Path Models
and Structural Equations Models
Structural Equations Modeling
Books
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Bagozzi, Richard P. (1980), Causal Modeling in Marketing, NY: Wiley.
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Bollen, Kenneth A. (1989) Structural Equation Models with Latent Variables, NY:
Wiley.
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Kline, Rex B. (2004) Principles and Practice of Structural Equation Modeling 2nd ed.,
New York: Guildford.
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Raykov, Tenko and George A. Marcoulides (2000) A First Course in Structural
Equation Modeling, Mahwah, NJ: Erlbaum.
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Schumacker, Randall E. and Richard G. Lomax (2004) A Beginner’s Guide to Structural
Equation Modeling (2nd ed.), Mahwah, NJ: Erlbaum.
A little more advanced:
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Bollen, Kenneth A. and J. Scott Long (eds.) (1993) Testing Structural Equation
Models, Newbury Park, CA: Sage.
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Kaplan, David (2000), Structural Equation Modeling: Foundations and Extensions,
Thousand Oaks, CA: Sage.
Structural Equations Modeling: Software
Lisrel:
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Byrne, Barbara M. (1998) Structural Equation Modeling with Lisrel, Prelis, and
Simplis: Basic Concepts, Applications, and Programming, Mahwah, NJ: Erlbaum.
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Hayduk, Leslie A. (1987), Structural Equation Modeling with Lisrel, Baltimore, MD:
Johns Hopkins University Press.
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Kelloway, E. Kevin (1998), Using LISREL for Structural Equation Modeling: A
Researcher's Guide, Sage.
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Long, J. Scott (1983), Covariance Structure Models: An Introduction to LISREL,
Newbury Park, CA: Sage.
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Jöreskog, Karl and Dag Sörbom (1996), Lisrel 8: User’s Reference Guide, Hillsdale, NJ:
SSI Scientific Software International.
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Also possibly: Jöreskog, Karl and Dag Sörbom (1993), Lisrel 8: Structural Equation
Modeling with the Simplis Command Language, Hillsdale, NJ: SSI Scientific
Software International.
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And: Jöreskog, Karl and Dag Sörbom (1996), Prelis 2: User’s Reference Guide,
Hillsdale, NJ: SSI Scientific Software International.
Structural Equations Modeling: Software
Eqs and Amos:
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Byrne, Barbara M. (2006) Structural Equation Modeling with Eqs: Basic Concepts,
Applications, and Programming, Mahwah, NJ: Erlbaum.
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Byrne, Barbara M. (2001) Structural Equation Modeling with Amos: Basic Concepts,
Applications, and Programming, Mahwah, NJ: Erlbaum.
Structural Equations Modeling Articles
Overviews/intros:
• Bagozzi, Richard P. and Youjae Yi (1989), “On the Use of Structural Equation Models in
Experimental Design,” Journal of Marketing Research, 26, 271-84.
• Bentler, Peter M. (1980), “Multivariate Analysis with Latent Variables: Causal
Analysis,” Annual Review of Psychology, 31, 419-56.
• Bentler, Peter M. and Paul Dudgeon (1996), “Covariance Structure Analysis: Statistical
Practice, Theory, and Directions,” Annual Review of Psychology, 47, 563-592.
• Browne, Michael (1982), “Covariance Structures,” In D. M. Hawkins (ed.), Topics in
Applied Multivariate Analysis, London: Cambridge University Press, pp. 72-141.
• Steenkamp, Jan-Benedict E.M. and Hans Baumgartner (2000), “On the Use of
Structural Equation Models in Marketing Modeling,” International Journal of Research
in Marketing, 17 (June), 195-202.
Structural Equations Modeling Articles
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Anderson, James C. and David W. Gerbing (1988), “Structural Equation Modeling in
Practice: A Review and Recommended Two-Step Approach,” Psychological Bulletin,
103 (3), 411-423.
Anderson, James C. and David W. Gerbing (1984), “The Effect of Sampling Error on
Convergence, Improper Solutions, and Goodness-of-Fit Indices for Maximum
Likelihood Confirmatory Factor Analysis,” Psychometrika, 49, 155-173.
Anderson, James C., David W. Gerbing and John E. Hunter (1987), “On the
Assessment of Unidimensional Measurement: Internal and External Consistency, and
Overall Consistency Criteria,” Journal of Marketing Research, 24 (November), 432437.
Anderson, James C. and James A. Narus (1990), “A Model of Distributor Firm and
Manufacturer Firm Working Partnerships,” Journal of Marketing, 54 (Jan.), 42-58. (a
B2B example)
Gerbing, David W. and James C. Anderson (1988), “An Updated Paradigm for Scale
Development Incorporating Unidimensionality and Its Assessment,” Journal of
Marketing Research, 25 (May), 186-192.
Structural Equations Modeling My Articles
Articles (I’m happy to send you any of these, just email me):
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Iacobucci, Dawn (2009), “Everything You Always Wanted to Know about S.E.M.
(Structural Equations Modeling) But Were Afraid to Ask,” Journal of Consumer
Psychology, 19 (4), 673-680.
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Iacobucci, Dawn (2010), “Structural Equations Modeling: Fit Indices, Sample Size,
and Advanced Issues,” Journal of Consumer Psychology, 20 (1), 90-98.
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Iacobucci, Dawn (2010), “Rejoinder to Commentators on Structural Equations
Modeling Primers: Bentler, Bagozzi, and Fabrigar, Porter, and Norris,” Journal of
Consumer Psychology, 20 (2), 226-227.
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More complex: Iacobucci, Dawn, Doug Grisaffe, Adam Duhachek and Alberto
Marcati (2003), “FAC-SEM: A Methodology for Modeling Factorial Structural
Equations Models, Applied to Cross-Cultural and Cross-Industry Drivers of Customer
Evaluations,” Journal of Service Research, 6 (1), 3-23. Research featured by Regina
Fazio Maruca, “Mapping the World of Customer Satisfaction,” Harvard Business
Review, 78 (May/June 2000), p.30.
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An application: Duhachek, Adam and Dawn Iacobucci (2005), “Consumer
Personality and Coping: Testing Rivaling Theories of Process,” Journal of Consumer
Psychology, 15 (1), 52-63.
Structural Equations Modeling
Advanced Topics
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Alwin, Duane F. and Robert M. Hauser (1975), “The Decomposition of Effects in Path
Analysis,” American Sociological Review, 40 (Feb.), 37-47.
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MacCallum, Robert C., Mary Roznowski, and Lawrence B. Necowitz (1992), “Model
Modifications in Covariance Structure Analysis: The Problem of Capitalization on
Chance,” Psychological Bulletin, 111 (3), 490-504. (Shows how to determine
whether a model you fit might have equally plausible alternatives—usually, yes.)
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McDonald, Roderick (1985), Factor Analysis and Related Methods, Hillsdale, NJ:
Erlbaum.
SEMs: Fit Indices
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Bearden, William O., Subhash Sharma and Jesse E. Teel (1982), “Sample Size Effects
on Chi Square and Other Statistics Used in Evaluating Causal Models,” Journal of
Marketing Research, 19 (Nov.), 425-430.
Bentler, Peter M. (1990), “Comparative Fit Indexes in Structural Models,”
Psychological Bulletin, 107 (2), 238-246.
Bentler, Peter M. and Douglas G. Bonett (1980), “Significance Tests and Goodness of
Fit in the Analysis of Covariance Structures,” Psychological Bulletin, 88 (3), 588-606.
Bollen, Kenneth A. (1990), “Overall Fit in Covariance Structure Models: Two Types of
Sample Size Effects,” Psychological Bulletin, 107 (2), 256-259.
Browne, Michael W., Robert C. MacCallum, Cheong-Tag Kim, Barbara L. Andersen and
Ronald Glaser (2002), “When Fit Indices and Residuals are Incompatible,”
Psychological Methods, 7 (4), 403-421.
Ding, Lin, Wayne F. Velicer and Lisa L. Harlow (1995), “Effects of Estimation Methods,
Number of Indicators per Factor, and Improper Solutions on Structural Equation
Modeling Fit Indices,” Structural Equation Modeling, 2 (2), 119-144.
Fan, Xitao and Stephen A. Sivo (2005), “Sensitivity of Fit Indexes to Misspecified
Structural or Measurement Model Components,” Structural Equation Modeling, 12
(3), 343-67.
SEMs: Fit Indices, continued
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Gerbing, David W. and James C. Anderson (1992), “Monte Carlo Evaluations of
Goodness of Fit Indices for Structural Equation Models, Sociological Methods and
Research, 21 (2), 132-160.
Hu, Li-tze and Peter M. Bentler (1999), “Cutoff Criteria for Fit Indexes in Covariance
Structure Analysis: Conventional Criteria Versus New Alternatives,” Structural
Equation Modeling, 6 (1), 1-55.
Kim, Kevin, H. (2005), “The Relation Among Fit Indexes, Power, and Sample Size in
Structural Equation Modeling,” Structural Equation Modeling, 12 (3), 368-390.
Marsh, Herbert W., Kit-Tai Hau and Zhonglin Wen (2004), “In Search of Golden Rules,”
Structural Equation Modeling, 11(3), 320-341.
Rigdon, Edward E. (1996), “CFI Versus RMSEA: A Comparison of Two Fit Indexes for
Structural Equation Modeling,” Structural Equation Modeling, 3 (4), 369-379.
Steiger, James H. (2000), “Point Estimation, Hypothesis testing, and Interval
Estimation Using the RMSEA: Some Comments and a Reply to Hayduk and Glaser,”
Structural Equation Modeling, 7 (2), 149-162.
Structural Equations Logic and Issues
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Asher, Herbert B. (1983), Causal Modeling, Newbury Park, CA: Sage.
Davis, James A. (1985), The Logic of Causal Order, Newbury Park, CA: Sage.
Holland, Paul W. (1986), “Statistics and Causal Inference,” Journal of the American
Statistical Association, 81 (396), 945-960.
Rubin, Donald B. (2005), “Causal Inference Using Potential Outcomes: Design,
Modeling, Decisions, Journal of the American Statistical Association, 100 (469), 322331.
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Cudeck, Robert (1989), “Analysis of Correlation Matrices Using Covariance Structure
Models,” Psychological Bulletin, 105 (2), 317-327. (not supposed to do SEM on
correlation matrices—overall test statistics are off, as are standard errors of
parameters, hence their test stats will be off also.)
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Berry, William D. (1985), Nonrecursive Causal Models, Newbury Park, CA: Sage.
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Jaccard, James and Choi K. Wan (1996), Lisrel Approaches to Interaction Effects in
Multiple Regression, Thousand Oaks, CA: Sage.
Mediation Analyses
Mediation Analysis
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Iacobucci, Dawn (2008), Mediation Analysis, Thousand Oaks, CA: Sage.
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Iacobucci, Dawn, Neela Saldanha and Jane Xiaoyan Deng (2007), “A Meditation on
Mediation: Evidence That Structural Equations Models Perform Better than
Regressions,” Journal of Consumer Psychology 17 (2), 140-154.
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Iacobucci, Dawn (2012), “Mediation with Categorical Variables: The Final Frontier,”
Journal of Consumer Psychology.
Miscellaneous Measurement Stuff
Issues with Binary Variables
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Christoftersson, Anders (1975), “Factor Analysis of Dichotomized Variables,”
Psychometrika, 40, 5-32.
Collins, Linda, Norman Cliff, Douglas McCormick, and Judith L. Zatkin (1986), “Factor
Recovery with Binary Data Sets: A Simulation,” Multivariate Behavioral Research, 21,
377-391.
Ethington, Corinna A. (1987), “The Robustness of Lisrel Estimates in Structural
Equation Models with Categorical Variables,” Journal of Experimental Education, 55
(2), 80-88.
Kupek, Emil (2005), “Log-Linear Transformation of Binary Variables: A Suitable Input
for SEM,” Structural Equation Modeling, 12 (1), 28-40.
Muthén, Bengt (1978), “Contributions to Factor Analysis of Dichotomous Variables,”
Psychometrika, 43, 551-560.
Muthén, Bengt (1984), “A General Structural Equation Model with Dichotomous,
Ordered Categorical, and Continuous Latent Variable Indicators,” Psychometrika, 49
(1), 115-132.
Winship, Christopher and Robert D. Mare (1983), “Structural Equations and Path
Analysis for Discrete Data,” The American Journal of Sociology, 89 (1), 54-110.
Item Response Theory (IRT)
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Andrich, David (1988), Rasch Models for Measurement, Newbury Park, CA: Sage.
Hulin, Charles L., Fritz Drasgow, and Charles K. Parsons (1983), Item Response Theory:
Application to Psychological Measurement, Homewood, IL: Dorsey Dow Jones-Irwin.
Lord, Frederic M. (1980), Applications of Item Response Theory to Practical Testing
Problems, Hillsdale, NJ: Erlbaum.