You Write, but Others Read: Common Methodological Misunderstandings in PLS and Related Methods

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 56)


PLS and related methods are currently enjoying widespread popularity in part due to the availability of easy to use computer programs that require very little technical knowledge. Most of these methods focus on examining a fit function with respect to a set of free or constrained parameters for a given collection of data under certain assumptions. Although much has been written about the assumptions underpinning these methods, many misconceptions are prevalent among users and sometimes even appear in premier scholarly journals. In this chapter, we discuss a variety of methodological misunderstandings that warrant careful consideration before indiscriminately applying these methods.

Key words

Structural equation models Path models Confirmatory factor analysis Multiple regression Path analysis Covariance structure analysis Latent class Mixture analysis Equivalent models Power Model identification Formative indicators Reflective indicators Mode A Mode B Scale invariance 


  1. [1]
    G.A. Marcoulides, Structural equation modeling for scientific research. Journal of Business and Society, 2, pp. 130–138, 1989.Google Scholar
  2. [2]
    F. Galton, Natural inheritance, New York: MacMillan, 1889.Google Scholar
  3. [3]
    G.A. Marcoulides, W.W. Chin, and C. Saunders, When imprecise statements become problematic: A response to Goodhue, Lewis, and Thompson. MIS Quarterly, 36, pp. 717–728, 2012.Google Scholar
  4. [4]
    J.L. Arbuckle and W. Wothke, Amos 4.0 User’s guide, Chicago, IL: SPSS, 1999.Google Scholar
  5. [5]
    P.M. Bentler, EQS structural equations program manual. Encino, CA: Multivariate Software, 2004.Google Scholar
  6. [6]
    K. G. Jöreskog, and D. Sörbom, LISREL 8 user’s reference guide. Chicago, IL: Scientific Software International, Inc, 2005.Google Scholar
  7. [7]
    J.B. Lohmoller, Latent variable path modeling with partial least squares, Heidelberg: Physica-Verlag, 1989.Google Scholar
  8. [8]
    L.K. Muthén, and B.O. Muthén, Mplus user’s guide (5th ed.). Los Angeles, CA: Muthén and Muthén, 2011.Google Scholar
  9. [9]
    M.C. Neale, S.M. Boker, G. Xie, and H.H. Maes, Mx: Statistical modeling (5th ed.). Richmond, VA: Virginia Commonwealth University, 1999.Google Scholar
  10. [10]
    W.W. Chin, The partial least squares approach for structural equation modeling. In G.A. Marcoulides (Ed.), Modern methods for business research (pp. 295–336), Mahwah, NJ: Lawrence Erlbaum, 1998.Google Scholar
  11. [11]
    W.W. Chin, Pls Graph User’s Guide—Version 3.0, Soft Modeling Inc, 1993–2003.Google Scholar
  12. [12]
    Y. Li, PLS-GUI: Graphic user interface for partial least squares (PLS-PC 1.8)–Version 2.0.1 beta, University of South Carolina, Columbia, SC, 2005.Google Scholar
  13. [13]
    N. Sellin, PLSPATH—Version 3.01. Application manual. Universität Hamburg, Hamburg, 1989.Google Scholar
  14. [14]
    M.W. Browne, and G. Mels, Path analysis (RAMONA). In SPSS Inc. SYSTAT 10 statistics II, Chapter  7, (pp. 233–291), Chicago: Author, 2000.Google Scholar
  15. [15]
    SAS Institute, SAS PROC CALIS User’s guide, Cary, NC: Author, 1989.Google Scholar
  16. [16]
    Statistica, User’s guide, Tulsa, OK: Statistica Inc, 1998.Google Scholar
  17. [17]
    C.M. Ringle, S. Wende and A. Will, SmartPLS–Version 2.0, Universität Hamburg, Hamburg, 2005.Google Scholar
  18. [18]
    J.-R. Fu, VisualPLS, Partial Least Square (PLS) Regression: An enhanced GUI for Lvpls (PLS 1.8 PC) Version 1.04, National Kaohsiung University of Applied Sciences, Taiwan, ROC, 2006.Google Scholar
  19. [19]
    J.-R. Fu, VisualPLS: Partial least square (PLS) regression, an enhanced GUI for LVPLS (PLS 1.8 PC) Version 1.04., 2006.Google Scholar
  20. [20]
    Addinsoft XLSTAT 2012, Data analysis and statistics software for Microsoft Excel,, Paris, France, 2012.
  21. [21]
    R.E. Schumacker and G.A. Marcoulides, Interaction and nonlinear effects in structural equation modeling, Mahwah, NJ: Lawrence Erlbaum, 1998.Google Scholar
  22. [22]
    D. Goodhue, W. Lewis, and R. Thompson, Comparing PLS to regression and LISREL: A response to Marcoulides, Chin, and Saunders. MIS Quarterly, 36(3), pp. 703–716, 2012.Google Scholar
  23. [23]
    H. Treiblmaier, P.M. Bentler, and P. Mair, Formative constructs implemented via common factors. Structural Equation Modeling, 18, pp. 1–17, 2010.MathSciNetGoogle Scholar
  24. [24]
    R. Cudeck, Analysis of correlation matrices using covariance structure models. Psychological Bulletin, 105, pp. 317–327, 1989.Google Scholar
  25. [25]
    J.H. Steiger, Driving fast in reverse: The relationship between software development, theory, and education in structural equation modeling. Journal of the American Statistical Association, 96, pp. 331–338, 2001.Google Scholar
  26. [26]
    K.G. Jöreskog, Testing structural equation models. In K.A. Bollen and J.S. Long (Eds.), Testing structural equation models (pp. 294–316). Newbury Park, CA: Sage, 1993.Google Scholar
  27. [27]
    H. Wold, Soft modeling: Intermediate between traditional model building and data analysis. Mathematical statistics, 6, pp. 333–346, 1982.MathSciNetGoogle Scholar
  28. [28]
    K. Hayashi, and G.A. Marcoulides, Examining identification issues in factor analysis. Structural Equation Modeling, 13, pp. 631–645, 2006.MathSciNetGoogle Scholar
  29. [29]
    C. Glymour, R. Scheines, R. Spirtes, and K. Kelly, Discovering causal structure: Artificial intelligence, philosophy of science, and statistical modeling, Orlando, FL: Academic Press, 1987.MATHGoogle Scholar
  30. [30]
    G.A. Marcoulides, Z.‘Drezner, and R.E.‘Schumacker, Model specification searches in structural equation modeling using Tabu search. Structural Equation Modeling, 5, pp. 365–376, 1998.Google Scholar
  31. [31]
    S.‘Salhi, Heuristic search methods. In G.A.‘Marcoulides (Ed.). Modern methods for business research (pp. 147–175). Mahwah, NJ: Lawrence Erlbaum, 1998.Google Scholar
  32. [32]
    G.A. Marcoulides, and Z. Drezner, Specification searches in structural equation modeling with a genetic algorithm. In G.A. Marcoulides and R.E. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 247–268). Mahwah, NJ: Lawrence Erlbaum, 2009.Google Scholar
  33. [33]
    W.L. Leite, I.C. Huang, and G.A. Marcoulides, Item selection for the development of short-form of scaling using an ant colony optimization algorithm. Multivariate Behavioral Research, 43, pp. 411–431, 2008.Google Scholar
  34. [34]
    W.L. Leite, and G.A. Marcoulides, Using the ant colony optimization algorithm for specification searches: A comparison of criteria, Paper presented at the Annual Meeting of the American Education Research Association, San Diego: CA, 2009, April.Google Scholar
  35. [35]
    G.A. Marcoulides, and W.L. Leite, Exploratory data mining algorithms for conducting searchers in structural equation modeling: A comparison of some fit criteria. In J.J. McArdle, and G. Ritschard (Eds.). Contemporary Issues in Exploratory Data Mining in the Behavioral Sciences, London: Taylor & Francis, 2013.Google Scholar
  36. [36]
    G.A. Marcoulides, and Z. Drezner, Model specification searchers using ant colony optimization algorithms. Structural Equation Modeling, 10, pp. 154–164, 2003.MathSciNetGoogle Scholar
  37. [37]
    G.A. Marcoulides, and Z. Drezner, A model selection approach for the identification of quantitative trait loci in experimental crosses: Discussion on the paper by Broman and Speed. Journal of the Royal Statistical Society, Series B, 64, pp. 754, 2002.Google Scholar
  38. [38]
    G.A. Marcoulides, Conducting specification searches in SEM using a ruin and recreate principle, Paper presented at the Annual Meeting of the American Psychological Society, San Francisco, CA, 2009, May.Google Scholar
  39. [39]
    G.A. Marcoulides, and Z. Drezner, Using simulated annealing for model selection in multiple regression analysis. Multiple Regression Viewpoints, 25, pp. 1–4, 1999.Google Scholar
  40. [40]
    G.A. Marcoulides, and Z. Drezner, Tabu search variable selection with resource constraints. Communications in Statistics: Simulation & Computation, 33, pp. 355–362, 2004.MathSciNetMATHGoogle Scholar
  41. [41]
    Z. Drezner, and G.A. Marcoulides, A distance-based selection of parents in genetic algorithms. In M. Resenda and J.P. Sousa (eds.). Metaheuristics: Computer decision-making (pp. 257–278). Boston, MA: Kluwer Academic Publishers, 2003.Google Scholar
  42. [42]
    G.A. Marcoulides, Using heuristic algorithms for specification searches and optimization, Paper presented at the Albert and Elaine Brochard Foundation International Colloquium, Missillac, France, 2010, July.Google Scholar
  43. [43]
    G.A. Marcoulides, and M. Ing., Automated structural equation modeling strategies. In R. Hoyle (Ed.), Handbook of structural equation modeling, New York: Guilford Press, 2012.Google Scholar
  44. [44]
    R. MacCallum, Specification searches in covariance structure modeling. Psychological Bulletin, 100, pp. 107–120, 1986.Google Scholar
  45. [45]
    S.J. Breckler, Applications of covariance structure modeling in Psychology: Cause for concern? Psychological Bulletin, 107, pp. 260–273, 1990.Google Scholar
  46. [46]
    S.L. Hershberger, The specification of equivalent models before the collection of data. In A. von Eye and C. Clogg (Eds.), The analysis of latent variables in developmental research (pp. 68–108). Beverly Hills, CA: Sage, 1994.Google Scholar
  47. [47]
    S. Lee., and S.L. Hershberger, A simple rule for generating equivalent models in covariance structure modeling. Multivariate Behavioral Research, 25, pp. 313–334, 1990.Google Scholar
  48. [48]
    S.L. Hershberger, and G.A. Marcoulides, The problem of equivalent models. In G.R. Hancock and R.O. Mueller (Eds.), Structural equation modeling: A second course (2nd Ed.). G. R. Greenwich, CT: Information Age Publishing, 2012.Google Scholar
  49. [49]
    T.C.W. Luijben, Equivalent models in covariance structure analysis. Psychometrika, 56, pp. 653–665, 1991.MathSciNetMATHGoogle Scholar
  50. [50]
    R.C. MacCallum, D.T. Wegener, B.N. Uchino, and L R. Fabrigar, The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin, 114, pp. 185–199, 1993.Google Scholar
  51. [51]
    R. Levy, and G.R. Hancock, A framework of statistical tests for comparing mean and covariance structure models. Multivariate Behavioral Research, 42, pp. 33–66, 2007.Google Scholar
  52. [52]
    K.A. Marcus, Statistical equivalence, semantic equivalence, eliminative induction and the Raykov-Marcoulides proof of infinite equivalence. Structural Equation Modeling, 9, pp. 503–522, 2002.MathSciNetGoogle Scholar
  53. [53]
    R.P. McDonald, What can we learn from the path equations?: Identifiability, constraints, equivalence. Psychometrika, 67, pp. 225–249, 2002.MathSciNetGoogle Scholar
  54. [54]
    T. Raykov, Equivalent structural equation models and group equality constraints. Multivariate Behavioral Research, 32, pp. 95–104, 1997.Google Scholar
  55. [55]
    T. Raykov, and G.A. Marcoulides, Can there be infinitely many models equivalent to a given covariance structure model? Structural Equation Modeling, 8, pp. 142–149, 2001.MathSciNetGoogle Scholar
  56. [56]
    T. Raykov, and G.A. Marcoulides, Equivalent structural equation models: A challenge and responsibility. Structural Equation Modeling, 14, pp. 527–532, 2007.MathSciNetGoogle Scholar
  57. [57]
    T. Raykov, and S. Penev, On structural equation model equivalence. Multivariate Behavioral Research, 34, pp. 199–244, 1999.Google Scholar
  58. [58]
    L. J. Williams, H. Bozdogan, and L. Aiman-Smith, Inference problems with equivalent models. In G.A. Marcoulides and R.E. Schumacker (Eds.), Advanced structural equation modeling: Issues and techniques (pp. 279–314). Mahwah, NJ: Erlbaum, 1996.Google Scholar
  59. [59]
    C. Hsiao, Identification. In Z. Griliches and M.D. Intriligator (Eds.), Handbook of econometrics, Vol. 1 (pp. 224–283). Amsterdam: Elsevier Science, 1983.Google Scholar
  60. [60]
    I. Stelzl, Changing a causal hypothesis without changing the fit: Some rules for generating equivalent path models. Multivariate Behavioral Research, 21, pp. 309–331, 1986.Google Scholar
  61. [61]
    J. Pearl, Causality: Models, reasoning, and inference (2nd ed.). New York: Cambridge University Press, 2009.Google Scholar
  62. [62]
    B. Shipley, Cause and correlation in biology, New York: Cambridge University Press, 2000.Google Scholar
  63. [63]
    P.A. Bekker, A. Merckens, and T.J. Wansbeek, Identification, equivalent models, and computer algebra, Boston: Academic Press, 1994.MATHGoogle Scholar
  64. [64]
    S.B. Green, M.S. Thompson, and J. Poirier, Exploratory analyses to improve model fit: Errors due to misspecification and a strategy to reduce their occurrence. Structural Equation Modeling, 6, pp. 113–126, 1999.Google Scholar
  65. [65]
    T. Raykov, and S. Penev, The problem of equivalent structural equation models: An individual residual perspective. In G.A. Marcoulides and R.E. Schumacker (Eds.). New developments and techniques in structural equation modeling, (pp. 297–321). Mahwah, NJ: Lawrence Erlbaum, 2001.Google Scholar
  66. [66]
    G.H. Scherr, Irreproducible science: Editor’s introduction. The best of the Journal of Irreproducible Results, New York: Workman Publishing, 1983.Google Scholar
  67. [67]
    H. Apel, and H. Wold, Simulation experiments on a case value basis with different sample lengths, different sample sizes, and different estimation models, including second dimension of latent variables. Unpublished manuscript, Department of Statistics, University of Uppsala, Sweden, 1978.Google Scholar
  68. [68]
    H. Apel, and H. Wold, Soft modeling with latent variables in two or more dimensions: PLS estimation and testing for predictive relevance. In K.G. Jöreskog and H. Wold (Eds.), Systems under indirect observation, Part II, (pp. 209–248). Amsterdam: North Holland, 1982.Google Scholar
  69. [69]
    B.E. Areskoug, The first canonical correlation: Theoretical PLS analysis and simulation experiments. In K.G. Jöreskog and H. Wold (Eds.), Systems under indirect observation, Part II (pp. 95–118). Amsterdam: North Holland, 1982.Google Scholar
  70. [70]
    W.W. Chin, and P R. Newsted, Structural equation modeling analysis with small samples using partial least squares. In R. H. Hoyle (Ed.), Statistical strategies for small sample research (pp. 307–341). Thousand Oaks, CA: Sage, 1999.Google Scholar
  71. [71]
    B.S. Hui, The partial least squares approach to path models of indirectly observed variables with multiple indicators. Unpublished doctoral dissertation, University of Pennsylvania, Philadelphia, PA, 1978.Google Scholar
  72. [72]
    B.S. Hui, and H. Wold, Consistency and consistency at large in partial least squares estimates. In K G. Jöreskog and H. Wold (Eds.), Systems under indirect observation, Part II (pp. 119–130). Amsterdam: North Holland, 1982.Google Scholar
  73. [73]
    G.A. Marcoulides, and C. Saunders, PLS: A Silver Bullet? MIS Quarterly, 30, pp. iv–viii, 2006.Google Scholar
  74. [74]
    G.A. Marcoulides, W.W. Chin, and C. Saunders, A critical look at partial least squares modeling. MIS Quarterly, 33, pp. 171–175, 2009.Google Scholar
  75. [75]
    R. Noonan, and H. Wold, PLS path modeling with indirectly observed variables: A comparison of alternative estimates for the latent variable. In K. G. Jöreskog and H. Wold (Eds.), Systems under indirect observation, Part II (pp. 75–94). Amsterdam: North Holland, 1982.Google Scholar
  76. [76]
    W.W. Chin, and J. Dibbern, A permutation based procedure for multi-group PLS analysis: Results of tests of differences on simulated data and a cross cultural analysis of the sourcing of information system services between Germany and the USA, In V.E. Vinzi, W.W. Chin, J. Henseler and H. Wang (Eds.), Handbook of partial least squares concepts, methods and applications (pp. 171–193), New York, NY: Springer Verlag, 2010.Google Scholar
  77. [77]
    W.W. Chin, A permutation procedure for multi-group comparison of PLS models. Invited presentation, In M. Valares, M. Tenenhaus, P. Coelho, V.E. Vinzi, and A. Morineau (Eds.), PLS and related methods, proceedings of the PLS-03 Iternational Symposium: “Focus on Customers,” Lisbon, September 15th to 17th, pp. 33–43, 2003.Google Scholar
  78. [78]
    K.G. Jöreskog, and H. Wold, Systems under indirect observation, Part I & II, North Holland: Amsterdam, 1982.Google Scholar
  79. [79]
    R.F. Falk, and N.B. Miller, A primer of soft modeling. Akron, OH: The University of Akron Press, 1992.Google Scholar
  80. [80]
    R.P. McDonald, Path analysis with composite variables. Multivariate Behavioral Research, 31, pp. 239–270, 1996.Google Scholar
  81. [81]
    I.R.R. Lu, Latent variable modeling in business research: A comparison of regression based on IRT and CTT scores with structural equation models, Doctoral dissertation, Carleton University, Canada, 2004.Google Scholar
  82. [82]
    I.R.R. Lu, D.R. Thomas, and B.D. Zumbo, Embedding IRT in structural equation models: A comparison with regression based on IRT scores. Structural Equation Modeling, 12, pp. 263–277, 2005.MathSciNetGoogle Scholar
  83. [83]
    T. Dijkstra, Some comments on maximum likelihood and partial least squares methods. Journal of Econometrics, 22, pp. 67–90, 1983.MathSciNetMATHGoogle Scholar
  84. [84]
    H. Schneeweiss, Consistency at large in models with latent variables. In K. Haagen, D.J. Bartholomew, and M. Deistler (Eds.). Statistical modelling and latent variables, Elsevier: Amsterdam, 1993.Google Scholar
  85. [85]
    P.M. Bentler, EQS structural equation program manual, Encino, CA: Multivariate Software, Inc., 1995.Google Scholar
  86. [86]
    L.-T. Hu, P.M. Bentler, and Y. Kano, Can test statistics in covariance structure analysis be trusted? Psychological Bulletin, 112, pp. 351–362, 1992.Google Scholar
  87. [87]
    J. Cohen, Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum, 1988.MATHGoogle Scholar
  88. [88]
    S.B. Green. How many subjects does it take to do a regression analysis? Multivariate Behavioral Research, 26, pp. 499–510, 1991.Google Scholar
  89. [89]
    A. Boomsma, The robustness of LISREL against small sample sizes in factor analysis models. In K.G. Jöreskog and H. Wold (Eds.), Systems under indirect observation, Part I (pp. 149–174). Amsterdam: North Holland, 1982.Google Scholar
  90. [90]
    R. Cudeck, and S.J. Hensly, Model selection in covariance structure analysis and the “problem” of sample size: A clarification. Psychological Bulletin, 109, pp. 512–519, 1991.Google Scholar
  91. [91]
    D.L. Jackson, Revisiting sample size and the number of parameter estimates: Some support for the N: q Hypothesis. Structural Equation Modeling, 10, pp. 128–141, 2003.MathSciNetGoogle Scholar
  92. [92]
    R.C. MacCallum, M.W. Browne, and H.M. Sugawara, Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1, pp. 130–149, 1996.Google Scholar
  93. [93]
    L.K. Muthén, and B.O. Muthén, How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 9, pp. 599–620, 2002.MathSciNetGoogle Scholar
  94. [94]
    C. Ringle, M. Sarstedt, and D. Straub, A critical look at the use of PLS-SEM in MIS Quarterly. MIS Quarterly, 36, pp. iii–xiv, 2012.Google Scholar
  95. [95]
    A. Bhattacherjee, and G. Premkumar, Understanding changes in belief and attitude toward information technology usage: A theoretical model and longitudinal test. MIS Quarterly, 28, pp. 229–254, 2004.Google Scholar
  96. [96]
    G. Bassellier, and I. Benbasat, Business competence of information technology professionals: Conceptual development and influence on IT-business partnerships. MIS Quarterly, 28, pp. 673–694, 2004.Google Scholar
  97. [97]
    M. Subramani, How do suppliers benefit from information technology use in supply chain relationships? MIS Quarterly, 28, pp. 45–73, 2004.Google Scholar
  98. [98]
    M.C. Denham, Prediction intervals in Partial Least Squares. Journal of Chemometrics, 11, pp. 39–52, 1997.Google Scholar
  99. [99]
    W. L. Hays, Statistics, Fort Worth, TX: Harcourt Brace Jovanovic, 1994.Google Scholar
  100. [100]
    T. Raykov, and G.A. Marcoulides, A first course in structural equation modeling (2nd ed.). Mahwah, NJ: Lawrence Erlbaum, 2006.Google Scholar
  101. [101]
    S. Serneels, P. Lemberge, and P.J. Van Espen, Calculation of PLS prediction intervals using efficient recursive relations for the Jacobian matrix. Journal of Chemometrics, 18, pp. 76–80, 2004.Google Scholar
  102. [102]
    T. Raykov, and G.A. Marcoulides, Using the delta method for approximate interval estimation of parameter functions in SEM. Structural Equation Modeling, 11, pp. 621–637, 2004.MathSciNetGoogle Scholar
  103. [103]
    G.A. Marcoulides, Evaluation of confirmatory factor analytic and structural equation models using goodness-of-fit indices. Psychological Reports, 67, pp. 669–671, 1990.Google Scholar
  104. [104]
    P. Paxton, P.J. Curran, K.A. Bollen, J. Kirby, and F. Chen, Monte Carlo experiments: Design and implementation. Structural Equation Modeling, 8, pp. 287–312, 2001.Google Scholar
  105. [105]
    A. Majchrak, C. Beath, R. Lim, and W.W. Chin, Managing client dialogues during information systems design to facilitate client learning. MIS Quarterly, 29, pp. 653–672, 2005.Google Scholar
  106. [106]
    J. Dibbern, W.W. Chin, A. Heinzl, Systemic determinants of the information systems outsourcing decision: A comparative study of German and United States firms. Journal of the Association for Information Systems, 13, pp. 466–497, 2012.Google Scholar
  107. [107]
    E. Walden, AIS World: Power analysis after the fact. [Monday, March 5, 2012 6:51pm], 2012.Google Scholar
  108. [108]
    T. Raykov, and G.A. Marcoulides, Basic statistics: An introduction with R. London, UK: Rowman & Littlefield Publishers, Inc., 2012.Google Scholar
  109. [109]
    A.A. Albert, The matrices of factor analysis. Proceedings of the National Academy of Science, 30, pp. 90–95, USA, 1944.MATHGoogle Scholar
  110. [110]
    A.A. Albert, The minimum rank of a correlation matrix. Proceedings of the National Academy of Science, 30, pp. 144–146, USA, 1944.MATHGoogle Scholar
  111. [111]
    T.C. Koopmans, and O. Reiersol, The identification of structural characteristics. Annals of Mathematical Statistics, 21, pp. 165–181, 1950.MathSciNetMATHGoogle Scholar
  112. [112]
    W. Ledermann, On the rank of reduced correlation matrices in multiple factor analysis. Psychometrika, 2, pp. 85–93, 1937.MATHGoogle Scholar
  113. [113]
    M. Sato, A study of identification problem and substitute use in principal component analysis in factor analysis. Hiroshima Mathematical Journal, 22, pp. 479–524, 1992.MathSciNetMATHGoogle Scholar
  114. [114]
    M. Sato, On the identification problem of the factor analysis model: A review and an application for an estimation of air pollution source profiles and amounts. In Factor analysis symposium at Osaka (pp. 179–184). Osaka: University of Osaka, 2004.Google Scholar
  115. [115]
    Y. Kano, Exploratory factor analysis with a common factor with two indicators. Behaviormetrika, 24, pp. 129–145, 1997.Google Scholar
  116. [116]
    K.A. Bollen, Structural equations with latent variables, New York, NY: Wiley, 1989.MATHGoogle Scholar
  117. [117]
    T. Raykov, G.A. Marcoulides, and T. Patelis, Saturated versus just identified models: A note on their distinction. Educational and Psychological Measurement, 73, pp. 162–168, 2013.Google Scholar
  118. [118]
    T.W. Anderson, and H. Rubin, Statistical inferences in factor analysis. In J. Neyman (Ed.), Proceedings of the third Berkeley symposium on mathematical statistics and probability (Vol. 5, pp. 111–150). Berkeley: University of California, 1956.Google Scholar
  119. [119]
    M. Ihara, and Y. Kano, A new estimator of the uniqueness in factor analysis. Psychometrika, 51, pp. 563–566, 1986.MathSciNetMATHGoogle Scholar
  120. [120]
    H. Yanai, K. Shigemasu, S. Maekawa, and M. Ichikawa, Factor analysis: Its theory and methods, Tokyo: Asakura-shoten (in Japanese), 1990.Google Scholar
  121. [121]
    J.S. Williams, A note on the uniqueness of minimum rank solutions in factor analysis. Psychometrika, 46, pp. 109–110, 1981.MathSciNetMATHGoogle Scholar
  122. [122]
    Y. Tumura, and M. Sato, On the identification in factor analysis. TRU Mathematics, 16, pp. 121–131, 1980.MathSciNetMATHGoogle Scholar
  123. [123]
    T. Raykov, and G.A. Marcoulides, Introduction to psychometric theory. New York, NY: Routledge, 2011.Google Scholar
  124. [124]
    R.P. McDonald, The dimensionality of tests and items. British Journal of Mathematical and Statistical Psychology, 34, pp. 100–117, 1981.MathSciNetGoogle Scholar
  125. [125]
    R.P. McDonald, Test theory. A unified treatment, Mahwah, NJ: Lawrence Erlbaum, 1999.Google Scholar
  126. [126]
    P.M. Bentler, Alpha, dimension-free, and model-based internal consistency reliability. Psychometrika, 74, pp. 137–144, 2009.MathSciNetMATHGoogle Scholar
  127. [127]
    L. Crocker, and J. Algina, Introduction to classical and modern test theory, Fort Worth, TX: Harcourt College Publishers, 1986.Google Scholar
  128. [128]
    S.B. Green, and Y. Yang, Commentary on coefficient alpha: A cautionary tale. Psychometrika, 74, pp. 121–136, 2009.MathSciNetMATHGoogle Scholar
  129. [129]
    S.B. Green, and Y. Yang, Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74, pp. 155–167, 2009.MathSciNetMATHGoogle Scholar
  130. [130]
    W. Revelle, and R. Zinbarg, Coefficients alpha, beta, and the GLB: Comments on Sijtsma. Psychometrika, 74, pp. 145–154, 2009.MathSciNetMATHGoogle Scholar
  131. [131]
    K. Sijtsma, On the use, the misuse, and the very limited usefulness of Cronbach’s alpha. Psychometrika, 74, pp. 107–120, 2009.MathSciNetMATHGoogle Scholar
  132. [132]
    K. Sijtsma, Reliability beyond theory and into practice. Psychometrika, 74, pp. 169–174, 2009.MathSciNetMATHGoogle Scholar
  133. [133]
    T. Raykov, Cronbach’s alpha and reliability of composite with interrelated nonhomogenous items. Applied Psychological Measurement, 22, pp. 375–385, 1998.Google Scholar
  134. [134]
    T. Raykov, Bias of coefficient alpha for congeneric measures with correlated errors. Applied Psychological Measurement, 25, pp. 69–76, 2001.MathSciNetGoogle Scholar
  135. [135]
    S.B. Green, R.W. Lissitz, and S.A. Mulaik, Limitations of coefficient alpha as an index of test unidimensionality. Educational and Psychological Measurement, 37, pp. 827–838, 1977.Google Scholar
  136. [136]
    I.T. Jolliffe, Principal component analysis (2nd Ed.). New York: Springer, 2002.MATHGoogle Scholar
  137. [137]
    D. Goodhue, W. Lewis, and R. Thompson, PLS, Small Sample Size, and Statistical Power in MIS Research. HICSS ’06 Proceedings of the 39th Annual Hawaii Conference on System Sciences, pp. 202b, 2006.Google Scholar
  138. [138]
    H. Hwang, N.K. Malhotra, Y. Kim, M.A. Tomiuk, and S. Hong, A comparative study of parameter recovery of the three approaches to structural equation modeling. Journal of Marketing Research, 67, pp. 699–712, 2010.Google Scholar
  139. [139]
    T. Dijkstra, Latent variables and indices: Herman Wold’s basic design and partial least squares. In V.E. Vinzi, W.W. Chin, J. Henseler, and H. Wang (Eds.), Handbook of partial least squares: Concepts, methods, and applications, computational statistics (pp. 23–46). New York: Springer Verlag, 2010.Google Scholar
  140. [140]
    D. Goodhue, W. Lewis, and R. Thompson, Does PLS have advantages for small sample size or non-normal data. MIS Quarterly, 36, pp. 981–1001, 2012.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Research Methods and Statistics, Graduate School of Education and Interdepartmental Graduate Program in Management, A. Gary Anderson Graduate School of ManagementUniversity of CaliforniaRiversideUSA
  2. 2.Department of Decision and Information Systems, C. T. Bauer College of BusinessUniversity of HoustonHoustonUSA

Personalised recommendations