Bootstrap

• Bootstrap analysis, both as a tool for nonparametric statistical inference and as a tool for describing sample results stability and replicability,
• using bootstrap for nonparametric statistical inference (Efron, 1985)
• Bootstrapping it has also been advocated as a descriptive tool and an internal replication mechanism for assessing the stability and replicability of sample results of an individual study (Thompson, 1993). This descriptive use of bootstrap is meaningful when our interest may not be about statistical inference but rather about understanding how stable the results may be across repeated sampling.
• distinct differences between the inferential and the descriptive applications of the bootstrap (cf. Thompson, 1993). Larger numbers of bootstrapped resamples are required in inferential (i.e., statistical significance) bootstrap applications as against descriptive
  applications of the bootstrap. when invoke the bootstrap to conduct statistical significance tests, extremely large numbers of resamples are required (e.g., 2,000, 5,000).
  However, when our application is descriptive, we are primarily interested in the
  mean (or median) statistic and the SD/SE from the sampling distribution. These values are less dependent on large numbers of resamples. (Thompson, 1999, p. 50) Of course, in an era of powerful microcomputers, we may elect to use large numbers of resamples even for descriptive applications of the bootstrap because the cost of additional resampling is effectively zero
• bootstrap analysis can be accomplished by using a standard statistical analysis package (e.g., SAS) with only a reasonable amount of effort.
• In Amos, "Perform Bootstrap” needs to be checked. One may choose the percentile confidence interval or the bias-corrected confidence interval and the desired confidence interval level (default is 90%).
• For doing regression analysis in Amos, if we are also interested in the replicability of the sample R2 of the regression model, under the “Output” tab of AMOS “Analysis
  Properties,” the option of “Squared Multiple Correlations” was checked, if the model R2 is very high (e.g., R2 = .93), and it is likely to be highly replicable across comparable samples.

Useful links:

• http://www.utexas.edu/its/rc/answers/amos/amos7.html

Reading lists:

• Efron,B., and Tibshirani,R.J. (1993) An introduction to the bootstrop. Chapman&Hall, Inc.
• Jun Shao and Dongsheng Tu (1995) The jackknife and bootstrap. Springer.
• Xitao Fan (2003) Using Commonly Available Software For Bootstrapping In Both Substantive And Measurement Analyses. Educational and Psychological Measurement, v63: 24-50.

Factor Analysis

• Thompson,B. (2004) Explorary and confirmatory factor analysis: understanding concepts and applications. American Psychological Association.

ordinal data in SEM

• use polychoric/polyserial correlations matrix as input, use weighted least squares (WLS) estimation method

handling non-normal data in SEM

• Handling non-normal data using AMOS http://www.utexas.edu/its/rc/answers/amos/amos7.html

interaction product term in SEM

• http://www2.kuas.edu.tw/prof/fred/vpls/moderating.htm
• Arminger, G., & Muthén, B.O. (1998). A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the Metropolis-Hastings algorithm. Psychometrika, v63:271-300.
• Bollen, K.A., & Paxton, P. (1998). Two-stage least squares estimation of interaction effects. In R.E. Schumacker & G.A.Marcoulides (Eds.), Interaction and nonlinear effects in structural equation modeling. (pp. 125-151). Mahwah, NJ: Erlbaum.
• Dimitruk, P., Schermelleh-Engel, K., Kelava, A. & Moosbrugger, H. (in press). Challenges in nonlinear structural equation modeling.
• Jaccard, J. & Wan, C. K. (1996). LISREL approaches to interaction effects in multiple regression. Thousand Oaks, CA: Sage Publications.
• Jöreskog, K. G., & Yang, F. (1996). Non-linear structural equation models: The Kenny-Judd model with interaction effects. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation modeling (pp. 57-87). Mahwah, NJ: Erlbaum.
• Jose M. Cortina, Gilad Chen, William P. Dunlap (2001) Testing interaction effects in LISEREL: examination and illustration of available procedures, Organizational Research Methods, v4 (4) : 324 - 360
• Kenny, D. A. & Judd, C. M. (1984). Estimating the non-linear and interactive effects of latent variables. Psychological Bulletin, v99: 422-431.
• Klein, A. G. & Moosbrugger, H. (2000). Maximum likelihood estimation of latent interaction effects with the LMS method. psychometrika, v65(4):457-474.
• Klein, A. G. & Muthén, B. O. (in press). Quasi maximum likelihood estimation of structural equation models with multiple interaction and quadratic effects. Journal of Multivariate and Behavioral Research.
• Lawrence R. James, Stanley A. Mulaik, Jeanne M. Brett (2006),A Tale of Two Methods,OrganizationalResearch Methods, v9 (2):233-244
• Marsh, W. H., Wen, Z. L. & Hau, K.-T. (2004). Structural equation models of latent interactions: Evaluation of alternative estimation strategies and indicator construction. Psychological methods, v9:275-300.
• Moosbrugger, H., Schermelleh-Engel, K., & Klein, A. (1997) Methodological problems of estimating latent interaction effects. Methods of Psychological Research Online,v2:95-111.
• Moulder, B. C., & Algina, J. (2002). Comparison of methods for estimating and testing latent variable interactions. Structural Equation Modeling, v9:1-19.
• Ping, R. A. (1996). Latent variable interaction and quadratic effect estimation: A two-step technique using structural equation analysis. Psychological Bulletin, v119: 166-175.
• Schermelleh-Engel, K., Klein, A., & Moosbrugger, H. (1998). Estimating nonlinear effects using a Latent Moderated Structural Equations Approach. In R.E. Schumacker & G.A. Marcoulides (Eds.), Interaction and nonlinear effects in structural equation modeling. (pp. 203-238). Mahwah, NJ: Erlbaum.
• Schumacker, R., & Marcoulides, G. (1998). Interaction and nonlinear effects in structural equation modeling. Mahwah, NJ: Lawrence Erlbaum Associates.
• Yang Jonsson, F. (1997). Non-linear structural equation models: Simulation studies of the Kenny-Judd model. Uppsala, Sweden:University of Uppsala.