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Simulation Study of PATHMOX with Non-Normal Data: Implications for Heterogeneity and Results

This simulation study examines the PATHMOX approach under non-normal data distributions. Conducted by Toms Aluja and Gastn Snchez at PLS'09 in Beijing, it explores the effects of data heterogeneity on test statistics, path coefficients, and the F-statistic. Key findings reveal that non-normality does not significantly compromise result validity, yet unbalanced segments can reduce p-value sensitivity. Statistical influences such as sample size, noise, and variable variance are also discussed, emphasizing the practical utility of PATHMOX in data mining contexts.

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Simulation Study of PATHMOX with Non-Normal Data: Implications for Heterogeneity and Results

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    1. A simulation study of Pathmox with non-normal data Gastn Snchez, Toms Aluja-Banet

    2. Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    3. Heterogeneity Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    4. Heterogeneity Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    5. Assignable sources of heterogeneity Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    6. Heterogeneity in PATHMOX Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    7. Heterogeneity in PATHMOX Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    8. The PATHMOX Approach Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    9. Split criterion Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    10. Hypothesis test Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    11. Stopping criterion Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    12. Simulation studies Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    13. Experimental conditions Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    14. Path coefficients Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    15. Data distributions Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    16. Symmetric distribution b (6,6) Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    17. Moderate skew distribution b (9,4) Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    18. High skew distribution b (9,1) Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    19. Global results Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    20. Influence of b distance by distribution Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    21. Influence of sample size by distribution Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    22. Influence of noise of LVs Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    23. Influence of noise of MVs Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    24. Unbalanced Segments (normal data) Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    25. Unbalanced Segments b (9,4) Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    26. Influence of different variances Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    27. Influence of different variances Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    28. Conclusions Non normality of distributions doesnt affect the results of the test statistic Splits with unbalanced children nodes delivers less sensitive p-values of the statistic. F-statistic favors balanced splits. Unequal variances of endogenous latent variables render less reliable the test statistic and hence the tree. The F test is used to discover unexpected segments by ordering the splits for a given node, as a data mining tool. Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    29. References Cassel, C., Hackl, P., & Westlund, A.H. (1999) Robustness of partial least squares method for estimating latent variable quality structures. Journal of Applied Statistics, 26(4): 435-446. Chin, W. (2000) Frequently Asked QuestionsPLS & PLS-Graph http://disc-nt.cba.uh.edu/chin/plsfaq/plsfaq.htm. Chin, W. (2003) A Permutation Based Procedure for Multi-Group Comparison of PLS Models. In: Proceedings of the PLS03 Intl. Symposium, 33-43. M. Vilares, M. Tenenhaus, P. Coelho, V. Esposito Vinzi, A. Morineau (Eds), Decisia. Chin, W.W., Marcolin, B.L., and Newsted, P.R. (2003) A Partial Least Squares Latent Variable Approach for Measuring Interaction Effects: Results from a Monte Carlo Simulation Study and Voice Mail Emotion/Adoption Study. Information Systems Research, 14(2): 189-217. Chow, G. (1960) Tests of Equality between Sets of Coeffs. in Two Linear Regressions. Econometrica, 28(3): 591-605. Dilon, W.R., & Kumar, A. (1994) Latent Structure and Other Mixture Models in Marketing: An Integrative Survey and Overview. In: Advanced Methods of Marketing Research, Richard P. Bagozzi (Ed.), Blackwell, 295-351. Esposito Vinzi, V., Trinchera, L., Squillacciotti, S., & Tenenhaus, M. (2008) REBUS-PLS, A Response-based procedure for detecting unit segments in PLS Path Modelling. App. Stoch. Models in Business & Industry, 24(5): 439-459. Goodhue, D., Lewis, W. & Thompson, R. PLS, Small Sample Size, and Statistical Power in MIS Research. (Proceedings of the 39th Hawaii International Conference on System Sciences - 2006, HICSS06, Track 8, 2006). Hahn, C., Johnson, M.D., Herrmann, A., & Huber, A. (2002) Capturing Customer Heterogeneity Using a Finite Mixture PLS Approach. Schmalenbach Business Review, 54: 243-269. Henseler, J. (2007) A New and Simple Approach to Multi-Group Analysis in PLS Path Modeling. In: H. Martens and T. Naes. (Eds), Proceedings of the PLS07 International Symposium, Matforsk, As, Norway, 104-107. Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

    30. References Jedidi, K., Jagpal, H.S., & DeSarbo, W.S. (1997) Finite-Mixture Structural Equation Models for Response-Based Segmentation and Unobserved Heterogeneity. Marketing Science, 16(1): 39-59. Lebart, L., Morineau, A., & Fnelon J.P. (1979) Traitement des donnes statistiques. Paris: Dunod. Lohmller, J. B. (1989) Latent Variable Path Modeling with Partial Least Squares. Heidelberg: Physica-Verlag. Lubke, G.H. & Muthn, B. (2005) Investigating Population Heterogeneity with Factor Mixture Models. Psychological Methods, 19(1): 21-39. Palumbo, F. & Romano, R. (2008) Possibilistic PLS Path Modeling: A New Approach to the Multigroup Comparison. In: Proceedings in Computational Statistics, 303-314. Paula Brito (Ed), Heidelberg: Physica-Verlag. Ringle, C. & Schlittgen, R. (2007) A Genetic Algorithm Segmentation Approach for Uncovering & Separating Groups of Data in PLS-PM. In: H. Martens & T. Naes. (Eds) Proceedings of the PLS07 Intl. Symposium, Matforsk, As, Norway, 75-78. Snchez, G. & Aluja, T. (2007) A Simulation Study of PATHMOX (PLS Path Modeling Segmentation Tree) Sensitivity. In: H. Martens & T. Naes. (Eds) Proceedings of the PLS07 Intl. Symposium, Matforsk, As, Norway, 33-36. Serch, O. (2008) Sistema de Visualitzaci de models PLS-PM. Projecte Final de Carrera. Facultat dInformtica de Barcelona, Universitat Politcnica de Catalunya. Enero, 2008. Squillacciotti, S. (2005) Prediction oriented classification in PLS Path Modelling. In: Proceedings of the PLS05 Intl. Symposium, T. Aluja, J. Casanovas, V. Esposito, A. Morineau, M. Tenenhaus (Eds), SPAD Test&Go, 499-506. Tenenhaus, M., Esposito Vinzi, V., Chatelin, Y.M., & Lauro, C. (2005) PLS path modeling. Computational Statistics & Data Analysis, 48: 159-205. Toms Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing

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