Advertisement

An Introduction to Structural Equation Models

  • J. Christopher Westland
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 22)

Abstract

Early twentieth century research into genetic pathways initiated a revolution on hybrid crops, industrial farming, and eugenics and initially motivated the work on structural equation models. Geneticist and statistician Sewall Wright’s seminal work in path analysis laid the groundwork for the Chicago and Scandinavian Schools of structural equation modeling. Though rooted in the natural sciences, structural equation models rose to prominence through their utility for determining relationships and structures of unobserved, latent constructs in the social sciences. Advances in computing in the 1970s gave the increasingly complex structural equation model methodologies the necessary capabilities to handle larger and larger datasets. Automation drove the move from the pairwise Pearsonian correlations of path analysis, to structures of canonical correlations in partial least squares path analysis, and finally to the full covariance structure methods of the Chicago and Scandinavian Schools.

References

  1. Allen, I. Elaine, and Christopher A. Seaman. 2007. “Likert Scales and Data Analyses.” Quality Progress 40 (7): 64–65.Google Scholar
  2. Altman, D.G., and P. Royston. 2000. “What Do We Mean by Validating a Prognostic Model?” Statistics in Medicine 19 (4): 453–473.Google Scholar
  3. Anderson, T.W. 2005. “Origins of the Limited Information Maximum Likelihood and Two-Stage Least Squares Estimators.” Journal of Econometrics 127 (1): 1–16.MathSciNetzbMATHGoogle Scholar
  4. Anderson, J.C., and D.W. Gerbing. 1988. “Structural Equation Modeling in Practice: A Review and Recommended Two-Step Approach.” Psychological Bulletin 103 (3): 411.Google Scholar
  5. Anderson, Theodore W., and Herman Rubin. 1949. “Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations.” The Annals of Mathematical Statistics 20 (1): 46–63.MathSciNetzbMATHGoogle Scholar
  6. ———. 1950. “The Asymptotic Properties of Estimates of the Parameters of a Single Equation in a Complete System of Stochastic Equations.” The Annals of Mathematical Statistics 21 (4): 570–582.MathSciNetzbMATHGoogle Scholar
  7. Anderson, T.W., N. Kunitomo, and Y. Matsushita. 2010. “On the Asymptotic Optimality of the Liml Estimator with Possibly Many Instruments.” Journal of Econometrics 157 (2): 191–204.MathSciNetzbMATHGoogle Scholar
  8. Bagozzi, Richard P., and Paul R. Warshaw. 1990. “Trying to Consume.” Journal of Consumer Research 17 (2): 127–140.Google Scholar
  9. Barclay, D., C. Higgins, and R. Thompson. 1995. “The Partial Least Squares (Pls) Approach to Causal Modeling: Personal Computer Adoption and Use as an Illustration.” Technology Studies 2 (2): 285–309.Google Scholar
  10. Basmann, Robert L. 1957. “A Generalized Classical Method of Linear Estimation of Coefficients in a Structural Equation.” Econometrica: Journal of the Econometric Society 25 (1): 77–83.MathSciNetzbMATHGoogle Scholar
  11. Bielby, William Thomas, and Robert Mason Hauser. 1977. “Structural Equation Models.” Annual Review of Sociology 3 (1): 137–161.Google Scholar
  12. Browne, Michael W., and Robert Cudeck. 1989. “Single Sample Cross-Validation Indices for Covariance Structures.” Multivariate Behavioral Research 24 (4): 445–455.Google Scholar
  13. ———. 1992. “Alternative Ways of Assessing Model Fit.” Sociological Methods & Research 21 (2): 230–258.Google Scholar
  14. ———. 1993. “Alternative Ways of Assessing Model Fit.” Sage Focus Editions 154: 136.Google Scholar
  15. Chin, W.W. 1998. “Commentary: Issues and Opinion on Structural Equation Modeling.” MIS Quarterly 22 (1): vii–xvi.Google Scholar
  16. Chin, W.W., and P.R. Newsted. 1999. “Structural Equation Modeling Analysis with Small Samples Using Partial Least Squares.” Statistical Strategies for Small Sample Research 2: 307–342.Google Scholar
  17. Christ, Carl F. 1994. “The Cowles Commission’s Contributions to Econometrics at Chicago, 1939–1955.” Journal of Economic Literature 32 (1): 30–59.Google Scholar
  18. Cochran, William G., Frederick Mosteller, and John W. Tukey. 1954. “Principles of Sampling.” Journal of the American Statistical Association 49 (265): 13–35.Google Scholar
  19. Cowles, A. 1933. “Can Stock Market Forecasters Forecast?” Econometrica: Journal of the Econometric Society 1 (3): 309–324.Google Scholar
  20. Davis, Fred D., Richard P. Bagozzi, and Paul R. Warshaw. 1989. “User Acceptance of Computer Technology: A Comparison of Two Theoretical Models.” Management Science 35 (8): 982–1003.Google Scholar
  21. ———. 1992. “Extrinsic and Intrinsic Motivation to Use Computers in the Workplace 1.” Journal of Applied Social Psychology 22 (14): 1111–1132.Google Scholar
  22. Dhrymes, Phoebus J. 1972. Distributed Lags: A Survey. Report. Los Angeles: UCLA Department of Economics.Google Scholar
  23. ———. 1974. Econometrics. Berlin: Springer.zbMATHGoogle Scholar
  24. Dhrymes, Phoebus J., E. Philip Howrey, Saul H. Hymans, Jan Kmenta, Edward E. Leamer, Richard E. Quandt, James B. Ramsey, Harold T. Shapiro, and Victor Zarnowitz. 1972. “Criteria for Evaluation of Econometric Models. Book Section.” In Annals of Economic and Social Measurement, Volume 1, Number 3, 291–325. Cambridge: NBER.Google Scholar
  25. Farebrother, R.W. 1999. Fitting Linear Relationships: A History of the Calculus of Observations 1750–1900. New York: Springer.zbMATHGoogle Scholar
  26. Fornell, Claes, and D. Larker. 1981. “Structural Equation Modeling and Regression: Guidelines for Research Practice.” Journal of Marketing Research 18 (1): 39–50.Google Scholar
  27. Fox, John. 2006. Teacher’s Corner: Structural Equation Modeling with the SEM Package in R. Structural Equation Modeling 13 (3): 465–486.MathSciNetGoogle Scholar
  28. Freedman, David A. 1987. “As Others See Us: A Case Study in Path Analysis.” Journal of Educational Statistics 12 (2): 101–128.Google Scholar
  29. Hauser, Robert M. 1972. “Disaggregating a Social-Psychological Model of Educational Attainment.” Social Science Research 1 (2): 159–188.Google Scholar
  30. Hauser, Robert M., and Arthur S. Goldberger. 1971. “The Treatment of Unobservable Variables in Path Analysis.” Sociological Methodology 3: 81–117.Google Scholar
  31. Hill, Bruce M. 1979. “Posterior Moments of the Number of Species in a Finite Population and the Posterior Probability of Finding a New Species.” Journal of the American Statistical Association 74 (367): 668–673.MathSciNetzbMATHGoogle Scholar
  32. ———. 1992. “Bayesian Nonparametric Prediction and Statistical Inference.” In Bayesian Analysis in Statistics and Econometrics, 43–94. Berlin: Springer.Google Scholar
  33. Hotelling, Harold. 1933. “Analysis of a Complex of Statistical Variables into Principal Components.” Journal of Educational Psychology 24 (6): 417.zbMATHGoogle Scholar
  34. ———. 1936. “Relations Between Two Sets of Variates.” Biometrika 28 (3/4): 321–377.zbMATHGoogle Scholar
  35. Jöreskog, Karl G. 1970. “A General Method for Estimating a Linear Structural Equation System.” ETS Research Bulletin Series 1970 (2): i–41.Google Scholar
  36. ———. 1993. “Testing Structural Equation Models.” Sage Focus Editions 154: 294.Google Scholar
  37. Jöreskog, Karl G., and Dag Sörbom. 1982. “Recent Developments in Structural Equation Modeling.” Journal of Marketing Research 19 (4): 404–416.Google Scholar
  38. Jöreskog, Karl G., and Marielle Van Thillo. 1972. “LISREL: A General Computer Program for Estimating a Linear Structural Equation System Involving Multiple Indicators of Unmeasured Variables.”Google Scholar
  39. Jöreskog, Karl G., Dag Sorbom, and Jay Magidson. 1979. “Advances in Factor Analysis and Structural Equation Models.”zbMATHGoogle Scholar
  40. Kailath, Thomas. 1967. “The Divergence and Bhattacharyya Distance Measures in Signal Selection.” IEEE Transactions on Communication Technology 15 (1): 52–60.Google Scholar
  41. Kaiser, Henry F. 1960. “The Application of Electronic Computers to Factor Analysis.” Educational and Psychological Measurement 20 (1): 141–151.Google Scholar
  42. Koopmans, Tjalling C. 1951. “Analysis of Production as an Efficient Combination of Activities.” Activity Analysis of Production and Allocation 13: 33–37.MathSciNetzbMATHGoogle Scholar
  43. Lohmöller, Jan-Bernd. 1988. “The PLS Program System: Latent Variables Path Analysis with Partial Least Squares Estimation.” Multivariate Behavioral Research 23 (1): 125–127.Google Scholar
  44. ———. 1989. Latent Variable Path Modeling with Partial Least Squares. Heidelberg: Physica-Verlag.zbMATHGoogle Scholar
  45. Lucas, Robert E. 1992. “On Efficiency and Distribution.” Economic Journal 102(411): 233–247.Google Scholar
  46. Lydtin, H., G Lohmöller, R. Lohmöller, H. Schmitz, and I. Walter. 1980. “Hemodynamic Studies on Adalat in Healthy Volunteers and in Patients.” Conference Proceedings. In 2nd International AdalatⓇSymposium, 112–123. Berlin: Springer.Google Scholar
  47. McArdle, John J. 1988. “Dynamic but Structural Equation Modeling of Repeated Measures Data.” In Handbook of Multivariate Experimental Psychology, 561–614. Berlin: Springer.Google Scholar
  48. McArdle, John J., and David Epstein. 1987. “Latent Growth Curves Within Developmental Structural Equation Models.” Child Development 58 (1): 110–133.Google Scholar
  49. Monecke, Armin, and Friedrich Leisch. 2012. “SemPLS: Structural Equation Modeling Using Partial Least Squares.” Journal of Statistical Software 48 (3): 1–32. http://www.jstatsoft.org/v48/i03/ Google Scholar
  50. Sargan, John D. 1958. “The Estimation of Economic Relationships Using Instrumental Variables.” Econometrica: Journal of the Econometric Society 26: 393–415.MathSciNetzbMATHGoogle Scholar
  51. Theil, Henri. 1980. System-Wide Explorations in International Economics, Input-Output Analysis, and Marketing Research. Vol. 2. Amsterdam: North-Holland.Google Scholar
  52. Theil, Henri, and John C.G. Boot. 1962. “The Final Form of Econometric Equation Systems.” Revue de L’Institut International de Statistique 30: 136–152.MathSciNetzbMATHGoogle Scholar
  53. Thurstone, Louis Leon. 1935. The Vectors of Mind: Multiple-Factor Analysis for the Isolation of Primary Traits. Chicago: University of Chicago Press.Google Scholar
  54. Turner, Malcolm E., and Charles D. Stevens. 1959. “The Regression Analysis of Causal Paths.” Biometrics 15 (2): 236–258.MathSciNetzbMATHGoogle Scholar
  55. Werts, Charles E., Karl G. Jöreskog, and Robert L. Linn. 1972. “A Multitrait-Multimethod Model for Studying Growth.” Educational and Psychological Measurement 32 (3): 655–678.Google Scholar
  56. Werts, Charles E., Robert L. Linn, and Karl G. Jöreskog. 1974. “Intraclass Reliability Estimates: Testing Structural Assumptions.” Educational and Psychological Measurement 34 (1): 25–33.Google Scholar
  57. Westland, J. Christopher. 2010. “Lower Bounds on Sample Size in Structural Equation Modeling.” Electronic Commerce Research and Applications 9 (6): 476–487.Google Scholar
  58. Wold, H. 1966. “Estimation of Principal Components and Related Models by Iterative Least Squares.” Multivariate Analysis 1: 391–420.MathSciNetzbMATHGoogle Scholar
  59. ———. 1974. “Causal Flows with Latent Variables: Partings of the Ways in the Light of Nipals Modelling.” European Economic Review 5 (1): 67–86.Google Scholar
  60. Wright, Sewall. 1920. The Relative Importance of Heredity and Environment in Determining the Piebald Pattern of Guinea-Pigs. Proceedings of the National Academy of Sciences of the United States of America 6 (6): 320.Google Scholar
  61. Wright, Sewall. 1921. “Correlation and Causation.” Journal of Agricultural Research 20 (7): 557–585.MathSciNetGoogle Scholar
  62. ———. 1934. “The Method of Path Coefficients.” The Annals of Mathematical Statistics 5 (3): 161–215.zbMATHGoogle Scholar
  63. ———. 1960. “Path Coefficients and Path Regressions: Alternative or Complementary Concepts?” Biometrics 16 (2): 189–202.zbMATHGoogle Scholar
  64. Zellner, A. 1962. “An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias.” Journal of the American Statistical Association 57: 348–368.MathSciNetzbMATHGoogle Scholar
  65. Zellner, Arnold, and Henri Theil. 1962. “Three-Stage Least Squares: Simultaneous Estimation of Simultaneous Equations.” Econometrica: Journal of the Econometric Society 30: 54–78.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Information & Decision SystemsUniversity of Illinois at ChicagoChicagoUSA

Personalised recommendations