Why So Many Arrows? Introduction to Structural Equation Modeling for the Novitiate User
- 755 Downloads
- 3 Citations
Abstract
Structural equation modeling (SEM) is the term for a broadly applicable set of statistical techniques that allow researchers to precisely represent constructs of interest, measure the extent to which data are consistent with a proposed conceptual model, and to adjust for the influence of measurement error. Although SEM may appear intimidating at first glance, it can be made accessible to researchers. The current manuscript provides a non-technical overview of SEM and its major constructs for a novitiate user. Concepts are illustrated using a simple example, representing a potential study performed in the field of youth and family research. The purpose of this manuscript is to offer interested scholars a conceptual overview and understanding of research questions and issues that may be addressed with this family of techniques.
Keywords
Statistics Structural equation modeling Measurement Confirmatory factor analysisReferences
- Anderson, J. C., & Gerbing, D. W. (1988). Structural equation modeling in practice: A review and recommended two-step approach. Psychological Bulletin, 103(3), 411–423.CrossRefGoogle Scholar
- Asparouhov, T., & Muthen, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 16(3), 397–438.CrossRefGoogle Scholar
- Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107(2), 238–246.PubMedCrossRefGoogle Scholar
- Bentler, P. M. (2007). On tests and indices for evaluating structural models. Personality and Individual Differences, 42, 825–829.CrossRefGoogle Scholar
- Bentler, P. M., & Chou, C. P. (1987). Practical issues in structural equation modeling. Sociological Methods Research, 16(1), 78–117.CrossRefGoogle Scholar
- Bollen, K. A. (1989). Structural equations with latent variables. Hoboken, NJ: Wiley-Interscience.Google Scholar
- Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York, NY: Guilford Press.Google Scholar
- Byrne, B. M. (2012). Structural equation modeling with Mplus: Basic concepts, applications, and programming. New York, NY: Taylor & Francis Group.Google Scholar
- DeShon, R. P. (1998). A cautionary note on measurement error corrections in structural equation models. Psychological Methods, 3(4), 412–423.CrossRefGoogle Scholar
- Enders, C. K. (2001). A primer on maximum likelihood algorithms available for use with missing data. Structural Equation Modeling, 8(1), 128–141.CrossRefGoogle Scholar
- Enders, C. K. (2011). Missing not at random models for latent growth curve analysis. Psychological Methods, 16, 1–16.PubMedCrossRefGoogle Scholar
- Enders, C. K., & Bandalos, D. L. (2001). The relative performance of full information maximum likelihood estimation for missing data in structural equation models. Structural Equation Modeling, 8(3), 430–457.CrossRefGoogle Scholar
- Finney, S. J., & DiStefano, C. (2006). Non-normal and categorical data in structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (pp. 269–314). Greenwich, CT: Information Age Publishing.Google Scholar
- Flora, D. B., & Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9(4), 466–491.PubMedCentralPubMedCrossRefGoogle Scholar
- Graham, J. W. (2009). Missing data analysis: Making it work in the real world. Annual Review of Psychology, 60, 549–576.PubMedCrossRefGoogle Scholar
- Hancock, G. R. (2006). Power analysis in covariance structure modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (pp. 69–115). Greenwich, CT: Information Age Publishing.Google Scholar
- Henley, A. B., Shook, C. L., & Peterson, M. (2006). The presence of equivalent models in strategic management research using structural equation modeling: Assessing and addressing the problem. Organizational Research Methods, 9(4), 516–535.CrossRefGoogle Scholar
- Hooper, D., Coughlan, J., & Mullen, M. R. (2008). Structural equation modeling: Guidelines for determining model fit. The Electronic Journal of Business Research Methods, 6(1), 53–60.Google Scholar
- Hox, J. J., & Bechger, T. M. (1998). An introduction to structural equation modeling. Family Science Review, 11, 354–373.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), 1–55.CrossRefGoogle Scholar
- Kline, R. B. (2011). Principles and practice of structural equation modeling (3rd ed.). New York, NY: Guilford Press.Google Scholar
- Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data (2nd ed.). New York, NY: Wiley.Google Scholar
- MacCallum, R. C., & Austin, J. T. (2000). Applications of structural equation modeling in psychological research. Annual Review of Psychology, 51, 201–226.PubMedCrossRefGoogle Scholar
- MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130–149.CrossRefGoogle Scholar
- MacCallum, R. C., Wegener, D. T., Uchino, B. N., & Fabrigar, L. R. (1993). The problem of equivalent models in applications of covariance structure analysis. Psychological Bulletin, 114(1), 185–199.PubMedCrossRefGoogle Scholar
- Marsh, H. W., Wen, Z., & Hau, K. T. (2006). Structural equation models of latent interactions and quadratic effects. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (pp. 225–265). Greenwich, CT: Information Age Publishing.Google Scholar
- Olsson, U. H., Foss, T., Troye, S. V., & Howell, R. D. (2000). The performance of ML, GLS, and WLS estimation in structural equation modeling under conditions of misspecification and nonnormality. Structural Equation Modeling, 7(4), 557–595.CrossRefGoogle Scholar
- Patterson, G. R., DeBaryshe, B. D., & Ramsey, E. (1989). A developmental perspective on antisocial behavior. American Psychologist, 44(2), 329–335.PubMedCrossRefGoogle Scholar
- Rindskopf, D. (1998). Explaining maximum likelihood estimation. Retrieved from http://www.rasch.org/rmt/rmt1237.htm.
- Rust, R. T., Lee, C., & Valente, E. (1995). Comparing covariance structure models: A general methodology. International Journal of Research in Marketing, 12, 279–291.CrossRefGoogle Scholar
- Schermelleh-Engel, K., Moosbrugger, H., & Muller, H. (2003). Evaluating the fit of structural equation models: Tests of significance and descriptive goodness-of-fit measures. Methods of Psychological Research, 8(2), 23–74.Google Scholar
- Schlomer, G. L., Bauman, S., & Card, N. A. (2010). Best practices for missing data management in counseling psychology. Journal of Counseling Psychology, 57(1), 1–10.PubMedCrossRefGoogle Scholar
- Schmidt, F. L., & Hunter, J. E. (1999). Theory testing and measurement error. Intelligence, 27(3), 183–198.CrossRefGoogle Scholar
- Schreiber, J. B., Stage, F. K., King, J., Nora, A., & Barlow, E. A. (2006). Reporting structural equation modeling and confirmatory factor analysis results: A review. Journal of Educational Research, 99(6), 323–337.CrossRefGoogle Scholar
- Steiger, J. H. & Lind, J.C. (1980). Statistically based tests for the number of common factors. Paper presented at the annual meeting of the Psychometric Society: Iowa City, IA.Google Scholar
- Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics (5th ed.). Boston, MA: Pearson Education.Google Scholar
- Tomarken, A. J., & Waller, N. G. (2003). Potential problems with ‘well fitting’ models. Journal of Abnormal Psychology, 112(4), 578–598.PubMedCrossRefGoogle Scholar
- Ullman, J. B. (2006). Structural equation modeling: Reviewing the basics and moving forward. Journal of Personality Assessment, 87(1), 35–50.PubMedCrossRefGoogle Scholar
- Vrieze, S. I. (2012). Model selection and psychological theory: A discussion of the differences between the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Psychological Methods, 17(2), 228–243. doi: 10.1037/a0027127.PubMedCentralPubMedCrossRefGoogle Scholar