Goodness-of-fit indices for partial least squares path modeling

This paper discusses a recent development in partial least squares (PLS) path modeling, namely goodness-of-fit indices. In order to illustrate the behavior of the goodness-of-fit index (GoF) and the relative goodness-of-fit index (GoF rel ), we estimate PLS path models with simulated data, and contr...

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Published inComputational statistics Vol. 28; no. 2; pp. 565 - 580
Main Authors Henseler, Jörg, Sarstedt, Marko
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.04.2013
Springer Nature B.V
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Abstract This paper discusses a recent development in partial least squares (PLS) path modeling, namely goodness-of-fit indices. In order to illustrate the behavior of the goodness-of-fit index (GoF) and the relative goodness-of-fit index (GoF rel ), we estimate PLS path models with simulated data, and contrast their values with fit indices commonly used in covariance-based structural equation modeling. The simulation shows that the GoF and the GoF rel are not suitable for model validation. However, the GoF can be useful to assess how well a PLS path model can explain different sets of data.
AbstractList This paper discusses a recent development in partial least squares (PLS) path modeling, namely goodness-of-fit indices. In order to illustrate the behavior of the goodness-of-fit index (GoF) and the relative goodness-of-fit index (GoF^sub rel^), we estimate PLS path models with simulated data, and contrast their values with fit indices commonly used in covariance-based structural equation modeling. The simulation shows that the GoF and the GoF^sub rel^ are not suitable for model validation. However, the GoF can be useful to assess how well a PLS path model can explain different sets of data. [PUBLICATION ABSTRACT]
This paper discusses a recent development in partial least squares (PLS) path modeling, namely goodness-of-fit indices. In order to illustrate the behavior of the goodness-of-fit index (GoF) and the relative goodness-of-fit index (GoF rel ), we estimate PLS path models with simulated data, and contrast their values with fit indices commonly used in covariance-based structural equation modeling. The simulation shows that the GoF and the GoF rel are not suitable for model validation. However, the GoF can be useful to assess how well a PLS path model can explain different sets of data.
This paper discusses a recent development in partial least squares (PLS) path modeling, namely goodness-of-fit indices. In order to illustrate the behavior of the goodness-of-fit index (GoF) and the relative goodness-of-fit index (GoF sub(rel)), we estimate PLS path models with simulated data, and contrast their values with fit indices commonly used in covariance-based structural equation modeling. The simulation shows that the GoF and the GoF sub(rel) are not suitable for model validation. However, the GoF can be useful to assess how well a PLS path model can explain different sets of data.
Author Henseler, Jörg
Sarstedt, Marko
Author_xml – sequence: 1
  givenname: Jörg
  surname: Henseler
  fullname: Henseler, Jörg
  organization: Institute for Management Research, Radboud University Nijmegen
– sequence: 2
  givenname: Marko
  surname: Sarstedt
  fullname: Sarstedt, Marko
  email: sarstedt@bwl.lmu.de
  organization: Institute for Market-based Management, Munich School of Management, Ludwig-Maximilians-Universität München
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Goodness-of-fit index (GoF)
Partial least squares path modeling (PLS)
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References FornellCLarckerDFEvaluating structural equation models with unobservable variables and measurement errorJ Market Res1981181395010.2307/3151312
Wold HOA (1985a) Partial least squares. In: Kotz S, Johnson NL (eds) Encyclopaedia of statistical sciences, vol 6. Wiley, New York, NY, pp 581–591
SteigerJHStructural model evaluation and modification: an interval estimation approachMultivar Behav Res1990252173180298394710.1207/s15327906mbr2502_4
ChinWWMarcolinBLNewstedPRA partial least squares latent variable modeling approach for measuring interaction effects. Results from a Monte Carlo simulation study and an electronic-mail emotion/adopion studyInf Syst Res200314218921710.1287/isre.14.2.189.16018
ChinWEspositoVinziVChinWWHenselerJWangHHow to write up and report PLS analysesHandbook of partial least squares: concepts, methods and applications2010HeidelbergSpringer65569010.1007/978-3-540-32827-8_29
Wold HOA (1985b) Partial least squares and LISREL models. In: Nijkamp P, Leitner H, Wrigley N (eds) Measuring the unmeasurable. Nijhoff, Dordrecht, Boston, Lancaster, pp 220–251
Ringle C, Sarstedt M, Straub D (2012) A critical look at the use of pls-sem in mis quarterly. MIS Q 36(1): iii–xiv
Lohmöller JB (1989) Latent variable path modeling with partial least squares. Physica, Heidelberg
HenselerJOn the convergence of the partial least squares path modeling algorithmComput Stat201025110712025867271224.6501910.1007/s00180-009-0164-x
SarstedtMRingleCMTreating unobserved heterogeneity in PLS path modelling: a comparison of FIMIX-PLS with different data analysis strategiesJ Appl Stat201037812991318275193610.1080/02664760903030213
ReinartzWJHaenleinMHenselerJAn empirical comparison of the efficacy of covariance-based and variance-based SEMInt J Res Market200926433234410.1016/j.ijresmar.2009.08.001
BagozziRPYiYBagozziRPAdvanced topics in structural equation modelsAdvanced methods of marketing research1994OxfordBlackwell151
EspositoVinziVTrincheraLSquillacciottiSTenenhausMREBUS-PLS: A response-based procedure for detecting unit segments in PLS path modellingAppl Stoch Models Bus Ind2008245439458246377510.1002/asmb.728
Arbuckle JL (2003) Amos 5 User’s Guide. SPSS
Soft Modeling, Inc (1992–2002) PLS-Graph Version 3.0. Houston, TX. http://www.plsgraph.com
KrijnenWDijkstraTGillRConditions for factor (in) determinacy in factor analysisPsychometrika1998634359367167171510.1007/BF02294860
WoldHOADavidFNNon-linear estimation by iterative least squares proceduresResearch papers in statistics1966LondonWiley411444
WheatonBMuthénBAlwinDFSummersGFHeiseDAssessing reliability and stability in panel modelsSociological methodology1977Washington, DCJossey-Bass84136
Wold HOA (1973) Nonlinear iterative partial least squares (NIPALS) modelling. Some current developments. In: Krishnaiah PR (ed) Proceedings of the 3rd international symposium on multivariate analysis, Dayton, OH. pp 383–407
Tenenhaus M, Amato S, Esposito Vinzi V (2004) A global goodness-of-fit index for PLS structural equation modelling. In: Proceedings of the XLII SIS scientific meeting. pp 739–742
HenselerJRingleCSinkovicsRThe use of partial least squares path modeling in international marketingAdv Int Market2009202009277319
Dijkstra TK (2010) Latent variables and indices: Herman Wold’s basic design and partial least squares. In: Vinzi VE, Chin WW, Henseler J, Wang H (eds) Handbook of partial least squares: concepts, methods, and applications, computational statistics, vol II, Springer, Heidelberg, pp 23–46 (in print)
Wold HOA (1989) Introduction to the second generation of multivariate analysis. In: Wold HOA (ed) Theoretical empiricism. A general rationale for scientific model-building. Paragon House, New York, pp VIII–XL
BollenKAStructural equations with latent variables1989New York, NYWiley0731.62159
Wold HOA (1982) Soft modelling: the basic design and some extensions. In: Jöreskog KG, Wold HOA (eds) Systems under indirect observation. Causality, structure, prediction, vol II. North-Holland, Amsterdam, New York, Oxford, pp 1–54
FornellCThe quality of economic output: empirical generalizations about its distribution and relationship to market shareMarket Sci1995143G203G21110.1287/mksc.14.3.G203
BollenKAA new incremental fit index for general structural equation modelsSociol Methods Res1989173303203779810.1177/0049124189017003004
Rigdon EE (1998) Structural equation modeling. In: Marcoulides GA (ed) Modern methods for business research, Lawrence Erlbaum Associates. Mahwah, pp 251–294
Esposito Vinzi V, Chin WW, Henseler J, Wang H (eds) (2010a) Handbook of partial least squares: concepts, methods and applications. Springer, Heidelberg
ChinWWNewstedPRHoyleRHStructural equation modeling analysis with small samples using partial least squaresStatistical strategies for small sample research1999Thousand Oaks, CASage334342
Ringle CM, Wende S, Will A (2005) SmartPLS 2.0 M3. University of Hamburg, Hamburg, Germany. http://www.smartpls.de
AkaikeHFactor analysis and AICPsychometrika19875233173329144590627.6206710.1007/BF02294359
MulaikSAJamesLRvan AlstineJBennettNLindSStilwellCDEvaluation of goodness-of-fit indices for structural equation modelsPsychol Bull198910543044510.1037/0033-2909.105.3.430
Rigdon EE, Ringle CM, Sarstedt M (2010) Structural modeling of heterogeneous data with partial least squares. In: Malhotra NK (ed) Review of marketing research, vol 7. Sharpe, pp 255–296
Dijkstra TK (1981) Latent variables in linear stochastic models: reflections on “Maximum Likelihood” and “Partial Least Squares” methods. PhD thesis, Groningen University, Groningen, a second edition was published in 1985 by Sociometric Research Foundation
Jöreskog KG, Sörbom D (1986) LISREL VI: Analysis of linear structural relationships by maximum likelihood and least squares methods. Scientific Software, Mooresville, IN
Monecke A, Leisch F (2012) semPLS: Structural equation modeling using partial least squares. J Stat Softw (forthcoming)
PaxtonPCurranPBollenKKirbyJChenFMonte carlo experiments: design and implementationStruct Equ Model20018228731210.1207/S15328007SEM0802_7
TenenhausATenenhausMRegularized generalized caconical correlation analysisPsychometrika201176225728427888850589996110.1007/s11336-011-9206-8
DuartePRaposoMEspositoVinziVChinWWHenselerJWangHA PLS model to study brand preference: an application to the mobile phone marketHandbook of partial least squares: concepts, methods and applications2010HeidelbergSpringer44948510.1007/978-3-540-32827-8_21
BentlerPMComparative fit indexes in structural modelsPsychol Bull1990107223824610.1037/0033-2909.107.2.238
Esposito VinziVTrincheraLAmatoSEspositoVinziVChinWWHenselerJWangHPLS path modeling: from foundations to recent developments and open issues for model assessment and improvementHandbook of partial least squares: concepts, methods and applications2010HeidelbergSpringer478210.1007/978-3-540-32827-8_3
FornellCBooksteinFLTwo structural equation models: LISREL and PLS applied to consumer exit-voice theoryJ Market Res198219444045210.2307/3151718
BassBAvolioBJungDBersonYPredicting unit performance by assessing transformational and transactional leadershipJ Appl Psychol200388220721810.1037/0021-9010.88.2.207
SarstedtMHenselerJRingleCMMultigroup analysis in partial least squares (PLS) path modeling: Alternative methods and empirical resultsAdv Int Market20112219521810.1108/S1474-7979(2011)0000022012
HullandJUse of partial least squares (PLS) in strategic management research: a review of four recent studiesStrateg Manag J199920219520410.1002/(SICI)1097-0266(199902)20:2<195::AID-SMJ13>3.0.CO;2-7
TenenhausMVinziVEChatelinYMLauroCPLS path modelingComput Stat Data Anal20054811592050537409910.1016/j.csda.2004.03.005
WoldHOACausal flows with latent variables: partings of the ways in the light of NIPALS modellingEur Econ Rev197451678610.1016/0014-2921(74)90008-7
SosikJKahaiSPiovosoMSilver bullet or voodoo statisticsGroup Organ Manag2009341510.1177/1059601108329198
Hair J, Sarstedt M, Ringle C, Mena J (2012) An assessment of the use of partial least squares structural equation modeling in marketing research. J Acad Market Sci (forthcoming)
Addinsoft SARL (2007–2008) XLSTAT-PLSPM. Paris, France. http://www.xlstat.com/en/products/xlstat-plspm
HanafiMPLS path modelling: computation of latent variables with the estimation mode BComput Stat200722227529223184601196.6210310.1007/s00180-007-0042-3
HuLTBentlerPMCutoff criteria for fit indexes in covariance structure analysis: conventional criteria versus new alternativesStruct Equ Model19996115510.1080/10705519909540118
J Hulland (317_CR26) 1999; 20
B Wheaton (317_CR46) 1977
P Duarte (317_CR14) 2010
WJ Reinartz (317_CR33) 2009; 26
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J Henseler (317_CR23) 2010; 25
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KA Bollen (317_CR8) 1989
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JH Steiger (317_CR42) 1990; 25
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WW Chin (317_CR10) 1999
A Tenenhaus (317_CR43) 2011; 76
RP Bagozzi (317_CR4) 1994
H Akaike (317_CR2) 1987; 52
SA Mulaik (317_CR31) 1989; 105
J Henseler (317_CR24) 2009; 20
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KA Bollen (317_CR7) 1989; 17
C Fornell (317_CR20) 1981; 18
W Krijnen (317_CR28) 1998; 63
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B Bass (317_CR5) 2003; 88
M Hanafi (317_CR22) 2007; 22
HOA Wold (317_CR47) 1966
P Paxton (317_CR32) 2001; 8
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V EspositoVinzi (317_CR15) 2008; 24
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PM Bentler (317_CR6) 1990; 107
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C Fornell (317_CR19) 1982; 19
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References_xml – reference: Ringle C, Sarstedt M, Straub D (2012) A critical look at the use of pls-sem in mis quarterly. MIS Q 36(1): iii–xiv
– reference: ChinWEspositoVinziVChinWWHenselerJWangHHow to write up and report PLS analysesHandbook of partial least squares: concepts, methods and applications2010HeidelbergSpringer65569010.1007/978-3-540-32827-8_29
– reference: FornellCLarckerDFEvaluating structural equation models with unobservable variables and measurement errorJ Market Res1981181395010.2307/3151312
– reference: TenenhausATenenhausMRegularized generalized caconical correlation analysisPsychometrika201176225728427888850589996110.1007/s11336-011-9206-8
– reference: SarstedtMHenselerJRingleCMMultigroup analysis in partial least squares (PLS) path modeling: Alternative methods and empirical resultsAdv Int Market20112219521810.1108/S1474-7979(2011)0000022012
– reference: DuartePRaposoMEspositoVinziVChinWWHenselerJWangHA PLS model to study brand preference: an application to the mobile phone marketHandbook of partial least squares: concepts, methods and applications2010HeidelbergSpringer44948510.1007/978-3-540-32827-8_21
– reference: SosikJKahaiSPiovosoMSilver bullet or voodoo statisticsGroup Organ Manag2009341510.1177/1059601108329198
– reference: Hair J, Sarstedt M, Ringle C, Mena J (2012) An assessment of the use of partial least squares structural equation modeling in marketing research. J Acad Market Sci (forthcoming)
– reference: Esposito VinziVTrincheraLAmatoSEspositoVinziVChinWWHenselerJWangHPLS path modeling: from foundations to recent developments and open issues for model assessment and improvementHandbook of partial least squares: concepts, methods and applications2010HeidelbergSpringer478210.1007/978-3-540-32827-8_3
– reference: KrijnenWDijkstraTGillRConditions for factor (in) determinacy in factor analysisPsychometrika1998634359367167171510.1007/BF02294860
– reference: HanafiMPLS path modelling: computation of latent variables with the estimation mode BComput Stat200722227529223184601196.6210310.1007/s00180-007-0042-3
– reference: BassBAvolioBJungDBersonYPredicting unit performance by assessing transformational and transactional leadershipJ Appl Psychol200388220721810.1037/0021-9010.88.2.207
– reference: Soft Modeling, Inc (1992–2002) PLS-Graph Version 3.0. Houston, TX. http://www.plsgraph.com
– reference: Wold HOA (1982) Soft modelling: the basic design and some extensions. In: Jöreskog KG, Wold HOA (eds) Systems under indirect observation. Causality, structure, prediction, vol II. North-Holland, Amsterdam, New York, Oxford, pp 1–54
– reference: Rigdon EE, Ringle CM, Sarstedt M (2010) Structural modeling of heterogeneous data with partial least squares. In: Malhotra NK (ed) Review of marketing research, vol 7. Sharpe, pp 255–296
– reference: WoldHOACausal flows with latent variables: partings of the ways in the light of NIPALS modellingEur Econ Rev197451678610.1016/0014-2921(74)90008-7
– reference: EspositoVinziVTrincheraLSquillacciottiSTenenhausMREBUS-PLS: A response-based procedure for detecting unit segments in PLS path modellingAppl Stoch Models Bus Ind2008245439458246377510.1002/asmb.728
– reference: Rigdon EE (1998) Structural equation modeling. In: Marcoulides GA (ed) Modern methods for business research, Lawrence Erlbaum Associates. Mahwah, pp 251–294
– reference: Lohmöller JB (1989) Latent variable path modeling with partial least squares. Physica, Heidelberg
– reference: Wold HOA (1985a) Partial least squares. In: Kotz S, Johnson NL (eds) Encyclopaedia of statistical sciences, vol 6. Wiley, New York, NY, pp 581–591
– reference: Dijkstra TK (1981) Latent variables in linear stochastic models: reflections on “Maximum Likelihood” and “Partial Least Squares” methods. PhD thesis, Groningen University, Groningen, a second edition was published in 1985 by Sociometric Research Foundation
– reference: Dijkstra TK (2010) Latent variables and indices: Herman Wold’s basic design and partial least squares. In: Vinzi VE, Chin WW, Henseler J, Wang H (eds) Handbook of partial least squares: concepts, methods, and applications, computational statistics, vol II, Springer, Heidelberg, pp 23–46 (in print)
– reference: Addinsoft SARL (2007–2008) XLSTAT-PLSPM. Paris, France. http://www.xlstat.com/en/products/xlstat-plspm/
– reference: ChinWWMarcolinBLNewstedPRA partial least squares latent variable modeling approach for measuring interaction effects. Results from a Monte Carlo simulation study and an electronic-mail emotion/adopion studyInf Syst Res200314218921710.1287/isre.14.2.189.16018
– reference: Tenenhaus M, Amato S, Esposito Vinzi V (2004) A global goodness-of-fit index for PLS structural equation modelling. In: Proceedings of the XLII SIS scientific meeting. pp 739–742
– reference: Monecke A, Leisch F (2012) semPLS: Structural equation modeling using partial least squares. J Stat Softw (forthcoming)
– reference: HenselerJOn the convergence of the partial least squares path modeling algorithmComput Stat201025110712025867271224.6501910.1007/s00180-009-0164-x
– reference: FornellCBooksteinFLTwo structural equation models: LISREL and PLS applied to consumer exit-voice theoryJ Market Res198219444045210.2307/3151718
– reference: Ringle CM, Wende S, Will A (2005) SmartPLS 2.0 M3. University of Hamburg, Hamburg, Germany. http://www.smartpls.de
– reference: HuLTBentlerPMCutoff criteria for fit indexes in covariance structure analysis: conventional criteria versus new alternativesStruct Equ Model19996115510.1080/10705519909540118
– reference: WoldHOADavidFNNon-linear estimation by iterative least squares proceduresResearch papers in statistics1966LondonWiley411444
– reference: BagozziRPYiYBagozziRPAdvanced topics in structural equation modelsAdvanced methods of marketing research1994OxfordBlackwell151
– reference: TenenhausMVinziVEChatelinYMLauroCPLS path modelingComput Stat Data Anal20054811592050537409910.1016/j.csda.2004.03.005
– reference: Arbuckle JL (2003) Amos 5 User’s Guide. SPSS
– reference: BollenKAA new incremental fit index for general structural equation modelsSociol Methods Res1989173303203779810.1177/0049124189017003004
– reference: HullandJUse of partial least squares (PLS) in strategic management research: a review of four recent studiesStrateg Manag J199920219520410.1002/(SICI)1097-0266(199902)20:2<195::AID-SMJ13>3.0.CO;2-7
– reference: AkaikeHFactor analysis and AICPsychometrika19875233173329144590627.6206710.1007/BF02294359
– reference: ReinartzWJHaenleinMHenselerJAn empirical comparison of the efficacy of covariance-based and variance-based SEMInt J Res Market200926433234410.1016/j.ijresmar.2009.08.001
– reference: WheatonBMuthénBAlwinDFSummersGFHeiseDAssessing reliability and stability in panel modelsSociological methodology1977Washington, DCJossey-Bass84136
– reference: PaxtonPCurranPBollenKKirbyJChenFMonte carlo experiments: design and implementationStruct Equ Model20018228731210.1207/S15328007SEM0802_7
– reference: Jöreskog KG, Sörbom D (1986) LISREL VI: Analysis of linear structural relationships by maximum likelihood and least squares methods. Scientific Software, Mooresville, IN
– reference: ChinWWNewstedPRHoyleRHStructural equation modeling analysis with small samples using partial least squaresStatistical strategies for small sample research1999Thousand Oaks, CASage334342
– reference: Wold HOA (1985b) Partial least squares and LISREL models. In: Nijkamp P, Leitner H, Wrigley N (eds) Measuring the unmeasurable. Nijhoff, Dordrecht, Boston, Lancaster, pp 220–251
– reference: FornellCThe quality of economic output: empirical generalizations about its distribution and relationship to market shareMarket Sci1995143G203G21110.1287/mksc.14.3.G203
– reference: BentlerPMComparative fit indexes in structural modelsPsychol Bull1990107223824610.1037/0033-2909.107.2.238
– reference: Wold HOA (1989) Introduction to the second generation of multivariate analysis. In: Wold HOA (ed) Theoretical empiricism. A general rationale for scientific model-building. Paragon House, New York, pp VIII–XL
– reference: SteigerJHStructural model evaluation and modification: an interval estimation approachMultivar Behav Res1990252173180298394710.1207/s15327906mbr2502_4
– reference: Wold HOA (1973) Nonlinear iterative partial least squares (NIPALS) modelling. Some current developments. In: Krishnaiah PR (ed) Proceedings of the 3rd international symposium on multivariate analysis, Dayton, OH. pp 383–407
– reference: Esposito Vinzi V, Chin WW, Henseler J, Wang H (eds) (2010a) Handbook of partial least squares: concepts, methods and applications. Springer, Heidelberg
– reference: MulaikSAJamesLRvan AlstineJBennettNLindSStilwellCDEvaluation of goodness-of-fit indices for structural equation modelsPsychol Bull198910543044510.1037/0033-2909.105.3.430
– reference: BollenKAStructural equations with latent variables1989New York, NYWiley0731.62159
– reference: HenselerJRingleCSinkovicsRThe use of partial least squares path modeling in international marketingAdv Int Market2009202009277319
– reference: SarstedtMRingleCMTreating unobserved heterogeneity in PLS path modelling: a comparison of FIMIX-PLS with different data analysis strategiesJ Appl Stat201037812991318275193610.1080/02664760903030213
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Snippet This paper discusses a recent development in partial least squares (PLS) path modeling, namely goodness-of-fit indices. In order to illustrate the behavior of...
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SubjectTerms Algorithms
Computation
Computational mathematics
Computer simulation
Correlation analysis
Customer satisfaction
Economic Theory/Quantitative Economics/Mathematical Methods
Estimates
Least squares method
Mathematical analysis
Mathematical models
Mathematics and Statistics
Original Paper
Probability and Statistics in Computer Science
Probability Theory and Stochastic Processes
Software
Statistics
Structural equation modeling
Studies
Variables
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Title Goodness-of-fit indices for partial least squares path modeling
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