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The function pathmox.pls calculates a binary segmentation tree in
the context PLS-SEM following the PATHMOX algorithm.
The procedure can be resumed in the following way. It starts with the
estimation of the global PLS-SEM Model at the root node. Then, using
the segmentation variables, all possible binary splits of data are produced,
and for each partition local models are calculated. Among all the splits,
the best one is selected by means of the F-test comparing the inner models.
This process is recursively applied for each child node. The stop criterion
is based on the significance level of the p-value associated with the F statistic.
Additionally, two stop parameters are also considered: the number
of individuals in a node and the growing level of the depth of the tree.
This function extends the pathmox algorithm introduced by Sanchez in 2009
including the two new test: the F-block test (to detect the responsible latent
endogenous equations of the difference), the F-coefficient test
(to detect the path coefficients responsible of the difference).The F-tests
used in the split process are implemented following the classic lest square
estimation. An implementation of the tests following the LAD regression also
are proposed to overcome the parametric hypothesis of the F-test.
pls.pathmox(
x,
inner,
outer,
mode,
scheme = "path",
scaling = NULL,
scaled = TRUE,
SVAR,
signif,
deep,
method = "lm",
size,
X = NULL,
n.node = 30,
...
)matrix or data frame containing the manifest variables.
A square (lower triangular) boolean matrix representing the inner model (i.e. the path relationships between latent variables).
list of vectors with column indices or column names
from x indicating the sets of manifest variables forming
each block (i.e. which manifest variables correspond to each block).
character vector indicating the type of measurement for each
block. Possible values are: "A", "B", "newA", "PLScore", "PLScow".
The length of mode must be equal to the length of outer.
string indicating the type of inner weighting
scheme. Possible values are "centroid", "factorial", or
"path".
optional argument for runing the non-metric approach;
it is a list of string vectors indicating the type of
measurement scale for each manifest variable specified in outer.
scaling must be specified when working with non-metric variables.
Possible values: "num" (linear transformation,
suitable for numerical variables), "raw" (no transformation),
"nom" (non-monotonic transformation, suitable for nominal variables),
and "ord" (monotonic transformation, suitable for ordinal variables).
whether manifest variables should be standardized.
Only used when scaling = NULL. By the default (TRUE, data is
scaled to standardized values (mean=0 and variance=1).
A data frame of factors contaning the segmentation variables.
A numeric value indicating the significance threshold of the F-statistic. Must be a decimal number between 0 and 1.
An integer indicating the depth level of the tree. Must be an integer greater than 1.
A string indicating the criterion used to calculate the
the test can be equal to "lm" or "lad".
A numeric value indicating the minimum size of elements inside a node.
Optional dataset (matrix or data frame) used when argument
dataset=NULL inside pls.
It is the minimum number of individuals to consider a candidate
partition (30 by default).
Further arguments passed on to pls.pathmox.
An object of class "xtree.pls". Basically a list with the
following results:
Data frame with the results of the segmentation tree
List of elements contanined in the root node
List of elements contanined in terminal nodes
List of elements contanined in all nodes: terminal and intermediate
List of data frames containing the candidate splits of each node partition
Data frame containing the results of the F-global test for each node partition
List of data frames containing the results of the F-block test for each node partition
A list of data frames containing the results of the F-coefficients test for each node partition
Informations about the internal paramenters
a hybird categorical factor defined according to the final segments idenfied by pathmox
The argument x must be a data frame containing the manifest variables of the
PLS-SEM model
The argument inner is a matrix of zeros and ones that indicates
the structural relationships between latent variables. inner
must be a lower triangular matrix; it contains a 1 when column j
affects row i, 0 otherwise.
The argument SVAR must be a data frame containing segmentation
variables as factors. The number of rows in
SVAR must be the same as the number of rows in the data used in
x.
The argument signif represent the p-value level takes as reference
to stop the tree partitions.
The argument deep represent the depth level of the tree takes as reference
to stop the tree partitions.
The argument method is a string contaning the criterion used to calculate the
tests; if method="lm" the classic least square approach is used to perform the tests;
if method="lad" the LAD (least absolute deviation regression) is used.
The argument size is defined as a decimal value (i.e. proportion
of elements inside a node).
The argument n.node is the minimum number of individuals to consider a candidate
partition. If the candidate split produces a partition where the number of individuals is less
then n.node, the partition is not considered.
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. et al. (2016) The Pathmox approach for PLS path modeling segmentation. Applied Stochastic Models in Business and Industry; doi: 10.1002/asmb.2168;
Lamberti, G. (2014) Modeling with Heterogeneity. PhD Dissertation.
# NOT RUN {
# }
# NOT RUN {
## example of PLS-PM in alumni satisfaction
data(fibtele)
# select manifest variables
data.fib <-fibtele[,12:35]
# define inner model matrix
Image = rep(0,5)
Qual.spec = rep(0,5)
Qual.gen = rep(0,5)
Value = c(1,1,1,0,0)
Satis = c(1,1,1,1,0)
inner.fib = rbind(Image,Qual.spec, Qual.gen, Value, Satis)
colnames(inner.fib) = rownames(inner.fib)
# blocks of indicators (outer model)
outer.fib = list(1:8,9:11,12:16,17:20,21:24)
modes.fib = rep("A", 5)
# re-ordering those segmentation variables with ordinal scale
seg.fib= fibtele[,2:11]
seg.fib$Age = factor(seg.fib$Age, ordered=T)
seg.fib$Salary = factor(seg.fib$Salary,
levels=c("<18k","25k","35k","45k",">45k"), ordered=T)
seg.fib$Accgrade = factor(seg.fib$Accgrade,
levels=c("accnote<7","7-8accnote","accnote>8"), ordered=T)
seg.fib$Grade = factor(seg.fib$Grade,
levels=c("<6.5note","6.5-7note","7-7.5note",">7.5note"), ordered=T)
# Pathmox Analysis
fib.pathmox=pls.pathmox(data.fib, inner.fib, outer.fib, modes.fib,SVAR=seg.fib,signif=0.05,
deep=2,size=0.2,n.node=20)
# }
# NOT RUN {
library(genpathmox)
data(fibtele)
# select manifest variables
data.fib <-fibtele[1:50,12:35]
# define inner model matrix
Image = rep(0,5)
Qual.spec = rep(0,5)
Qual.gen = rep(0,5)
Value = c(1,1,1,0,0)
Satis = c(1,1,1,1,0)
inner.fib = rbind(Image,Qual.spec, Qual.gen, Value, Satis)
colnames(inner.fib) = rownames(inner.fib)
# blocks of indicators (outer model)
outer.fib = list(1:8,9:11,12:16,17:20,21:24)
modes.fib = rep("A", 5)
# re-ordering those segmentation variables with ordinal scale
seg.fib = fibtele[1:50,c(2,7)]
seg.fib$Salary = factor(seg.fib$Salary,
levels=c("<18k","25k","35k","45k",">45k"), ordered=TRUE)
# Pathmox Analysis
fib.pathmox=pls.pathmox(data.fib, inner.fib, outer.fib, modes.fib,SVAR=seg.fib,signif=0.05,
deep=2,size=0.2,n.node=20)
# }
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