Path coefficient extraction

Description

############################################################################################

Usage

.path(x, l)

Arguments

Details

Internal function

Value

a vector of path coefficients

Data preprocessing for F-tests

Description

############################################################################################

Usage

F.data(x, inner, .model, .scheme, .consistent, modtwo)

Arguments

Details

Internal function

Value

list containing matrices needed for the tests.

F-coefficient test

Description

############################################################################################

Usage

Fc.test(Y1, X1, path.name, info.block)

Arguments

Details

Internal function

Value

a list containing the statistic and the p-value obtained by applying the F-coefficient. test

F-global test

Description

############################################################################################

Usage

Fg.test(Y0, X0, Y1, X1)

Arguments

Details

Internal function

Value

a list containing the statistic and the p-value obtained by applying F-global test

Candidates to the bets partition for each of segmentation variables

Description

############################################################################################

Usage

all_part(x, y, inner, .model, .scheme, .consistent, size_candidate, ...)

Arguments

Details

Internal function

Value

a list containing information of the candidates to the optimum partition for each of segmentation variables

Bar Plot of a ranking of categorical variables by importance

Description

"bar_impvar" returns a bar plot to visualize the ranking of variables by importance in obtaining the terminal nodes of Pathmox.

Usage

bar_impvar(x, .cex.names = 1, .cex.axis = 1.2, .cex.main = 1, ...)

Arguments

Details

The importance of each variable is determined by adding the F-statistic calculated for the variable in each split node of Pathmox.

Author(s)

Giuseppe Lamberti

References

Lamberti, G., Aluja, T. B., and Sanchez, G. (2016). The Pathmox approach for PLS path modeling segmentation. Applied Stochastic Models in Business and Industry, 32(4), 453-468. doi: 10.1002/asmb.2168

Lamberti, G. (2015). Modeling with Heterogeneity, PhD Dissertation.

Sanchez, G. (2009). PATHMOX Approach: Segmentation Trees in Partial Least Squares Path Modeling, PhD Dissertation.

See Also

summary.plstree, print.plstree, pls.pathmox, bar_terminal, and plot.plstree

Examples

 ## Not run: 
# Example of PATHMOX approach in customer satisfaction analysis 
# (Spanish financial company).
# Model with 5 LVs (4 common factor: Image (IMAG), Value (VAL), 
# Satisfaction (SAT), and Loyalty (LOY); and 1 composite construct: 
# Quality (QUAL)

# load library and dataset csibank
library(genpathmx)
data("csibank")

# Define the model using the lavaan syntax. Use a set of regression formulas to define
# first the structural model and then the measurement model

CSImodel <- "
# Structural model
VAL  ~ QUAL
SAT  ~ IMAG  + QUAL + VAL
LOY  ~ IMAG + SAT

# Measurement model
# Composite
QUAL <~ qual1 + qual2 + qual3 + qual4 + qual5 + qual6 + qual7 
     
# Common factor
IMAG =~ imag1 + imag2 + imag3 + imag4 + imag5 + imag6 
VAL  =~ val1  + val2  + val3  + val4
SAT  =~ sat1  + sat2  + sat3           
LOY  =~ loy1  + loy2  + loy3           

"

# Identify the categorical variable to be used as input variables 
in the split process
CSIcatvar = csibank[,1:5]

# Check if variables are well specified (they have to be factors 
# and/or ordered factors)
str(CSIcatvar)

# Transform age and education into ordered factors
CSIcatvar$Age = factor(CSIcatvar$Age, levels = c("<=25", 
                                     "26-35", "36-45", "46-55", 
                                     "56-65", ">=66"),ordered = T)

CSIcatvar$Education = factor(CSIcatvar$Education, 
                            levels = c("Unfinished","Elementary", "Highschool",
                            "Undergrad", "Graduated"),ordered = T)
       
# Run Pathmox analysis (Lamberti et al., 2016; 2017)
csi.pathmox = pls.pathmox(
 .model = CSImodel ,
 .data  = csibank,
 .catvar= CSIcatvar,
 .alpha = 0.05,
 .deep = 2
)                     
 
bar_impvar(csi.pathmox)


## End(Not run)

Comparative plot for the Pathmox terminal nodes

Description

bar_terminal returns the path coefficient bar plots of the Pathmox terminal nodes.

Usage

bar_terminal(
  x,
  .LV,
  .bycoef = FALSE,
  .cex.names = 1,
  .cex.axis = 1.2,
  .cex.main = 1,
  ...
)

Arguments

Details

This function aims to visualize, using bar plots, the path coefficients of the dependnet latent construct associated with the terminal nodes. The user indicates the dependnet latent construct they want to visualize. This is done using the same label as used in the structural model definition (lavaan syntax). The comparison is done by analyzing the path coefficient values for each node, or the values estimated in each node for each path coefficient. In the former, the plot also returns the R^2. In the latter, the bar corresponding to the node with the highest path coefficient value shows in a different color. By default the comparison is done by analyzing the path coefficient values for each node.

Author(s)

Giuseppe Lamberti

References

Lamberti, G., Aluja, T. B., and Sanchez, G. (2016). The Pathmox approach for PLS path modeling segmentation. Applied Stochastic Models in Business and Industry, 32(4), 453-468. doi: 10.1002/asmb.2168

Lamberti, G. (2015). Modeling with Heterogeneity, PhD Dissertation.

Sanchez, G. (2009). PATHMOX Approach: Segmentation Trees in Partial Least Squares Path Modeling, PhD Dissertation.

See Also

summary.plstree, print.plstree, pls.pathmox, plot.plstree, and bar_impvar

Examples

 ## Not run: 
# Example of PATHMOX approach in customer satisfaction analysis 
# (Spanish financial company).
# Model with 5 LVs (4 common factor: Image (IMAG), Value (VAL), 
# Satisfaction (SAT), and Loyalty (LOY); and 1 composite construct: 
# Quality (QUAL)

# load library and dataset csibank
library(genpathmx)
data("csibank")

# Define the model using the lavaan syntax. Use a set of regression formulas to define 
# first the structural model and then the measurement model

CSImodel <- "
# Structural model
VAL  ~ QUAL
SAT  ~ IMAG  + QUAL + VAL
LOY  ~ IMAG + SAT

# Measurement model
# Composite
QUAL <~ qual1 + qual2 + qual3 + qual4 + qual5 + qual6 + qual7 
     
# Common factor
IMAG =~ imag1 + imag2 + imag3 + imag4 + imag5 + imag6 
VAL  =~ val1  + val2  + val3  + val4
SAT  =~ sat1  + sat2  + sat3           
LOY  =~ loy1  + loy2  + loy3           

"

# Run pathmox on one single variable 
age = csibank[,2]

# Transform age into an ordered factor
age = factor(age, levels = c("<=25", "26-35", "36-45", "46-55",
                                      "56-65", ">=66"),ordered = T)
                                     
csi.pathmox.age = pls.pathmox(
 .model = CSImodel ,
 .data  = csibank,
 .catvar= age,
 .alpha = 0.05,
 .deep = 1
)  

# Visualize the bar plot by comparing the nodes
bar_terminal(csi.pathmox.age, .LV = "SAT")

# Visualize the bar plot by comparing path coefficients
bar_terminal(csi.pathmox.age, .LV = "SAT", .bycoef = TRUE)


## End(Not run)

Labels of a categorical variable a binary partions

Description

############################################################################################

Usage

bin.levels(z, spl)

Arguments

Details

Internal function

Value

a list of labels

Bart matrix

Description

############################################################################################

Usage

blockdiag(x, ...)

Arguments

Details

Internal function

Value

the Bart matrix

Linear relations between latent variables.

Description

############################################################################################

Usage

build.block(inner, latent)

Arguments

Details

Internal function.

Value

a list of matrices containing for each endogenous latent variable the the own predictors

Posibble partions for each node of the tree

Description

############################################################################################

Usage

candidates.tree(moxtree)

Arguments

Details

Internal function

Value

the Posibble partions for each node of the tree

Checks arguments

Description

############################################################################################

Usage

check_arg_mox(
  .model,
  .data,
  .catvar,
  .scheme,
  .consistent,
  .alpha,
  .deep,
  .size,
  .size_candidate,
  .tree
)

Arguments

Details

Internal function

Value

a list checked arguments

Check consistence

Description

############################################################################################

Usage

check_const(.model, .data)

Arguments

Details

Internal function

Value

a logical value

climate

Description

climate

Usage

climate

Format

climate data refers to the younger emplyees (<=30) of an international bank organizational study. It consists of 32 variables for 669 employees divided into 3 qualitative variables and 29 indicator (or manifest) variables. The 3 categorical variables, reflecting specific employee characteristics as potential observed sources of heterogeneity, gender, job level, and seniority. The 31 indicator (or manifest) variables were loyalty (3 indicators), satisfaction (6 indicators), and the 5 work climate constructs of empowerment (5 indicators), company reputation (3 indicators), pay (4 indicators), work conditions (3 indicators), leadership (5 indicators)

Latent variable description

Loyalty:

Employee commitment to the organization

Satisfaction:

Employee contentedness with their job and aspects such as kind of work, supervision, etc

Empowerment:

Employee perceptions of management vision (vertical or horizontal)

Reputation:

Employee perceptions of the company’s reputation

Leadership:

Employee perceptions of leadership practices such as feedback and appraisal

Pay:

Employee perceptions of pay and of its equity

Conditions:

Employee perceptions regarding the conditions in which they perform their work

Manifest variables description

Emp1:

Employee treatment as responsible

Emp2:

Teamwork is empowered

Emp3:

Autonomy is favored

Emp4:

Confidence in performed tasks

Emp5:

Creativity and initiative are endorsed

Imag1:

Organization’s reputation

Imag2:

Organization’s values

Imag3:

Organization’s customer relationships

Pay1:

Salary

Pay2:

Social benefits

Pay3:

My salary corresponds to my duties

Pay4:

My salary corresponds to my effort

Work1:

Enough personnel in the office

Work2:

Enough time to perform the tasks

Work3:

Conditions and tools for work

Lead1:

Agenda and planning

Lead2:

Receptiveness

Lead3:

Encouraging

Lead4:

Communication

Lead5:

Celebrating success

Sat1:

Overall rating of satisfaction

Sat2:

Tasks in accordance with capabilities

Sat3:

Possibility to know efficiency

Sat4:

Possibility to learn new things

Sat5:

Usefulness of performed job

Sat6:

Fulfilment of expectations

Loy1:

I am unwilling to leave in case of not finding alternative

Loy2:

I am committed to the institution

Loy3:

I trust in the proper direction of the management

Segmentation variables description

Gender:

Gender of the employees, a factor with levels: male and female

Level:

Level of the employees, a factor with levels: low, medium, and high

Seniority:

Time working in the bank, a factor with levels: <5y and 15-5y

References

Lamberti, G., Aluja Banet, T., & Rialp Criado, J. (2020). Work climate drivers and employee heterogeneity. The International Journal of Human Resource Management, 1-33. doi: 10.1080/09585192.2020.1711798.

Lamberti, G. (2021). Hybrid multigroup partial least squares structural equation modelling: an application to bank employee satisfaction and loyalty. Quality and Quantity, doi: 10.1007/s11135-021-01096-9.

Combinations of a vector element

Description

############################################################################################

Usage

comb(n, r, v = 1:n, set = TRUE, repeats.allowed = FALSE)

Arguments

Details

Internal function

Value

a matrix of combinations

csibank

Description

csibank

Usage

csibank

Format

csibank data refers to a 2008 marketing research study of a leading Spanish firm providing retail financial services. For confidentiality reasons, the complete details of the survey-based study will not be provided, only a description of the variables. The data include a total of 32 variables, measured for 1707 clients. The 32 variables are divided into two groups: a group formed of 27 indicator variables for the structural model, and a group formed of 5 categorical variables. Each block of indicators refers to a specific construct.

Latent variable description:

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, solution provision, and expectations for 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 satisfaction rating, fulfillment of expectations, satisfaction relative to other banks, and performance relative to an ideal bank

LOY:

Includes variables such as likelihood of choosing the same bank again, likelihood of switching to another bank, intention to recommend the bank to friends, and feeling of loyalty

Manifest variables description:

imag1:

Bank's reputation

imag2:

Trustworthiness

imag3:

Bank's solidity

imag4:

Innovation and forward looking

imag5:

Bank's emphasis on public affairs

imag6:

Caring about the customer’s needs

expe1:

Providing products and services to meet the customer's needs

expe2:

Providing customer service

expe3:

Providing solutions to daily banking needs

expe4:

Expectations of overall quality

qual1:

Reliable products and services

qual2:

Range of products and services

qual3:

Degree to which customer feels well informed

qual4:

Personal advice

qual5:

Customer service

qual6:

Overall rating of perceived quality

qual7:

Overall rating of satisfaction

val1:

Beneficial services and products

val2:

Valuable investments

val3:

Quality relative to price

val4:

Price relative to quality

sat1:

Overall rating of satisfaction

sat2:

Fulfillment of expectations

sat3:

Rating the performance relative to customer's ideal bank

loy1:

Propensity to choose the same bank if the customer had to choose again

loy2:

Propensity to switch to other banks if they offered better terms

loy3:

Customer's intention to recommend the bank to friends or colleagues

Categorical variables description:

Gender:

Gender of the customers, a factor with levels: Female and Male

Age:

Age of the customers, a factor with levels: <=25, 26-35, 36-45, 46-55, 56-65, and >=66

Education:

Education of the customers, a factor with levels: Elementary, Graduated, Highschool, Undergrad, and Unfinished

Occupation:

Occupation of the customers, a factor with levels: Manager, MediumEmplo, Notemploy, OwnFreelan, and Retired

Region:

Region of residence of the customers, a factor with levels: Center, East, North

Source

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

References

Lamberti, G. et al. (2017). The Pathmox approach for PLS path modeling: discovering which constructs differentiate segments.Applied Stochastic Models in Business and Industry, doi: 10.1002/asmb.2270.

Lamberti, G. (2014) Modeling with Heterogeneity. PhD Dissertation.

Path coefficient labels

Description

############################################################################################

Usage

element(x, l)

Arguments

Details

Internal function

Value

a vector of path coefficients labels

Vector minimum position

Description

############################################################################################

Usage

f.min(x)

Arguments

Details

Internal function

Value

a list containing minimun value, the position of the minimun and the values different from NA of a vactor

F-coefficients test results for each tree partition

Description

############################################################################################

Usage

fcoef.tree(moxtree)

Arguments

Details

Internal function

Value

the F-coefficients test results for each tree partition

F-global test results for each tree partition

Description

############################################################################################

Usage

fglobal.tree(moxtree)

Arguments

Details

Internal function

Value

the F-global test results for each tree partition

footdata

Description

footdata

Usage

footdata

Format

footdata data refers to a marketing research study from 2018 concerning the experience of watching a football match in the stadium of a top Spanish football club. For confidentiality reasons, the complete details of the survey-based study will not be provided. Only the description of the variables is given. The data consist of a total of 20 variables, measured for 362 spectators. The 20 variables are divided into two groups. One group is formed of 15 indicator variables for the structural model, and the other group is formed of 5 categorical variables. Each block of indicator refers to a specific construct.

Latent variable description

QUA:

Spectators’ perception of service performance, based on evaluations of service dimensions

IMA:

Spectators’ perception of the attributes, players, management and condition of the club

SAT:

Spectators’ evaluation of the perceived benefits of attending a match

LOY:

Spectators’ deeply held commitment to repeat and recommend assisting a match

Manifest variables description

QUA1:

Tickets (availability, information, and staff attitudes)

QUA2:

Accessibility (accessibility, signposting, queue safety, and admission organization)

QUA3:

Facilities (shops, restrooms, seating, restaurants)

QUA4:

Stadium (loudspeakers, appearance, staff competence, cleanliness, Security/safety)

IMA1:

It is a great club

IMA2:

It has a good team

IMA3:

It is an ambitious club

IMA4:

It is a heroic club

SAT1:

The stadium experience was satisfactory

SAT2:

The time spent at the stadium was worth it

SAT3:

The money spent at the stadium was worth it

SAT4:

The experience met all my expectations

SAT5:

Overall satisfaction

LOY1:

I would recommend the experience at this stadium

LOY2:

I intend to repeat the experience at this stadium

Categorical Variables description

gender:

Gender of the spectators, a factor with levels: FEMALE and MALE

age:

Age of the spectators, a factor with levels <=30, 31-45, and >=46

tourist:

Whether the spectator was a tourist or not, a factor with levels: YES or NO

companion:

Who Accompanying the spectator, a factor with levels: FRIENDS, FAMILY, and OTHERS

Involvement:

Degree of involvement, a factor with levels: FAN, MEMBER, and OTHERS

Source

Universitat Autonoma of Barcelona . Business departament, Universitat Autonoma de Barcelona.

References

Lamberti, G., Rialp, J., and Simon, A. (2021). Antecedents of satisfaction and loyalty in different spectator tribes in a football context. International Journal of Sports Marketing and Sponsorship, doi: 10.1108/IJSMS-12-2020-0210;

info class

Description

info is an S4 class that contains info about the tree partition and the the the Fischer statitistcs: F-global and F-coefficientes

General information about the pathmox algorithm

Description

############################################################################################

Usage

info.mox(signif, size, deep, y)

Arguments

Details

Internal function

General information about the tree

Description

############################################################################################

Usage

mox.tree(moxtree)

Arguments

Details

Internal function

Value

a dataframe containing information about the tree and its nodes

moxtree class

Description

moxtree is an S4 class that contains info about moxtree

node class

Description

node is an S4 class that contains info about the node of the tree

Observations belonging to the nodes

Description

############################################################################################

Usage

nodes.tree(moxtree)

Arguments

Details

Internal function

Value

the observations belonging to the nodes

Binary partitions given a segmentation variable (factor).

Description

############################################################################################

Usage

partition(x)

Arguments

Details

Internal function

Value

a list of matrices containing all possibiles binary partions given a segmenation variable

Best partition given a set of segmentation variables

Description

############################################################################################

Usage

partopt(x, y, inner, .model, .scheme, .consistent, size_candidate)

Arguments

Details

Internal function

Value

a list containing information of the best partition given a set of segmentation variables

Calculating size (numeber of individual of a node)

Description

############################################################################################

Usage

percent.node(x, size)

Arguments

Details

Internal function

Value

the number of observations in a node

Plot function for the pathmox segmentation tree

Description

The function plot.plstree allows to drow PATHMOX tree

Usage

## S3 method for class 'plstree'
plot(
  x,
  .root.col = "#CCFFFF",
  .node.col = "#99CCCC",
  .leaf.col = "#009999",
  .shadow.size = 0.003,
  .node.shadow = "#669999",
  .leaf.shadow = "#006666",
  .cex = 0.7,
  .seg.col = "#003333",
  .lwd = 1,
  .show.pval = TRUE,
  .pval.col = "#009999",
  .main = NULL,
  .cex.main = 1,
  ...
)

Arguments

Author(s)

Giuseppe Lamberti

References

Lamberti, G., Aluja, T. B., and Sanchez, G. (2016). The Pathmox approach for PLS path modeling segmentation. Applied Stochastic Models in Business and Industry, 32(4), 453-468. doi: 10.1002/asmb.2168

Lamberti, G. (2015). Modeling with Heterogeneity, PhD Dissertation.

Sanchez, G. (2009). PATHMOX Approach: Segmentation Trees in Partial Least Squares Path Modeling, PhD Dissertation.

See Also

summary.plstree, print.plstree, pls.pathmox, bar_terminal, and bar_impvar

Examples

 ## Not run: 
# Example of PATHMOX approach in customer satisfaction analysis 
# (Spanish financial company).
# Model with 5 LVs (4 common factor: Image (IMAG), Value (VAL), 
# Satisfaction (SAT), and Loyalty (LOY); and 1 composite construct: 
# Quality (QUAL)

# load library and dataset csibank
library(genpathmx)
data("csibank")

# Define the model using the lavaan syntax. Use a set of regression formulas to define
# first the structural model and then the measurement model

CSImodel <- "
# Structural model
VAL  ~ QUAL
SAT  ~ IMAG  + QUAL + VAL
LOY  ~ IMAG + SAT

# Measurement model
# Composite
QUAL <~ qual1 + qual2 + qual3 + qual4 + qual5 + qual6 + qual7 
     
# Common factor
IMAG =~ imag1 + imag2 + imag3 + imag4 + imag5 + imag6 
VAL  =~ val1  + val2  + val3  + val4
SAT  =~ sat1  + sat2  + sat3           
LOY  =~ loy1  + loy2  + loy3           

"

# Identify the categorical variable to be used as input variables 
in the split process
CSIcatvar = csibank[,1:5]

# Check if variables are well specified (they have to be factors 
# and/or ordered factors)
str(CSIcatvar)

# Transform age and education into ordered factors
CSIcatvar$Age = factor(CSIcatvar$Age, levels = c("<=25", 
                                     "26-35", "36-45", "46-55", 
                                     "56-65", ">=66"),ordered = T)

CSIcatvar$Education = factor(CSIcatvar$Education, 
                            levels = c("Unfinished","Elementary", "Highschool",
                            "Undergrad", "Graduated"),ordered = T)
       
# Run Pathmox analysis (Lamberti et al., 2016; 2017)
csi.pathmox = pls.pathmox(
 .model = CSImodel ,
 .data  = csibank,
 .catvar= CSIcatvar,
 .alpha = 0.05,
 .deep = 2
)                     

Visualize the tree
plot(csi.pathmox)


## End(Not run)

Pathmox Segmentation Trees in Partial Least Squares Structural Equation Modeling (PLS-SEM)

Description

pls.pathmox calculates a binary segmentation tree in the context of partial least squares structural equation modeling (PLS-SEM) following the PATHMOX algorithm. It detects heterogeneity in PLS-SEM models when the segmentation variables (categorical variables), external to the model, are available, and when the objective of the research is exploratory. pls.pathmox function returns the most significant different models associated with the terminal nodes of the tree. It also returns a ranking according to importance of the categorical variables used in the split process. pls.pathmox also enables the hybrid multigroup analysis (Lamberti, 2021) to be run. In fact, the function returns an object, .hybrid, containing the datasets associated with the terminal nodes prepared to be treated with the cSEM package (Rademaker and Schuberth, 2020). It thus enables the MICOM and MGA procedures to be run (Hair et al., 2017; Henseler et al., 2016; Henseler et al., 2009).

Usage

pls.pathmox(
  .model,
  .data,
  .catvar,
  .scheme = "path",
  .consistent = TRUE,
  .alpha = 0.05,
  .deep = 2,
  .size = 0.1,
  .size_candidate = 50,
  .tree = TRUE
)

Arguments

Details

pls.pathmox uses the classical lavaan syntax to define inner and outer models and mode. The user can choose to perform the analysis for a single categorical variable or a set of factors. In the latter case, categorical variables must be organized as a dataframe. Scheme is equal to path by default following other PLS-SEM softwares (SMART-PLS (Ringle at al., 2015), cSEM R package (Rademaker and Schuberth, 2020)), but can be modified by the user to "centroid" or "factorial". Stops parameters (.alpha (threshold significance for the partitioning algorithm), .deep (maximum tree depth), and .size (minimum admissible sample size for a node)) are fixed respectively to .alpha = 0.05, .deep = 2, and .size = 0.10 according to Lamberti et al. (2016). However, again the user can modify these parameters according to the specific objectives of the analysis. pls.pathmox also defines a minimum admissible size for a candidate node that restricts the search of the optimal split to that partitions that produce nodes with an adequate number of observations. This parameter (.size_candidate) is fixed to 50 observations by default. PLS-SEM model coefficients used in the split process are estimated by applying the consistent PLS-SEM algorithm proposed by Dijkstra and Henseler (2015). However, the user can choose to run the analysis by using the classical algorithm by setting to FASLE the paramenter .consistent. pls.pathmox also returns an object containing the datasets associated with the terminal nodes (object$hybrid) prepared to be treated with the cSEM package (Rademaker and Schuberth, 2020). This means that, once the pathmox finalizes the search for the most significant different groups associated with the most significant different PLS-SEM models, the user can perform a detailed analysis for each group using the cSEM package, or can run the MICOM and MGA procedures (Hair et al. 2017; Henseler et al. 2016) on the terminal nodes.

Value

An object of class "plstree". This is a list with the following results:

Author(s)

Giuseppe Lamberti

References

Klesel, M., Schuberth, F., Niehaves, B., and Henseler, J. (2022). Multigroup analysis in information systems research using PLS-PM: A systematic investigation of approaches. ACM SIGMIS Database: the DATABASE for Advances in Information Systems, 53(3), 26-48. doi: 10.1145/3551783.3551787

Hair, J. F., Risher, J. J., Sarstedt, M., and Ringle, C. M. (2019). When to use and how to report the results of PLS-SEM. European business review, 31(1), 2-24. doi: 10.1108/EBR-11-2018-0203

Hair, J. F., Sarstedt, M., Ringle, C. M., and Gudergan, S. P. (2017). Advanced issues in partial least squares structural equation modeling. SAGE publications: Los Angeles

Henseler, J., Ringle, C. M., and Sarstedt, M. (2016). Testing measurement invariance of composites using partial least squares. International marketing review, 33(3), 405-431. doi: 10.1108/IMR-09-2014-0304

Ringle, C. M., and Sinkovics, R. R. (2009). The use of partial least squares path modeling in international marketing. Advances in International Marketing, 20, 277-319. doi: 10.1108/S1474-7979(2009)0000020014

Dijkstra, T. K., and Henseler, J. (2015). Consistent partial least squares path modeling. MIS quarterly, 39(2), 297-316. doi: 10.25300/MISQ/2015/39.2.02

Lamberti, G. (2021). Hybrid multigroup partial least squares structural equation modelling: an application to bank employee satisfaction and loyalty. Quality and Quantity, doi: 10.1007/s11135-021-01096-9

Lamberti, G., Aluja, T. B., and Sanchez, G. (2017). The Pathmox approach for PLS path modeling: Discovering which constructs differentiate segments. Applied Stochastic Models in Business and Industry, 33(6), 674-689. doi: 10.1007/s11135-021-01096-9

Lamberti, G., Aluja, T. B., and Sanchez, G. (2016). The Pathmox approach for PLS path modeling segmentation. Applied Stochastic Models in Business and Industry, 32(4), 453-468. doi: 10.1002/asmb.2168

Lamberti, G. (2015). Modeling with Heterogeneity, PhD Dissertation.

Rademaker, M. E., and Schuberth, F. (2020). cSEM: Composite-Based Structural Equation Modeling. Available at https://CRAN.R-project.org/package=cSEM.

Ringle, C.M., Wende, S. and Becker, J.M. (2015). SmartPLS 3. Boenningstedt: SmartPLS. Retrieved from https://www.smartpls.com.

Sanchez, G. (2009). PATHMOX Approach: Segmentation Trees in Partial Least Squares Path Modeling, PhD Dissertation.

Sanchez, G., and Aluja, T. B. (2006). PATHMOX: A PLS-PM Segmentation Algorithm, in Proceedings of the IASC Symposium on Knowledge Extraction by Modelling, International Association for Statistical Computing Island of Capri, Italy 4-6 September.

See Also

print.plstree, summary.plstree, bar_terminal, bar_impvar and plot.plstree

Examples

 ## Not run: 
# Example of PATHMOX approach in customer satisfaction analysis 
# (Spanish financial company).
# Model with 5 LVs (4 common factor: Image (IMAG), Value (VAL), 
# Satisfaction (SAT), and Loyalty (LOY); and 1 composite construct: 
# Quality (QUAL)

# Load library and dataset csibank
library(genpathmx)
data("csibank")

# Define the model using the laavan syntax. Use a set of regression formulas that define 
# first the structural model and then the measurement model

CSImodel <- "
# Structural model
VAL  ~ QUAL
SAT  ~ IMAG  + QUAL + VAL
LOY  ~ IMAG + SAT

# Measurement model
# composite
QUAL <~ qual1 + qual2 + qual3 + qual4 + qual5 + qual6 + qual7 
     
# common factor
IMAG =~ imag1 + imag2 + imag3 + imag4 + imag5 + imag6 
VAL  =~ val1  + val2  + val3  + val4
SAT  =~ sat1  + sat2  + sat3           
LOY  =~ loy1  + loy2  + loy3          

"

# Identify the categorical variable to be used as input variables 
# in the split process
CSIcatvar = csibank[,1:5]

# Check if variables are well specified (they have to be factors 
# and/or ordered factors)
str(CSIcatvar)

# Transform Age and Education into ordered factors
CSIcatvar$Age = factor(CSIcatvar$Age, levels = c("<=25", 
                                     "26-35", "36-45", "46-55", 
                                     "56-65", ">=66"),ordered = T)

CSIcatvar$Education = factor(CSIcatvar$Education, 
                            levels = c("Unfinished","Elementary", "Highschool",
                            "Undergrad", "Graduated"),ordered = T)
       
# Run Pathmox analysis (Lamberti et al., 2016; 2017)
csi.pathmox = pls.pathmox(
 .model = CSImodel ,
 .data  = csibank,
 .catvar= CSIcatvar,
 .alpha = 0.05,
 .deep = 2
)                     
                      
# Visualize results by summary
# summary(csi.pathmox)

# Run pathmox on one single variable
age = csibank[,2]

#' # Transform Age into an ordered factor
age = factor(age, levels = c("<=25", 
                                     "26-35", "36-45", "46-55", 
                                     "56-65", ">=66"),ordered = T)
csi.pathmox.age = pls.pathmox(
 .model = CSImodel ,
 .data  = csibank,
 .catvar= age,
 .alpha = 0.05,
 .deep = 1
)  

# Run hybrid multigroup analysis (Lamberti, 2021) using 
# the cSEM package (Rademaker and Schuberth, 2020)
# Install and load cSEM library
# Install.packages("cSEM")
# library(cSEM)

# Run cSEM Model for Pathmox terminal nodes

csilocalmodel = csem(
 .model = CSImodel,
 .data = csi.pathmox.age$hybrid)

# Check invariance and run MGA analysis (Hair et al., 2019)

testMICOM(csilocalmodel, .R = 60)

to_compare <- "
#' # Structural model
VAL  ~ QUAL
SAT  ~ IMAG  + QUAL + VAL
LOY  ~ IMAG + SAT
"

testMGD(csilocalmodel, .parameters_to_compare = to_compare, 
.R_bootstrap = 60,.approach_mgd = "Henseler")


## End(Not run)

create method plstree

Description

create method plstree

Usage

plstree(x, ...)

Arguments

Details

Internal function.

Value

internal method

Print function for Pathmox Segmentation Trees

Description

The function print.plstree returns the pls.pathmox results.

Usage

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

Arguments

Author(s)

Giuseppe Lamberti

References

Lamberti, G. (2021). Hybrid multigroup partial least squares structural equation modelling: an application to bank employee satisfaction and loyalty. Quality and Quantity, doi: 10.1007/s11135-021-01096-9

Lamberti, G., Aluja, T. B., and Sanchez, G. (2017). The Pathmox approach for PLS path modeling: Discovering which constructs differentiate segments. Applied Stochastic Models in Business and Industry, 33(6), 674-689. doi: 10.1007/s11135-021-01096-9

Lamberti, G., Aluja, T. B., and Sanchez, G. (2016). The Pathmox approach for PLS path modeling segmentation. Applied Stochastic Models in Business and Industry, 32(4), 453-468. doi: 10.1002/asmb.2168

Lamberti, G. (2015). Modeling with Heterogeneity, PhD Dissertation.

Sanchez, G. (2009). PATHMOX Approach: Segmentation Trees in Partial Least Squares Path Modeling, PhD Dissertation.

See Also

summary.plstree, pls.pathmox, bar_terminal, bar_impvar and plot.plstree

Examples

 ## Not run: 
# Example of PATHMOX approach in customer satisfaction analysis 
# (Spanish financial company).
# Model with 5 LVs (4 common factor: Image (IMAG), Value (VAL), 
# Satisfaction (SAT), and Loyalty (LOY); and 1 composite construct: 
# Quality (QUAL)

# load library and dataset csibank
library(genpathmx)
data("csibank")

# Define the model using the laavan syntax. Use a set of regression formulas to define 
# first the structural model and then the measurement model

CSImodel <- "
# Structural model
VAL  ~ QUAL
SAT  ~ IMAG  + QUAL + VAL
LOY  ~ IMAG + SAT

# Measurement model
# Composite
QUAL <~ qual1 + qual2 + qual3 + qual4 + qual5 + qual6 + qual7 
     
# Common factor
IMAG =~ imag1 + imag2 + imag3 + imag4 + imag5 + imag6 
VAL  =~ val1  + val2  + val3  + val4
SAT  =~ sat1  + sat2  + sat3           
LOY  =~ loy1  + loy2  + loy3           

"

# Run pathmox on one single variable
age = csibank[,2]

# Transform age into an ordered factor
age = factor(age, levels = c("<=25", "26-35", "36-45", "46-55",
                                      "56-65", ">=66"),ordered = T)
                                      
csi.pathmox.age = pls.pathmox(
 .model = CSImodel ,
 .data  = csibank,
 .catvar= age,
 .alpha = 0.05,
 .deep = 1
)  

# Visualize the Pathmox results
print(csi.pathmox.age)


## End(Not run)

printing the tree structure

Description

############################################################################################

Usage

printTree(moxtree)

Arguments

Details

Internal function.

Value

the tree structure

Observations belonging to the root node

Description

############################################################################################

Usage

root.tree(moxtree)

Arguments

Details

Internal function

Value

the observations belonging to the root node

Calculating Deepth stop criterion

Description

############################################################################################

Usage

showDeepth(node)

Arguments

Details

Internal function

Value

deepth of the tree

Best partition for a specific segmentation variable

Description

############################################################################################

Usage

splitopt(x, inner, .model, .scheme, .consistent, splits, fact, size_candidate)

Arguments

Details

Internal function

Value

a list containing information about the bets partition for a specific segmentation variable.

Summary function for Pathmox Segmentation Trees

Description

The function summary.plstrees returns the most important results obtained by the function pls.pathmox. In order, it provides the parameters of the algorithm (threshold significance, node size limit, tree depth level and the method used for the split partition), the basic characteristics of the tree (depth and number of terminal nodes), the split results (F-global and F-coefficient). It also returns a ranking of the categorical variables by importance and the terminal node results (path coefficients and R^2).

Usage

## S3 method for class 'plstree'
summary(object, ...)

Arguments

Author(s)

Giuseppe Lamberti

References

Lamberti, G. (2021). Hybrid multigroup partial least squares structural equation modelling: an application to bank employee satisfaction and loyalty. Quality and Quantity, doi: 10.1007/s11135-021-01096-9

Lamberti, G., Aluja, T. B., and Sanchez, G. (2017). The Pathmox approach for PLS path modeling: Discovering which constructs differentiate segments. Applied Stochastic Models in Business and Industry, 33(6), 674-689. doi: 10.1007/s11135-021-01096-9

Lamberti, G., Aluja, T. B., and Sanchez, G. (2016). The Pathmox approach for PLS path modeling segmentation. Applied Stochastic Models in Business and Industry, 32(4), 453-468. doi: 10.1002/asmb.2168

Lamberti, G. (2015). Modeling with Heterogeneity, PhD Dissertation.

Sanchez, G. (2009). PATHMOX Approach: Segmentation Trees in Partial Least Squares Path Modeling, PhD Dissertation.

See Also

print.plstree, pls.pathmox, bar_terminal, bar_impvar and plot.plstree

Examples

 ## Not run: 
# Example of PATHMOX approach in customer satisfaction analysis 
# (Spanish financial company).
# Model with 5 LVs (4 common factor: Image (IMAG), Value (VAL), 
# Satisfaction (SAT), and Loyalty (LOY); and 1 composite construct: 
# Quality (QUAL)

# load library and dataset csibank
library(genpathmx)
data("csibank")

# Define the model using the laavan syntax. Use a set of regression formulas to define 
# first the structural model and then the measurement model

CSImodel <- "
# Structural model
VAL  ~ QUAL
SAT  ~ IMAG  + QUAL + VAL
LOY  ~ IMAG + SAT

# Measurement model
# Composite
QUAL <~ qual1 + qual2 + qual3 + qual4 + qual5 + qual6 + qual7 
     
# common factor
IMAG =~ imag1 + imag2 + imag3 + imag4 + imag5 + imag6 
VAL  =~ val1  + val2  + val3  + val4
SAT  =~ sat1  + sat2  + sat3           
LOY  =~ loy1  + loy2  + loy3           

"

# Run pathmox on one single variable
age = csibank[,2]

# Transform age into an ordered factor
age = factor(age, levels = c("<=25", "26-35", "36-45", "46-55",
                                      "56-65", ">=66"),ordered = T)
                                      
csi.pathmox.age = pls.pathmox(
 .model = CSImodel ,
 .data  = csibank,
 .catvar= age,
 .alpha = 0.05,
 .deep = 1
)  

# Visualize the Pathmox results
summary(csi.pathmox.age)


## End(Not run)

Observations belonging to the terminal nodes

Description

############################################################################################

Usage

terminal.tree(moxtree)

Arguments

Details

Internal function

Value

the observations belonging to the terminal nodes

Cheking F-tests results

Description

############################################################################################

Usage

test.partition(x, inner, .model, .scheme, .consistent, modtwo, alpha)

Arguments

Details

Internal function

Value

list containing matrices needed for the comparison test.

Ranking of variables importance

Description

############################################################################################

Usage

var_imp_mox(x, y)

Arguments

Details

Internal function

Value

a dataframe containg the ranking of the categorical variable