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Path Models and Structural Equations Models 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 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 • • • • • 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): • 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 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 • • • • 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. • 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 Analyses Mediation Analysis • Iacobucci, Dawn (2008), Mediation Analysis, Thousand Oaks, CA: Sage. • 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. • Iacobucci, Dawn (2012), “Mediation with Categorical Variables: The Final Frontier,” Journal of Consumer Psychology. Miscellaneous Measurement Stuff 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.