The Pathmox approach for PLS path modeling segmentation
Modeling has often failed to meet expectations, mostly because of the difficulty of comprehending relationships within phenomena and expressing them in mathematical models. Reality is frequently too complex to be reflected in a single model. This is often the case of marketing research, where variab...
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| Vydáno v: | Applied stochastic models in business and industry Ročník 32; číslo 4; s. 453 - 468 |
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| Jazyk: | angličtina |
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Blackwell Publishing Ltd
01.07.2016
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| ISSN: | 1524-1904, 1526-4025 |
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| Abstract | Modeling has often failed to meet expectations, mostly because of the difficulty of comprehending relationships within phenomena and expressing them in mathematical models. Reality is frequently too complex to be reflected in a single model. This is often the case of marketing research, where variables relating to socioeconomics or psychographics constitute potential sources of heterogeneity. In such cases, the assumption of ‘one model fits all’ is unrealistic and may lead to inaccurate decisions. Thus, heterogeneity is a major issue in modeling. Once a model has been fitted to a complete data set that fulfills all validation criteria, it is difficult to establish whether it is valid for the whole population or it is merely an average artifact from several sub‐populations. The purpose of this paper is to present the Pathmox approach to deal with heterogeneity in partial least squares path modeling. The idea behind Pathmox is to build a tree of path models that have look‐alike structure as a binary decision tree, with different models for each of its nodes. The split criterion consists of an F statistic comparing two structural models. In order to ensure the suitability of the split criterion, a simulation study was conducted. Finally, we have applied Pathmox to a survey that measured Satisfaction among Spanish mobile phone operators. Results suggest that the Pathmox approach performs adequately in detecting partial least squares path modeling heterogeneity. Copyright © 2016 John Wiley & Sons, Ltd. |
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| AbstractList | Modeling has often failed to meet expectations, mostly because of the difficulty of comprehending relationships within phenomena and expressing them in mathematical models. Reality is frequently too complex to be reflected in a single model. This is often the case of marketing research, where variables relating to socioeconomics or psychographics constitute potential sources of heterogeneity. In such cases, the assumption of ‘one model fits all’ is unrealistic and may lead to inaccurate decisions. Thus, heterogeneity is a major issue in modeling. Once a model has been fitted to a complete data set that fulfills all validation criteria, it is difficult to establish whether it is valid for the whole population or it is merely an average artifact from several sub‐populations. The purpose of this paper is to present the Pathmox approach to deal with heterogeneity in partial least squares path modeling. The idea behind Pathmox is to build a tree of path models that have look‐alike structure as a binary decision tree, with different models for each of its nodes. The split criterion consists of an
F
statistic comparing two structural models. In order to ensure the suitability of the split criterion, a simulation study was conducted. Finally, we have applied Pathmox to a survey that measured
Satisfaction
among Spanish mobile phone operators. Results suggest that the Pathmox approach performs adequately in detecting partial least squares path modeling heterogeneity. Copyright © 2016 John Wiley & Sons, Ltd. Modeling has often failed to meet expectations, mostly because of the difficulty of comprehending relationships within phenomena and expressing them in mathematical models. Reality is frequently too complex to be reflected in a single model. This is often the case of marketing research, where variables relating to socioeconomics or psychographics constitute potential sources of heterogeneity. In such cases, the assumption of ‘one model fits all’ is unrealistic and may lead to inaccurate decisions. Thus, heterogeneity is a major issue in modeling. Once a model has been fitted to a complete data set that fulfills all validation criteria, it is difficult to establish whether it is valid for the whole population or it is merely an average artifact from several sub‐populations. The purpose of this paper is to present the Pathmox approach to deal with heterogeneity in partial least squares path modeling. The idea behind Pathmox is to build a tree of path models that have look‐alike structure as a binary decision tree, with different models for each of its nodes. The split criterion consists of an F statistic comparing two structural models. In order to ensure the suitability of the split criterion, a simulation study was conducted. Finally, we have applied Pathmox to a survey that measured Satisfaction among Spanish mobile phone operators. Results suggest that the Pathmox approach performs adequately in detecting partial least squares path modeling heterogeneity. Copyright © 2016 John Wiley & Sons, Ltd. This is the peer reviewed version of the following article: Giuseppe Lamberti, Aluja, T., Sanchez, G. The Pathmox approach for PLS path modeling segmentation. "Applied stochastic models in business and industry", Agost 2016, vol. 32, núm. 4, p. 453-468, which has been published in final form at DOI: 10.1002/asmb.2168. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Modeling has often failed to meet expectations, mostly because of the difficulty of comprehending relationships within phenomena and expressing them in mathematical models. Reality is frequently too complex to be reflected in a single model. This is often the case of marketing research, where variables relating to socioeconomics or psychographics constitute potential sources of heterogeneity. In such cases, the assumption of ‘one model fits all’ is unrealistic and may lead to inaccurate decisions. Thus, heterogeneity is a major issue in modeling. Once a model has been fitted to a complete data set that fulfills all validation criteria, it is difficult to establish whether it is valid for the whole population or it is merely an average artifact from several sub-populations. The purpose of this paper is to present the Pathmox approach to deal with heterogeneity in partial least squares path modeling. The idea behind Pathmox is to build a tree of path models that have look-alike structure as a binary decision tree, with different models for each of its nodes. The split criterion consists of an F statistic comparing two structural models. In order to ensure the suitability of the split criterion, a simulation study was conducted. Finally, we have applied Pathmox to a survey that measured Satisfaction among Spanish mobile phone operators. Results suggest that the Pathmox approach performs adequately in detecting partial least squares path modeling heterogeneity. Copyright © 2016 John Wiley & Sons, Ltd. Peer Reviewed Modeling has often failed to meet expectations, mostly because of the difficulty of comprehending relationships within phenomena and expressing them in mathematical models. Reality is frequently too complex to be reflected in a single model. This is often the case of marketing research, where variables relating to socioeconomics or psychographics constitute potential sources of heterogeneity. In such cases, the assumption of 'one model fits all' is unrealistic and may lead to inaccurate decisions. Thus, heterogeneity is a major issue in modeling. Once a model has been fitted to a complete data set that fulfills all validation criteria, it is difficult to establish whether it is valid for the whole population or it is merely an average artifact from several sub-populations. The purpose of this paper is to present the Pathmox approach to deal with heterogeneity in partial least squares path modeling. The idea behind Pathmox is to build a tree of path models that have look-alike structure as a binary decision tree, with different models for each of its nodes. The split criterion consists of an F statistic comparing two structural models. In order to ensure the suitability of the split criterion, a simulation study was conducted. Finally, we have applied Pathmox to a survey that measured Satisfaction among Spanish mobile phone operators. Results suggest that the Pathmox approach performs adequately in detecting partial least squares path modeling heterogeneity. |
| Author | Lamberti, Giuseppe Aluja, Tomas Banet Sanchez, Gaston |
| Author_xml | – sequence: 1 givenname: Giuseppe surname: Lamberti fullname: Lamberti, Giuseppe email: Correspondence to: Giuseppe Lamberti, Universitat Politècnica de Catalunya - Barcelona Tech, Department of Statistics and Operation, Research Campus Nord, C5204 c. Jordi Girona 1-3, Barcelona 08034, Spain., giuseppelamb@hotmail.com organization: Department of Statistics and Operation Research, Universitat Politècnica de Catalunya - Barcelona Tech, Campus Nord, C5204 c. Jordi Girona 1-3, 08034, Barcelona, Spain – sequence: 2 givenname: Tomas Banet surname: Aluja fullname: Aluja, Tomas Banet organization: Department of Statistics and Operation Research, Universitat Politècnica de Catalunya - Barcelona Tech, Campus Nord, C5204 c. Jordi Girona 1-3, 08034, Barcelona, Spain – sequence: 3 givenname: Gaston surname: Sanchez fullname: Sanchez, Gaston organization: Data Science Insight, CA, Palo Alto, U.S.A |
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| References | Henseler J, Chin WW. A comparison of approaches for the analysis of interaction effects between latent variables using partial least squares modeling. Structural Equation Modeling: A Multidisciplinary Journal 2010; 17(1):82-109. Fornell C, Bookstein FL. Two structural equation models: LISREL and PLS applied to consumer Exit-Voice theory. Journal of Marketing Research 1982; 19(4):440-452. Lohmöller JB. Latent Variable Path Modeling with Partial Least Squares. Physica: Heildelberg, 1989. Hackl P, Westlund AH. On structural equation modeling for customer satisfaction measurement. Total Quality Management 2000; 11(4,5,6):820-825. Esposito Vinzi V, Trinchera L, Squillacciotti S, Tenenhaus M. REBUS-PLS: a response-based procedure for detecting unit segments in PLS path modeling. Applied Stochastic Models in Business and Industry 2008; 24:439-458. 10.1002/asmb.728. Hair JF, Sarstedt M, Ringle CM. An assessment of the use of partial least squares structural equation modeling in marketing research. Journal of the Academy of Marketing Science 2012; 40:414-430. 10.1007/s11747-011-0261-6. Jedidi K, Jagpal HS, DeSarbo WS. Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity. Marketing Science 1997; 16:39-59. 10.1287/mksc.16.1.39. Bagozzi RP, Yi Y. Specification, evaluation, and interpretation of structural equation models. Journal of the Academy of Marketing Science 2012; 40:8-34. 10.1007/s11747-011-0278-x. Fornell CG, Johnson MD, Anderson EW, Cha J, Everitt B. The American Customer Satisfaction Index: nature, purpose and findings. Journal of Marketing 1996; 60(4):7-18. Lebart L, Morineau A, Fénelon JP. Traitement des donnes statistiques. Dunod: Paris, France, 1979. Anderson E, Fornell C. Foundations of the American Customer Satisfaction Index. Total Quality Management 2000; 11(7):869-882. Hahn C, Johnson MD, Herrmann A, Huber A. Capturing customer heterogeneity using a finite mixture PLS approach. Schmalenbach Business Review 2002; 54:243-269. Muthén BO. Latent variable modeling in heterogeneous populations. Psychometrika 1989; 54:557-585. 10.1007/BF02296397. Brandmaier AM, Oertzen T, McArdle JJ, Lindenberger U. Structural equation model trees. Psychological methods. American Psychological Association 2013; 18(1):71-86. Tenenhaus M, Esposito Vinzi V, Chatelin YM, Lauro C. PLS path modeling. Computational Statistics and Data Analysis 2005; 48:159-205. 10.1016/j.csda.2004.03.005. Baron RM, Kenny DA. The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology 1986; 5(6):1173-1182. Chin WW, Marcolin BL, Newsted PR. Partial least squares latent variable modeling approach for measuring interaction effects: results from a Monte Carlo simulation study and an electronic-mail emotion/adoption study. Information Systems Research 2003; 14(2):189-217. Westlund AH, Cassel CM, Eklöf J, Hackl P. Structural analysis and measurement of customer perceptions, assuming measurement and specifications errors. Total Quality Management 2001; 12(7,8):873-881. Reinartz WJ, Echambadi R, Chin WW. Generating non-normal data for simulation of structural equation models using Mattson's method. Multivariate Behavioral Research 2002; 37(2):227-244. 2002; 37 1982; 19 2010 2010; 17 2002; 54 1998 2009 2003; 14 2007 2006 2005 2003 2005; 48 1979 2013; 18 1989; 54 2000; 11 1986; 5 1996; 60 1985 1997; 16 2008; 24 1982 2001; 12 1989 2012; 40 e_1_2_9_30_1 e_1_2_9_31_1 Wold H (e_1_2_9_8_1) 1985 e_1_2_9_11_1 e_1_2_9_13_1 e_1_2_9_32_1 e_1_2_9_12_1 e_1_2_9_33_1 Henseler J (e_1_2_9_35_1) 2005 Esposito Vinzi V (e_1_2_9_14_1) 2010 Sanchez G (e_1_2_9_27_1) 2007 Ringle CM (e_1_2_9_19_1) 2005 e_1_2_9_15_1 e_1_2_9_38_1 Chin WW (e_1_2_9_34_1) 2003 e_1_2_9_39_1 e_1_2_9_17_1 e_1_2_9_36_1 e_1_2_9_16_1 e_1_2_9_18_1 Sanchez G (e_1_2_9_28_1) 2009 Lebart L (e_1_2_9_37_1) 1979 e_1_2_9_20_1 e_1_2_9_22_1 e_1_2_9_24_1 e_1_2_9_7_1 e_1_2_9_5_1 Sanchez G (e_1_2_9_26_1) 2006 e_1_2_9_4_1 e_1_2_9_3_1 e_1_2_9_2_1 Chin WW (e_1_2_9_10_1) 1998 Squillacciotti S (e_1_2_9_21_1) 2005 Brandmaier AM (e_1_2_9_29_1) 2013; 18 e_1_2_9_9_1 Trinchera L (e_1_2_9_23_1) 2007 Wold H (e_1_2_9_6_1) 1982 e_1_2_9_25_1 |
| References_xml | – reference: Bagozzi RP, Yi Y. Specification, evaluation, and interpretation of structural equation models. Journal of the Academy of Marketing Science 2012; 40:8-34. 10.1007/s11747-011-0278-x. – reference: Fornell C, Bookstein FL. Two structural equation models: LISREL and PLS applied to consumer Exit-Voice theory. Journal of Marketing Research 1982; 19(4):440-452. – reference: Fornell CG, Johnson MD, Anderson EW, Cha J, Everitt B. The American Customer Satisfaction Index: nature, purpose and findings. Journal of Marketing 1996; 60(4):7-18. – reference: Hackl P, Westlund AH. On structural equation modeling for customer satisfaction measurement. Total Quality Management 2000; 11(4,5,6):820-825. – reference: Lebart L, Morineau A, Fénelon JP. Traitement des donnes statistiques. Dunod: Paris, France, 1979. – reference: Hahn C, Johnson MD, Herrmann A, Huber A. Capturing customer heterogeneity using a finite mixture PLS approach. Schmalenbach Business Review 2002; 54:243-269. – reference: Hair JF, Sarstedt M, Ringle CM. An assessment of the use of partial least squares structural equation modeling in marketing research. Journal of the Academy of Marketing Science 2012; 40:414-430. 10.1007/s11747-011-0261-6. – reference: Baron RM, Kenny DA. The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology 1986; 5(6):1173-1182. – reference: Jedidi K, Jagpal HS, DeSarbo WS. Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity. Marketing Science 1997; 16:39-59. 10.1287/mksc.16.1.39. – reference: Brandmaier AM, Oertzen T, McArdle JJ, Lindenberger U. Structural equation model trees. Psychological methods. American Psychological Association 2013; 18(1):71-86. – reference: Chin WW, Marcolin BL, Newsted PR. 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| SubjectTerms | 60 Probability theory and stochastic processes 60H Stochastic analysis 62 Statistics 62H Multivariate analysis Anàlisi multivariable Anàlisi multivariant Classificació AMS Construction Criteria Decision trees Decisions Estadística matemàtica Heterogeneity Least squares method Matemàtiques i estadística Mathematical models model comparison Modelling Multivariate analysis Mètodes estadístics partial least squares path modeling Processos estocàstics segmentation segmentation trees Stochastic processes Àrees temàtiques de la UPC |
| Title | The Pathmox approach for PLS path modeling segmentation |
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