# Finite Mixture Partial Least Squares (FIMIX-PLS)

## Abstract

Finite mixture partial least squares (FIMIX-PLS) segmentation is a method to uncover unobserved heterogeneity in the inner (structural) model. It captures heterogeneity by estimating the probabilities of segment memberships for each observation and simultaneously estimates the path coefficients for all segments.

## Description

Finite mixture partial least squares (FIMIX-PLS) segmentation is a method to uncover unobserved heterogeneity in the inner (structural) model (Hahn et al. 2002). It captures heterogeneity by estimating the probabilities of segment memberships for each observation and simultaneously estimates the path coefficients of all segments.

Because heterogeneity is often present in empirical research, researchers should always consider potential sources of heterogeneity, for example, by forming groups of data based on observable characteristics such as demographics (e.g., age or gender). When heterogeneous data structures can be traced back to observable characteristics, we refer to this situation as observed heterogeneity. Unfortunately, the sources of heterogeneity in data can never be fully known a priori. Consequently, situations arise in which differences related to unobserved heterogeneity prevent the PLS path model from being accurately estimated so that validity problems may arise (Becker et al. 2013). Since researchers never know if unobserved heterogeneity is causing estimation problems, they need to apply complementary techniques for response-based segmentation (so-called latent class techniques) that allow for identifying and treating unobserved heterogeneity.

Several latent class techniques have recently been proposed that generalize statistical concepts such as finite mixture modeling, typological regression, and genetic PLS-SEM algorithms. One of the most prominent latent class approaches is finite mixture partial least squares (FIMIX-PLS; Hahn et al., 2002; Sarstedt et al., 2011). Based on a mixture regression concept, FIMIX-PLS simultaneously estimates the path coefficients and ascertains the data’s heterogeneity by calculating the probability of the observations’ segment membership so that they fit into a predetermined number of groups.

In light of the approach’s performance in prior studies (e.g., Sarstedt and Ringle, 2010) and its availability through the software application SmartPLS, Hair et al. (2012) suggest that researchers should routinely use the technique to evaluate whether PLS-SEM results are distorted by unobserved heterogeneity. For a more detailed discussion and step-by-step illustration of the approach on empirical data, see Ringle et al. (2010), Rigdon et al. (2010), Hair et al. (2016), and Matthews et al. (2016). For applications of FIMIX-PLS, see, for example, Sarstedt et al. (2009) and Rigdon et al. (2011).

## FIMIX-PLS 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.

### Stop Criterion

The FIMIX-PLS algorithm stops if the change in the log-likelihood (LnL) between two consecutive iterations is smaller than this stop criterion value (or the maximum number of iterations is reached).