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## Path Models and Structural Equations Models

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**Structural Equations Modeling**Books • Bagozzi, Richard P. (1980), Causal Modeling in Marketing, NY: Wiley. • Bollen, Kenneth A. (1989) Structural Equation Models with Latent Variables, NY: Wiley. • Kline, Rex B. (2004) Principles and Practice of Structural Equation Modeling 2nd ed., New York: Guildford. • Raykov, Tenko and George A. Marcoulides (2000) A First Course in Structural Equation Modeling, Mahwah, NJ: Erlbaum. • 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: • Bollen, Kenneth A. and J. Scott Long (eds.) (1993) Testing Structural Equation Models, Newbury Park, CA: Sage. • Kaplan, David (2000), Structural Equation Modeling: Foundations and Extensions, Thousand Oaks, CA: Sage.**Structural Equations Modeling: Software**Lisrel: • Byrne, Barbara M. (1998) Structural Equation Modeling with Lisrel, Prelis, and Simplis: Basic Concepts, Applications, and Programming, Mahwah, NJ: Erlbaum. • Hayduk, Leslie A. (1987), Structural Equation Modeling with Lisrel, Baltimore, MD: Johns Hopkins University Press. • Kelloway, E. Kevin (1998), Using LISREL for Structural Equation Modeling: A Researcher's Guide, Sage. • Long, J. Scott (1983), Covariance Structure Models: An Introduction to LISREL, Newbury Park, CA: Sage. • Jöreskog, Karl and Dag Sörbom(1996), Lisrel 8: User’s Reference Guide, Hillsdale, NJ: SSI Scientific Software International. • Also possibly: Jöreskog, Karl and Dag Sörbom(1993), Lisrel 8: Structural Equation Modeling with the Simplis Command Language, Hillsdale, NJ: SSI Scientific Software International. • 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: • Byrne, Barbara M. (2006) Structural Equation Modeling with Eqs: Basic Concepts, Applications, and Programming, Mahwah, NJ: Erlbaum. • 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 inApplied 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**• 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), 432-437. • 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): • 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. • Iacobucci, Dawn (2010), “Structural Equations Modeling: Fit Indices, Sample Size, and Advanced Issues,” Journal of Consumer Psychology, 20 (1), 90-98. • 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. • 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. • 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 • Alwin, Duane F. and Robert M. Hauser (1975), “The Decomposition of Effects in Path Analysis,” American Sociological Review, 40 (Feb.), 37-47. • 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.) • McDonald, Roderick (1985), Factor Analysis and Related Methods, Hillsdale, NJ: Erlbaum.**SEMs: Fit Indices**• 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**• 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 ZhonglinWen (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**• 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), 322-331. • 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.) • Berry, William D. (1985), Nonrecursive Causal Models, Newbury Park, CA: Sage. • Jaccard, James and Choi K. Wan (1996), Lisrel Approaches to Interaction Effects in Multiple Regression, Thousand Oaks, CA: Sage.**Mediation Analysis**• Iacobucci, Dawn (2008), Mediation Analysis, Thousand Oaks, CA: Sage. • Iacobucci, Dawn, NeelaSaldanha 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. • Iacobucci, Dawn (2012), “Mediation with Categorical Variables: The Final Frontier,” Journal of Consumer Psychology.**Issues with Binary Variables**• 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)**• 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.