# PLS Prediction-oriented Segmentation (PLS-POS)

## Abstract

PLS prediction-oriented segmentation (PLS-POS; Becker et al. 2013) is a distance-based segmentation method. It follows a clustering approach with a deterministic assignment of observations to groups and uses a distance measure for the reassignment of observations; as such, it has no distributional assumptions.

## Description

PLS prediction-oriented segmentation (PLS-POS) (Becker et al. 2013) is a distance-based segmentation method that builds on earlier work on distance measure-based segmentation (i.e., the PLS typological path modeling, PLS-TPM, approach, Squillacciotti 2005, and its enhancement, the response-based detection of respondent segments in PLS, REBUS-PLS, Esposito Vinzi et al. 2008).

PLS-POS algorithm introduces three novel features: (1) it uses an explicit PLS-specific objective criterion to form homogeneous groups, (2) it includes a new distance measure that is appropriate for PLS path models with both reflective and formative measures and is able to uncover unobserved heterogeneity in formative measures, and (3) it ensures continuous improvement of the objective criterion throughout the iterations of the algorithm (hill-climbing approach).

PLS-POS follows a clustering approach with a deterministic assignment of observations to groups and uses a distance measure for the reassignment of observations; as such, it has no distributional assumptions. The segmentation objective in a PLS path model is to form homogenous groups of observations with increased predictive power (R² of the endogenous latent variables) of the group-specific path model estimates (compared to the overall sample model).

A repeated application of PLS-POS with different starting partitions is
advisable to avoid local optima.

Becker et al. (2013) and Hair et al. (2024) describe the PLS-POS method in detail.

## PLS-POS Settings in SmartPLS

### Number of Segments

The number of pre-defined segments for which the segmentation will be performed.

### Maximum Iterations

The maximum number of iterations that the segmentation algorithm will perform. Should be sufficiently high for a good segmentation solution.

### Search Depth

The maximum search depth is the maximum number of observations in the sorted list of candidate observations for reassignment that will be tested if they improve the PLS-POS objective criterion.

This number may not exceed the number of observations in the overall sample. In initial explorative research stages, one may use a reduced search depth for reasons of performance. However, to determine the final segmentation result, the search depth should equal the maximum number of observations to ensure that the segmentation solution minimizes the PLS-POS objective criterion.

### Initial Separation

The initial separation of data into the pre-specified number of groups can either be based on a

*Random Assignment*to groups or on a prior*FIMIX segmentation*solution.If the

*FIMIX Segmentation*is chosen, the user also has to specify the nessesary FIMIX-PLS setting in a separate settings tab.### Pre-Segmentation

If this option is selected, the algorithm will perform a pre-segmentation in the first round that assigns all units to its best fitting group according to the distance measure.

It will not be checked whether this improves the objective criterion.

### Optimization Criterion

The optimization criterion (also objective criterion) will be optimized when estimating the segments in the PLS-POS algorithm. There are two options:

**Sum of All Construct R-Squares**: Uses the sum of all R-Squares in the model for all segments as the PLS-POS objective criterion that will be optimized (maximized) when reassigning observations in the course of the segmentation.**Sum of Target Construct R-Square**: Uses the target constructs sum of R-square values over all segments as the PLS-POS objective criterion that will be optimized (maximized) when reassigning observations in the course of the segmentation.**Sum of All Construct Weighted R-Squares**: Uses the sum of all weighted R-Squares in the model for all segments as the PLS-POS objective criterion that will be optimized (maximized) when reassigning observations in the course of the segmentation The weighting of the R-Squares is done by using the relative segment sizes.**Sum of Target Construct Weighted R-Square**: Uses the target constructs sum of weighted R-square values over all segments as the PLS-POS objective criterion that will be optimized (maximized) when reassigning observations in the course of the segmentation. The weighting of the R-Squares is done by using the relative segment sizes.

### Target Construct

If

**Optimization Criterion**is*Sum of all Construct R-Squares*or "Sum of All Construct Weighted R-Squares*, then this option does not have to be specified.If

**Optimization Criterion**is*Sum of Target Construct R-Square*or*Sum of Target Construct Weighted R-Square*, then this option defines the target construct for which the outer residuals or R-square value is calculated.## References

- Becker, J.-M., Rai, A., Ringle, C. M., and Völckner, F. (2013).
**Discovering Unobserved Heterogeneity in Structural Equation Models to Avert Validity Threats**,*MIS Quarterly*, 37(3): 665-694. - Hair, J. F., Sarstedt, M., Ringle, C. M., & Gudergan, S. P. (2024).
**Advanced Issues in Partial Least Squares Structural Equation Modeling (PLS-SEM)**, 2nd Ed., Thousand Oaks, CA: Sage. - Esposito Vinzi, V., Trinchera, L., Squillacciotti, S., and Tenenhaus, M. (2008).
**REBUS-PLS: A Response-Based Procedure for Detecting Unit Segments in PLS Path Modelling**,*Applied Stochastic Models in Business & Industry*24(5): 439-458. - Squillacciotti, S. (2005).
**Prediction Oriented Classification in PLS Path Modeling**,*PLS & Marketing: Proceedings of the 4th International Symposium on PLS and Related Methods*, T. Aluja, J. Casanovas, V. Esposito Vinzi and M. Tenenhaus (eds.), Paris: DECISIA: 499-506. - More literature ...