QUAL = c(0,1,0,0,0,0)
 VAL = c(0,1,1,0,0,0)
 SAT = c(1,1,1,1,0,0)
 LOY = c(1,0,0,0,1,0)
 sat_path = rbind(IMAG, EXPE, QUAL, VAL, SAT, LOY)

 # define outer model list
 sat_blocks = list(1:5, 6:10, 11:15, 16:19, 20:23, 24:27)

 # define vector of reflective modes
 sat_modes = rep("A", 6)

 # apply plspm
 my_pls = plspm(satisfaction, sat_path, sat_blocks, modes = sat_modes,
              scaled=FALSE)

 # rescaling standardized scores of latent variables
 new_scores = rescale(my_pls)

 # compare standardized LVs against rescaled LVs
 summary(my_pls$scores)
 summary(new_scores)
 
## End(Not run)

Dillon-Goldstein's rho

Description

Dillon-Goldstein's rho of a single block of variables

Usage

  rho(X)

Arguments

Value

Dillon-Goldstein's rho

Author(s)

Gaston Sanchez

See Also

alpha, unidim

Examples

## Not run: 
 # load dataset satisfaction
 data(satisfaction)

 # block Image (first 5 columns of satisfaction)
 Image = satisfaction[,1:5]

 # compute Dillon-Goldstein's rho for Image block
 rho(Image)
 
## End(Not run)

Russett A

Description

Russett dataset with variable demo as numeric variable

Format

A data frame with 47 rows and 9 columns

Russett B

Description

Russett dataset with variable demo as factor

Format

A data frame with 47 rows and 9 columns

Russett dataset

Description

Data set from Russett (1964) about agricultural inequality, industrial development and political instability.

Usage

data(russett)

Format

A data frame with 47 observations on the following 11 variables. The variables may be used to construct three latent concepts: 1) AGRIN=Agricultural Inequality, 2) INDEV=Industrial Development, 3) POLINS=Political Instability.

References

Russett B.M. (1964) Inequality and Instability: The Relation of Land Tenure to Politics. World Politics 16:3, pp. 442-454.

Examples

  data(russett)
  russett

Satisfaction dataset

Description

This data set contains the variables from a customer satisfaction study of a Spanish credit institution on 250 customers.

Format

A data frame with 250 observations and 28 variables. Variables from 1 to 27 refer to six latent concepts: 1) IMAG=Image, 2) EXPE=Expectations, 3) QUAL=Quality, 4) VAL=Value, 5) SAT=Satisfaction, and 6) LOY=Loyalty. The last variable is a categorical variable indicating the gender of the individual.

IMAG: Includes variables such as reputation, trustworthiness, seriousness, solidness, and caring about customer's needs.
EXPE: Includes variables such as products and services provided, customer service, providing solutions, and expectations for the overall quality.
QUAL: Includes variables such as reliable products and services, range of products and services, personal advice, and overall perceived quality.
VAL: Includes variables such as beneficial services and products, valuable investments, quality relative to price, and price relative to quality.
SAT: Includes variables such as overall rating of satisfaction, fulfillment of expectations, satisfaction relative to other banks, and performance relative to customer's ideal bank.
LOY: Includes variables such as propensity to choose the same bank again, propensity to switch to other bank, intention to recommend the bank to friends, and sense of loyalty.

Source

Laboratory of Information Analysis and Modeling (LIAM). Facultat d'Informatica de Barcelona, Universitat Politecnica de Catalunya.

Examples

  data(satisfaction)
  satisfaction

Simulated data for REBUS with two groups

Description

Simulated data with two latent classes showing different local models.

Usage

data(simdata)

Format

A data frame of simulated data with 400 observations on the following 14 variables.

mv1

first manifest variable of the block Price Fairness

mv2

second manifest variable of the block Price Fairness

mv3

third manifest variable of the block Price Fairness

mv4

fourth manifest variable of the block Price Fairness

mv5

fifth manifest variable of the block Price Fairness

mv6

first manifest variable of the block Quality

mv7

second manifest variable of the block Quality

mv8

third manifest variable of the block Quality

mv9

fourth manifest variable of the block Quality

mv10

fifth manifest variable of the block Quality

mv11

first manifest variable of the block Customer Satisfaction

mv12

second manifest variable of the block Customer Satisfaction

mv13

third manifest variable of the block Customer Satisfaction

group

a numeric vector

Details

The postulated model overlaps the one used by Jedidi et al. (1997) and by Esposito Vinzi et al. (2007) for their numerical examples. It is composed of one latent endogenous variable, Customer Satisfaction, and two latent exogenous variables, Price Fairness and Quality. Each latent exogenous variable (Price Fairness and Quality) has five manifest variables (reflective mode), and the latent endogenous variable (Customer Satisfaction) is measured by three indicators (reflective mode).

Two latent classes showing different local models are supposed to exist. Each one is composed of 200 units. Thus, the data on the aggregate level for each one of the numerical examples includes 400 units.

The simulation scheme involves working with local models that are different at both the measurement and the structural model levels. In particular, the experimental sets of data consist of two latent classes with the following characteristics:
(a) Class 1 - price fairness seeking customers - characterized by a strong relationship between Price Fairness and Customer Satisfaction (close to 0.9) and a weak relationship between Quality and Customer Satisfaction (close to 0.1), as well as by a weak correlation between the 3rd manifest variable of the Price Fairness block (mv3) and the corresponding latent variable;
(b) Class 2 - quality oriented customers - characterized by a strong relationship between Quality and Customer Satisfaction (close to 0.1) and a weak relationship between Price Fairness and Customer Satisfaction (close to 0.9), as well as by a weak correlation between the 3rd manifest variable (mv8) of the Quality block and the corresponding latent variable.

Source

Simulated data from Trinchera (2007). See References below.

References

Esposito Vinzi, V., Ringle, C., Squillacciotti, S. and Trinchera, L. (2007) Capturing and treating unobserved heterogeneity by response based segmentation in PLS path modeling. A comparison of alternative methods by computational experiments. Working paper, ESSEC Business School.

Jedidi, K., Jagpal, S. and De Sarbo, W. (1997) STEMM: A general finite mixture structural equation model. Journal of Classification 14, pp. 23-50.

Trinchera, L. (2007) Unobserved Heterogeneity in Structural Equation Models: a new approach to latent class detection in PLS Path Modeling. Ph.D. Thesis, University of Naples "Federico II", Naples, Italy.

Examples

data(simdata)
simdata

Spanish football dataset

Description

This data set contains the results of the teams in the Spanish football league 2008-2009.

Format

A data frame with 20 observations on 14 variables. The variables may be used to construct four latent concepts: 1) ATTACK=Attack, 2) DEFENSE=Defense, 3) SUCCESS=Success, 4) INDIS=Indiscipline.

Source

League Day.
Cero a cero. https://www.ceroacero.es/

Examples

  data(spainfoot)
  spainfoot

Technology data set

Description

This data set contains the variables from a "user and acceptance of technology" model on 300 users.

Usage

data(technology)

Format

A data frame with 300 observations and 21 variables. Variables can be grouped in six latent concepts: 1) PERF_EXP=Performance Expectancy, 2) EFF_EXP=Effort Expectancy, 3) SUB_NORM=Subjective Norm, 4) FAC_COND=Facilitating Conditions, 5) BEH_INT=Behavioral Intention, and 6) USE_BEH=Use Behavior.

References

Venkatesh V., Morris M.G., Davis G.B., Davis F.D. (2003) User Acceptance of Information Technology: Toward a Unified View. MIS Quarterly, Vol. 27 (3): 425-478.

Examples

  data(technology)
  summary(technology)

Test Data Set Availibility

Description

Internal function not to be called by the user

Usage

  test_dataset(Dataset, pls_data, num_obs)

Arguments

Details

Internal function. test_dataset checks whether a dataset is available for plspm.groups, rescale, it.reb, rebus.pls, rebus.test

Value

TRUE if dataset is available, otherwise FALSE

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Test presence of factors

Description

Internal function not to be called by the user

Usage

  test_factors(DF)

Arguments

Details

Internal function. test_factors is called by get_treated_data.

Value

whether DF contains factors or not

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Note

Test presence of factors in a data.frame

Test scaling of selected manifest variables

Description

Internal function not to be called by the user

Usage

  test_manifest_scaling(MV, scaling)

Arguments

Details

Internal function. test_manifest_scaling is called by plspm. Basically checks that unordered factors have nominal scaling.

Value

gives an error when factors in MV have bad scaling

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Test outer weights convergence within specified maxiter

Description

Internal function not to be called by the user

Usage

  test_null_weights(wgs, specs)

Arguments

Details

Internal function. test_weights_output is called by plspm. Basically checks that weights are not NULL.

Value

gives an error when wgs is NULL (i.e. non-convergence)

Warning

Do NOT use this function unless you are ME, a package developer, or a jedi user who really knows what is doing (seriously!)

Unidimensionality of blocks

Description

Compute unidimensionality indices (a.k.a. Composite Reliability indices)

Usage

  unidim(Data, blocks = NULL)

Arguments

Value

A data frame with the following columns:

Author(s)

Gaston Sanchez

See Also

alpha, rho

Examples

## Not run: 
 # load dataset satisfaction
 data(satisfaction)

 # blocks Image and Expectations
 ima_expe = list(Image=1:5, Expec=6:10)

 # compute unidimensionality indices
 unidim(satisfaction, ima_expe)
 
## End(Not run)

Wines dataset

Description

These data are the results of a chemical analysis of wines grown in the same region in Italy but derived from three different cultivars. The analysis determined the quantities of 13 constituents found in each of the three types of wines.

Format

A data frame with 178 observations and 14 variables.

Source

Machine Learning Repository. https://archive.ics.uci.edu/ml/datasets/Wine

References

Forina, M. et al, PARVUS An Extendible Package for Data Exploration, Classification and Correlation. Institute of Pharmaceutical and Food Analysis and Technologies, Via Brigata Salerno, 16147 Genoa, Italy.

Examples

  data(wines)
  wines