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Aleksandr Blekh

Georgia Institute of Technology

Optimal sampling strategy for EFA, CFA and SEM

The following is a copy of my question on StackExchange's CrossValidated site: http://stats.stackexchange.com/questions/90386/optimal-sampling-strategy-for-efa-cfa-and-sem. Please feel free to answer there or here at ResearchGate at your convinience.

I'm wondering what should be the optimal sampling strategy for my dissertation research. I have four data sources (two open source software projects meta-repositories and two global startup databases). I'd like to perform EFA to discover (or, rather, confirm my theory-based assumptions) the factor structure of the study's constructs. Then I plan to perform CFA to determine validity and reliability of the measurement model. Finally, I plan to perform SEM analysis to test the study's structural model and hypotheses. Having said that, I plan to perform data analysis (at least, SEM - not sure about EFA/CFA) on two data sets: pilot and main. I believe that pilot analysis will allow me to modify model, if fit indices will be inadequate. Then I plan to perform main SEM analysis of the modified model (and, possibly, alternative models) on the main data set. In addition, I plan to perform both covariance-based (CB) and partial least squares (PLS) SEM analysis to compare them for my study. What should be the optimal approach and its steps in terms of the following:

1. Sampling technique. I was thinking about randomized sampling of data from each OSS meta-repo or from a merged data set; then selecting corresponding data from startup databases.

2. Strategy on dividing the sample data set into pilot and main data sets.

3. Any special steps for sampling due to multiple methods (EFA/CFA/SEM).

4. Any special steps for sampling due to alternative models.

5. Any special steps for sampling due to analyzing via both CB-SEM and PLS-SEM.

Problem(Abstract)

Does any version of Amos offer the Satorra-Bentler Scaled Chi-square test statistic?

Satorra, A., & Bentler, EM. (1988a). Scaling corrections for chi-square statistics in covariance structure analysis. ASA 1988 Proceedings of the Business and Eeonomic Statistics ,Section (308-313). Alexandria, VA: American Statistical Association.

Satorra, A., & Bentler, EM. (1988b). Scaling corrections for statistics in covariance structure analysis (UCLA Statistics Series #2). Los Angeles, CA: University of California.

Satorra, A., & Bentler, EM. (1994). Corrections to test statistics and standard enors in covariance structure analysis. In A. von Eye & C.C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399-419). Thousand Oaks, CA: Sage.

Resolving the problem

Amos does not provide the Satorra-Bentler scaled Chi-square. Instead, Amos provides bootstrapping for situations where the assumptions underlying maximum likelihood chi-squares and standard errors may be violated. In fact, for large samples, both Amos and the Satorra-Bentler scaled Chi- square have the same p-value. Some simulation results show that bootstrapping is even better than the Satorra-Bentler scaled Chi-square.

Here are references for these simulation studies:

Fouladi, R.T. (1998) Covariance structure analysis techniques under conditions of multivariate normality and nonnormality--modified and bootstrap based test statistics. Paper presented at the annual meeting of the American Educational Research Association, San Diego, April 14, 1997.

Nevitt, J. and Hancock, G.R. (1998) Relative performance of rescaling and resampling approaches to model Chi-square and parameter standard error estimation in structural equation modeling. Paper presented at the annual meeting of the American Educational Research Association, San Diego, April 14, 1997.

A feature request to add the Satorra-Bentler Scaled Chi-Square has been filed with AMOS Development

You help and advice on this is greatly appreciated!

Dear Conal,

ULS doesn´t have assumptions, is consistent, but is not asymptotically efficient. The majority of the softwares doesn’t produces tests to the quality of fit based on ULS estimation, because it is not possible to ascertain that the Clue of the fit show a knowing distribution – please, see Blunch (2008), p. 82

Blunch, N. J. (2008). Introduction to structural equation modeling using SPS and AMOS. London: Sage

The GFI (goodness-of-fit index) by Jöreskog and Sörbom (1984) is ideal for Unweighted Least Squares estimation. GFI is less than or equal to 1, with a value of 1 indicating a perfect fit.