Finite Mixture Partial Least Squares (FIMIX-PLS)
Finite mixture partial least squares (FIMIX-PLS) is a latent class segmentation method for uncovering unobserved heterogeneity in the inner (structural) model of a PLS-SEM analysis. It captures such heterogeneity by estimating, for each observation, the probability of belonging to each of several segments, while simultaneously estimating the path coefficients for every segment. Researchers use FIMIX-PLS to check whether unexplained heterogeneity in the data threatens the validity of their PLS-SEM results.
Understanding FIMIX-PLS
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), Rigdon et al. (2011), and Wilden and Gudergan (2015). Sarstedt, Ringle, and Hair (2017) show how to use the two latent class segmentation methods FIMIX-PLS and prediction-oriented segmentation (PLS-POS) in tandem (see also Hair et al., 2024, Chapter 6).
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).
Advanced Settings
- Use Unstandardized Latent Variable Scores: Unstandardizes the latent variable scores to their original metric before performing the finite mixture segmentation.
- Estimate Regression Intercept: Includes a regression intercept in the structural regression that is used for the finite mixtures segmentation algorithm. Estimates segment-specific intercepts. Useful if latent variable scores are unstandardized before performing the segmentation task.
Number of Repetitions
FIMIX-PLS can be executed several times and selects the solution with the best LnL value to avoid local optima. This value defines how often the FIMIX-PLS algorithm will be executed.
Frequently Asked Questions
What is FIMIX-PLS used for?
FIMIX-PLS is a latent class segmentation method that uncovers unobserved heterogeneity in the structural model of a PLS-SEM analysis. It estimates, for each observation, the probability of belonging to one of several segments while simultaneously estimating segment-specific path coefficients.
What is the difference between observed and unobserved heterogeneity?
Observed heterogeneity can be traced back to observable characteristics, such as demographic variables like age or gender, and can be addressed by forming groups based on those characteristics. Unobserved heterogeneity, in contrast, stems from sources that are not known a priori and can distort PLS-SEM results without researchers being aware of it, which is why latent class techniques like FIMIX-PLS are needed.
Should I run FIMIX-PLS routinely in every PLS-SEM study?
Given the method's demonstrated performance in prior research and its availability in SmartPLS, Hair et al. (2012) suggest that researchers should routinely use FIMIX-PLS to evaluate whether their PLS-SEM results are distorted by unobserved heterogeneity.
Can FIMIX-PLS be combined with other segmentation methods?
Yes. Sarstedt, Ringle, and Hair (2017) show how to use FIMIX-PLS together with prediction-oriented segmentation (PLS-POS) in tandem (see also Hair et al., 2024, Chapter 6).
What do the "Maximum Iterations" and "Number of Repetitions" settings control?
Maximum iterations limits how many iterations the segmentation algorithm performs and should be set high enough to reach a good segmentation solution. Number of repetitions controls how often the algorithm is executed with different starting values; SmartPLS then selects the solution with the best log-likelihood (LnL) value to avoid local optima.
Related SmartPLS Methods
References
- Becker, J.-M., Rai, A., Ringle, C. M., & Völckner, F. (2013). Discovering unobserved heterogeneity in structural equation models to avert validity threats. MIS Quarterly, 37(3), 665–694.
- Hahn, C., Johnson, M. D., Herrmann, A., & Huber, F. (2002). Capturing customer heterogeneity using a finite mixture PLS approach. Schmalenbach Business Review, 54(3), 243–269.
- 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.). Sage.
- Hair, J. F., Sarstedt, M., Matthews, L., & Ringle, C. M. (2016). Identifying and treating unobserved heterogeneity with FIMIX-PLS: Part I - Method. European Business Review, 28(1), 63–76.
- Hair, J. F., Sarstedt, M., Ringle, C. M., & Mena, J. A. (2012). An assessment of the use of partial least squares structural equation modeling in marketing research. Journal of the Academy of Marketing Science, 40(3), 414–433.
- Matthews, L., Sarstedt, M., Hair, J. F., & Ringle, C. M. (2016). Identifying and treating unobserved heterogeneity with FIMIX-PLS: Part II – A case study. European Business Review, 28(2), 208–224.
- Rigdon, E. E., Ringle, C. M., & Sarstedt, M. (2010). Structural modeling of heterogeneous data with partial least squares. In N. K. Malhotra (Ed.), Review of marketing research (pp. 255–296). Sharpe.
- Rigdon, E. E., Ringle, C. M., Sarstedt, M., & Gudergan, S. P. (2011). Assessing heterogeneity in customer satisfaction studies: Across industry similarities and within industry differences. Advances in International Marketing, 22, 169–194.
- Ringle, C. M., Sarstedt, M., & Mooi, E. A. (2010). Response-based segmentation using finite mixture partial least squares: Theoretical foundations and an application to American Customer Satisfaction Index data. Annals of Information Systems, 8, 19–49.
- Sarstedt, M., Becker, J.-M., Ringle, C. M., & Schwaiger, M. (2011). Uncovering and treating unobserved heterogeneity with FIMIX-PLS: Which model selection criterion provides an appropriate number of segments? Schmalenbach Business Review, 63(1), 34–62.
- Sarstedt, M., Radomir, L., Moisescu, O. I., & Ringle, C. M. (2022). Latent class analysis in PLS-SEM: A review and recommendations for future applications. Journal of Business Research, 138, 398–407.
- Sarstedt, M., & Ringle, C. M. (2010). Treating unobserved heterogeneity in PLS path modelling: A comparison of FIMIX-PLS with different data analysis strategies. Journal of Applied Statistics, 37(8), 1299–1318.
- Sarstedt, M., Ringle, C. M., & Gudergan, S. P. (2016). Guidelines for treating unobserved heterogeneity in tourism research: A comment on Marques and Reis (2015). Annals of Tourism Research, 57(March), 279–284.
- Sarstedt, M., Ringle, C. M., & Hair, J. F. (2017). Treating unobserved heterogeneity in PLS-SEM: A multi-method approach. In R. Noonan & H. Latan (Eds.), Partial least squares structural equation modeling: Basic concepts, methodological issues and applications (pp. 197–217). Springer.
- Sarstedt, M., Schwaiger, M., & Ringle, C. M. (2009). Do we fully understand the critical success factors of customer satisfaction with industrial goods? - Extending Festge and Schwaiger's model to account for unobserved heterogeneity. Journal of Business Market Management, 3(3), 185–206.
- Wilden, R., & Gudergan, S. P. (2015). The impact of dynamic capabilities on operational marketing and technological capabilities: Investigating the role of environmental turbulence. Journal of the Academy of Marketing Science, 43(2), 181–199.
- More literature ...
Cite correctly
Please always cite the use of SmartPLS!
Ringle, Christian M., Wende, Sven, & Becker, Jan-Michael. (2024). SmartPLS 4. Bönningstedt: SmartPLS. Retrieved from https://www.smartpls.com
