plspm (version 0.2-2)

it.reb: Response Based Unit Segmentation (REBUS) Algorithm - Iterative Steps

Description

REBUS-PLS is an iterative algorithm for performing response based clustering in a PLS-PM framework. This function allows to perform the iterative steps of the REBUS-PLS Algorithm (Steps 5-9). 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

pls

Object of class "plspm" returned by plspm.

hclus.res

Object of class "hclust" returned by res.clus

nk

Number of classes to take into account. This value should be defined according to the dendrogram obtained by performing res.clus.

Y

Optional dataset (matrix or data frame) used when argument dataset=NULL inside pls.

stop.crit

Number indicating the stop criterion for the iterative algorithm. The author suggests using the threshold of less than 0.05% of units changing class from one iteration to the other as stopping rule.

iter.max

An integer indicating the maximum number of iterations. Default value = 100.

Value

• An object of class "rebus", basically a list with the following elements:
• loadings
  Matrix of standardized loadings (i.e. correlations with LVs.) for each local model.
• path.coefs
  Matrix of path coefficients for each local model.
• quality
  Matrix containing the average communalities, the average redundancies, the R2 values, and the GoF index for each local model.
• segments
  Vector defining the class membership of each unit.
• origdata.clas
  The numeric matrix with original data and with a new column defining class membership of each unit.

Details

This function allows us to perform Steps 5-9 and the iteration procedure of the REBUS-PLS Algorithm. Moreover, this function provides the final class membership for each unit and summary results for the final local models. A threshold of 6 units per class is fixed. If there is a class with less than 6 units, the algorithm stops. For more details refer to rebus.pls. For expert users: if you want to test REBUS-PLS on several number of classes you need to run this function several times by changing nk. 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.

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. http://www.fedoa.unina.it/view/people/Trinchera,_Laura.html

See Also

plspm, rebus.pls, res.clus

Examples

## example of rebus analysis with simulated data
  data(sim.data)
  ## First compute GLOBAL model
  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(sim.data, inner=sim.inner, 
                      outer=sim.outer, modes=sim.mod)
  sim.global
  ## Then compute cluster analysis on residuals of global model
  sim.res.clus <- res.clus(sim.global)
  ## To conclude run iteration algorithm
  rebus.sim <- it.reb(sim.global, sim.res.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)