A simulation study of Pathmox with non-normal data

1. A simulation study of Pathmox with non-normal data Gast�n S�nchez, Tom�s Aluja-Banet

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

28. Conclusions Non normality of distributions doesn�t 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. Tom�s 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 Questions�PLS & 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 PLS�03 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, HICSS�06, 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 PLS�07 International Symposium, Matforsk, As, Norway, 104-107. Tom�s 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., & F�nelon J.P. (1979) Traitement des donn�es statistiques. Paris: Dunod. Lohm�ller, J. B. (1989) Latent Variable Path Modeling with Partial Least Squares. Heidelberg: Physica-Verlag. Lubke, G.H. & Muth�n, 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 PLS�07 Intl. Symposium, Matforsk, As, Norway, 75-78. S�nchez, G. & Aluja, T. (2007) A Simulation Study of PATHMOX (PLS Path Modeling Segmentation Tree) Sensitivity. In: H. Martens & T. Naes. (Eds) Proceedings of the PLS�07 Intl. Symposium, Matforsk, As, Norway, 33-36. Serch, O. (2008) Sistema de Visualitzaci� de models PLS-PM. Projecte Final de Carrera. Facultat d�Inform�tica de Barcelona, Universitat Polit�cnica de Catalunya. Enero, 2008. Squillacciotti, S. (2005) Prediction oriented classification in PLS Path Modelling. In: Proceedings of the PLS�05 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. Tom�s Aluja. A simulation study of PATHMOX with non-normal data. PLS'09. Beijing