Skip to main content
SpringerLink
Log in

Specification, evaluation, and interpretation of structural equation models

  • Published:
Journal of the Academy of Marketing Science Aims and scope Submit manuscript

Abstract

We provide a comprehensive and user-friendly compendium of standards for the use and interpretation of structural equation models (SEMs). To both read about and do research that employs SEMs, it is necessary to master the art and science of the statistical procedures underpinning SEMs in an integrative way with the substantive concepts, theories, and hypotheses that researchers desire to examine. Our aim is to remove some of the mystery and uncertainty of the use of SEMs, while conveying the spirit of their possibilities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Notes

  1. Although parameter estimates in simple regression are always biased downward to the extent of measurement error, no general statements in this regard can be made with respect to multiple regression.

References

  • Arbuckle, J. L. (2009). AMOS 18 user’s guide. Crawfordville: Amos Development Corporation.

    Google Scholar 

  • Audi, R. (Ed.). (1995). The Cambridge dictionary of philosophy. Cambridge: Cambridge University Press.

    Google Scholar 

  • Bagozzi, R. P. (1977). Structural equation models in experimental research. Journal of Marketing Research, 14, 209–226.

    Article  Google Scholar 

  • Bagozzi, R. P. (1980). Causal models in marketing. New York: Wiley.

    Google Scholar 

  • Bagozzi, R. P. (1984). A prospectus for theory construction in marketing. Journal of Marketing, 48, 11–29.

    Article  Google Scholar 

  • Bagozzi, R. P. (1994). The effects of arousal on the organization of positive and negative affect and cognitions: application to attitude theory. Structural Equation Modeling, 1, 222–252.

    Article  Google Scholar 

  • Bagozzi, R. P. (1996). The role of arousal in the creation and control of the halo effect in attitude models. Psychology and Marketing, 13, 235–264.

    Article  Google Scholar 

  • Bagozzi, R. P. (2007). On the meaning of formative measurement and how it differs from reflective measurement: comment on Howell, Breivik, and Wilcox. Psychological Methods, 12, 229–237.

    Article  Google Scholar 

  • Bagozzi, R. P. (2010). Structural equation models are modeling tools with many ambiguities: comments acknowledging the need for caution and humility in their use. Journal of Consumer Psychology, 20, 208–214.

    Article  Google Scholar 

  • Bagozzi, R. P. (2011a). Measurement and meaning in information systems and organizational research: methodological and philosophical foundations. MIS Quarterly, 35, 261–292.

    Google Scholar 

  • Bagozzi, R. P. (2011b). Alternative perspectives in philosophy of mind and their relationship to structural equation models in psychology. Psychological Inquiry, 22, 88–99.

    Article  Google Scholar 

  • Bagozzi, R. P., & Baumgartner, H. (1994). The evaluation of structural equation models and hypothesis testing. In R. P. Bagozzi (Ed.), Basic principles of marketing research (pp. 386–422). Oxford: Blackwell.

    Google Scholar 

  • Bagozzi, R. P., & Dholakia, U. M. (2006). Antecedents and purchase consequences of customer participation in small group brand communities. International Journal of Research in Marketing, 23, 45–61.

    Article  Google Scholar 

  • Bagozzi, R. P., & Edwards, J. R. (1998). A general approach for representing constructs in organizational research. Organizational Research Methods, 1, 45–87.

    Article  Google Scholar 

  • Bagozzi, R. P., & Heatherton, T. F. (1994). A general approach to representing multifaceted personality constructs: application to state self-esteem. Structural Equation Modeling, 1, 35–67.

    Article  Google Scholar 

  • Bagozzi, R. P., & Phillips, L. (1982). Representing and testing organizational theories: a holistic construal. Administrative Science Quarterly, 27, 459–489.

    Article  Google Scholar 

  • Bagozzi, R. P., & Yi, Y. (1988). On the evaluation of structural equation models. Journal of the Academy of Marketing Science, 16, 74–94.

    Article  Google Scholar 

  • Bagozzi, R. P., & Yi, Y. (1989). On the use of structural equation models in experimental designs. Journal of Marketing Research, 26, 271–284.

    Article  Google Scholar 

  • Bagozzi, R. P., & Yi, Y. (1990). Assessing method variance in multitrait-multimethod matrices: the case of self-reported affect and perceptions at work. Journal of Applied Psychology, 75, 547–560.

    Article  Google Scholar 

  • Bagozzi, R. P., & Yi, Y. (1992). Testing hypotheses about methods, traits, and communalities in the direct product model. Applied Psychological Measurement, 16, 373–380.

    Article  Google Scholar 

  • Bagozzi, R. P., Fornell, C., & Larcker, D. (1981). Canonical correlation analysis as a special case of a structural relations model. Multivariate Behavioral Research, 16, 437–454.

    Article  Google Scholar 

  • Bagozzi, R. P., Yi, Y., & Phillips, L. (1991a). Assessing construct validity in organizational research. Administrative Science Quarterly, 36, 421–458.

    Article  Google Scholar 

  • Bagozzi, R. P., Yi, Y., & Singh, S. (1991b). On the use of structural equation models in experimental designs: two extensions. International Journal of Research in Marketing, 8, 125–140.

    Article  Google Scholar 

  • Bagozzi, R. P., Yi, Y., & Nassen, K. (1999). Representation of measurement error in marketing variables: review of approaches and extension to three facet designs. Journal of Econometrics, 89, 393–421.

    Article  Google Scholar 

  • Bagozzi, R. P., Lee, K., & Van Loo, M. F. (2001). Decisions to donate bone marrow: the role of attitudes and subjective norms across cultures. Psychology and Health, 16, 29–56.

    Article  Google Scholar 

  • Bagozzi, R. P., Moore, D. J., & Leone, L. (2004). Self-control and the self-regulation of dieting decisions: the role of prefactual attitudes, subjective norms, and resistance to temptation. Basic and Applied Social Psychology, 26, 199–213.

    Google Scholar 

  • Bagozzi, R. P., Bergami, M., Marzocchi, G. L., & Morandin, G. (2011). Customer-organization relationships: development and test of a theory of extended identities. Journal of Applied Psychology, in press.

  • Barrett, P. (2007). Structural equation modeling: adjusting model fit. Personality and Individual Difference, 42, 815–824.

    Article  Google Scholar 

  • Bechger, T. M., & Maris, G. (2004). Structural equation modeling of multiple facet data: extending models for multitrait-multimethod data. Psicologica, 25, 253–274.

    Google Scholar 

  • Bentler, P. M. (2008). EQS 6: Structural equations program manual. Encino: Multivariate Software.

    Google Scholar 

  • Bentler, P. M. (2010). SEM with simplicity and accuracy. Journal of Consumer Psychology, 20, 215–220.

    Article  Google Scholar 

  • Bentler, P. M., & Chou, C. P. (1987). Practical issues in structural equation modeling. Sociological Methods & Research, 16, 78–117.

    Article  Google Scholar 

  • Bentler, P. M., & Weeks, D. G. (1980). Linear structural equations with latent variables. Psychometrika, 45, 289–308.

    Article  Google Scholar 

  • Bergami, M., & Bagozzi, R. P. (2000). Self-categorization and commitment as distinct aspects of social identity in the organization: conceptualization, measurement, and relation to antecedents and consequences. British Journal of Social Psychology, 39, 555–557.

    Article  Google Scholar 

  • Blackburn, S. (1994). The Oxford dictionary of philosophy. Oxford: Oxford University Press.

    Google Scholar 

  • Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.

    Google Scholar 

  • Curran, P. J., & Hussong, A. M. (2002). Structural equation modeling of repeated measures data. In D. Moskowitz & S. Hershberger (Eds.), Modeling intraindividual variability with repeated measures data: Methods and applications (pp. 59–86). New York: Lawrence Erlbaum.

    Google Scholar 

  • Davis, F. D. (1989). Perceived usefulness, perceived ease of use, and user acceptance of information technology. MIS Quarterly, 13, 319–340.

    Article  Google Scholar 

  • Davis, F. D., Bagozzi, R. P., & Warshaw, P. R. (1989). User acceptance of computer technology: a comparison of two theoretical models. Management Science, 35, 982–1003.

    Article  Google Scholar 

  • Diamantopoulos, A., & Siguaw, J. A. (2006). Formative versus reflective indicators in organizational measure development: a comparison and empirical illustration. British Journal of Management, 17, 263–282.

    Article  Google Scholar 

  • Diamantopoulos, A., & Winklhofer, H. M. (2001). Index construction with formative indicators: an alternative to scale development. Journal of Marketing Research, 38, 269–277.

    Article  Google Scholar 

  • Duncan, T. E., Duncan, S., & Strycker, L. A. (2006). An introduction to latent variable growth curve modeling. Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of relationships between constructs and measures. Psychological Methods, 5, 155–174.

    Article  Google Scholar 

  • Fan, X., & Sivo, S. A. (2005). Sensitivity of fit indices to misspecified structural or measurement model components: rationale of two-index strategy revisited. Structural Equation Modeling, 12, 343–367.

    Article  Google Scholar 

  • Gefen, D., Straub, D. W., & Boudreau, M. (2000). Structural equation modeling and regression: guidelines for research practice. Communications of the Association for Information Systems, 4, 1–78.

    Google Scholar 

  • Heck, R. H., & Thomas, S. L. (2009). An introduction to multilevel modeling techniques. New York: Routledge.

    Google Scholar 

  • Howell, R. D., Breivik, E., & Wilcox, J. B. (2007a). Reconsidering formative measurement. Psychological Methods, 12, 205–218.

    Article  Google Scholar 

  • Howell, R. D., Breivik, E., & Wilcox, J. B. (2007b). Is formative measurement really measurement: reply to Bollen (2007) and Bagozzi (2007). Psychological Methods, 12, 238–245.

    Article  Google Scholar 

  • Hu, L., & Bentler, P. M. (1998). Fit indexes in covariance structure modeling: sensitivity to underparameterized model misspecification. Psychological Methods, 3, 424–453.

    Article  Google Scholar 

  • Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1–55.

    Article  Google Scholar 

  • Iacobucci, D. (2009). Everything you always wanted to know about SEM (structural equation modeling) but were afraid to ask. Journal of Consumer Psychology, 19, 673–680.

    Article  Google Scholar 

  • Iacobucci, D. (2010). Structural equation modeling: fit indices, sample size, and advanced topics. Journal of Consumer Psychology, 20, 90–98.

    Article  Google Scholar 

  • Jamshidian, M., & Bentler, P. M. (1999). ML estimation of mean and covariance structures with missing data using complete data routines. Journal of Educational and Behavioral Statistics, 24, 21–41.

    Google Scholar 

  • Jarvis, C. B., MacKenzie, S. B., & Podsakoff, P. M. (2003). A critical review of construct indicators and measurement model misspecification in marketing and consumer research. Journal of Consumer Research, 30, 199–219.

    Article  Google Scholar 

  • Jöreskog, K. G., & Goldberger, A. S. (1975). Estimation of a model with multiple indicators and multiple causes of a single latent variable. Journal of the American Statistical Association, 70, 631–639.

    Article  Google Scholar 

  • Jöreskog, K. G., & Sörbom, D. (1996a). LISREL 8: User’s reference guide. Chicago: Scientific Software International.

    Google Scholar 

  • Jöreskog, K. G., & Sörbom, D. (1996b). LISREL 8: Structural equation modeling with the SIMPLIS command language. Chicago: Scientific Software International.

    Google Scholar 

  • Jöreskog, K. G., & Yang, F. (1996). Nonlinear structural equation models: The Kenney-Judd model with interaction effects. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation modeling: Issues and techniques (pp. 57–88). Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Kühnel, S. M. (1988). Testing Manova designs with LISREL. Sociological Methods & Research, 16, 504–523.

    Article  Google Scholar 

  • Little, T. D., Cunningham, W. A., Shahar, G., & Widaman, K. F. (2002). To parcel or not to parcel: exploring the question, weighing the merits. Structural Equation Modeling, 9, 151–173.

    Article  Google Scholar 

  • Lord, F., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading: Addison-Wesley.

    Google Scholar 

  • Markland, D. (2007). The golden rule is that there are no golden rules: a commentary on Paul Barrett’s recommendations for reporting model fit in structural equation modeling. Personality and Individual Difference, 42, 851–858.

    Article  Google Scholar 

  • Marsh, H. W., Hau, K., & Wen, J. (2004). In search of golden rules: comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler’s (1999) findings. Structural Equation Modeling, 11, 320–341.

    Article  Google Scholar 

  • Marsh, H. W., Wen, J., & Hau, K. (2004). Structural equation models of latent interactions: evaluation of alternative estimation strategies and indicator construction. Psychological Methods, 9, 275–300.

    Article  Google Scholar 

  • McDonald, R. P. (1999). Test theory: A unified treatment. Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • McDonald, R. P., & Ho, M.-H. R. (2002). Principles and practices in reporting nonlinear latent variables models. Psychological Methods, 7, 64–82.

    Article  Google Scholar 

  • Mooyaart, A., & Bentler, P. M. (2010). An alternative approach for nonlinear latent variable models. Structural Equation Modeling, 17, 357–373.

    Article  Google Scholar 

  • Muthén, L. K., & Muthén, B. O. (2010). Mplus: Statistical analysis with latent variables user’s guide. Los Angeles: Muthén and Muthén.

    Google Scholar 

  • Petter, S., Straub, D., & Rai, A. (2007). Specifying formative constructs in information systems research. MIS Quarterly, 31, 623–656.

    Google Scholar 

  • Podsakoff, P., Mackenzie, S. B., Podsakoff, N. P., & Lee, J. (2003). The mismeasure of man(agement) and its implications for leadership research. The Leadership Quarterly, 14, 615–656.

    Article  Google Scholar 

  • Russell, D. W., Kahn, J. H., Spoth, R., & Altmaier, E. M. (1998). Analyzing data from experimental studies: illustration of a latent variable structural equation modeling approach. Journal of Counseling Psychology, 45, 18–29.

    Article  Google Scholar 

  • Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variable analysis: Applications to development research (pp. 399–419). Newbury Park: Sage.

    Google Scholar 

  • Savalei, V., & Bentler, P. M. (2006). Structural equation modeling. In R. Grover & M. Vriens (Eds.), The handbook of marketing research: Uses, misuses, and future advances (pp. 330–364). Newbury Park: Sage.

    Google Scholar 

  • Savalei, V., & Bentler, P. M. (2009). A two-stage approach to missing data: theory and application to auxiliary variables. Structural Equation Modeling, 16, 477–497.

    Article  Google Scholar 

  • Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference. Boston: Houghton Mifflin.

    Google Scholar 

  • Von Wright, G. H. (1974). Causality and determinism. New York: Columbia University Press.

    Google Scholar 

  • Wothke, W., & Browne, M. W. (1990). The direct product model for the MTMM matrix parameterized as a second order factor analysis model. Psychometrika, 55, 255–262.

    Article  Google Scholar 

  • Yuan, K., & Bentler, P. M. (1998). Robust means and covariance structure analysis. British Journal of Mathematical and Statistical Psychology, 51, 63–88.

    Article  Google Scholar 

  • Yuan, K., & Bentler, P. M. (2007). Robust procedures in structural equation models. In S. Lee (Ed.), Handbook of latent variable and related models (pp. 367–397). Amsterdam: North-Holland.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ross School of Business, University of Michigan, Ann Arbor, MI, USA

    Richard P. Bagozzi

  2. College of Business Administration, Seoul National University, Seoul, Korea

    Youjae Yi

Authors
  1. Richard P. Bagozzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Youjae Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Richard P. Bagozzi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bagozzi, R.P., Yi, Y. Specification, evaluation, and interpretation of structural equation models. J. of the Acad. Mark. Sci. 40, 8–34 (2012). https://doi.org/10.1007/s11747-011-0278-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11747-011-0278-x

Keywords

Search

Navigation