Computing power and minimum sample size for RMSEA
Kristopher J. Preacher (Vanderbilt University)
Donna L. Coffman (Pennsylvania State University)
This web utility may be cited in APA style in the following manner:
Preacher, K. J., & Coffman, D. L. (2006, May). Computing power and minimum sample size for RMSEA [Computer software]. Available from http://quantpsy.org/.
If the Rweb server is not working
The code generated by this utility can be pasted directly into an R console window. R (a free, open-source statistical computing environment) may be obtained here: http://cran.r-project.org/.
The purpose of this page, and how to use it
This web page generates R code that can compute (1) statistical power for testing a covariance structure model using RMSEA, (2) the minimum sample size required to achieve a given level of power, (3) power for testing the difference between two nested models using RMSEA, or (4) the minimum sample size required to achieve a given level of power for a test of nested models using RMSEA. We strongly urge the user to read the sources below (see References) before proceeding. We have another calculator for plotting power curves here
Make sure all fields in the relevant table are filled in; otherwise values of 0 will be automatically entered. These tables assume that Model A is parametrically nested within (and therefore more constrained than) Model B. Therefore df(A) should be larger than df(B), and RMSEA(A) should be larger than RMSEA(B).
When you are finished, click the button labeled "Submit above to Rweb" to compute the desired value. Alternatively, the R syntax may be copied and pasted into a command window of any PC installation of R.
Compute Power for RMSEA (nested models)
Compute Sample Size for RMSEA (nested models)
MacCallum, R. C., Browne, M. W., & Cai, L. (2006). Testing differences between nested covariance structure models: Power analysis and null hypotheses. Psychological Methods, 11, 19-35.
MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1, 130-149.
MacCallum, R. C., Lee, T., & Browne, M. W. (2010). The issue of isopower in power analysis for tests of structural equation models. Structural Equation Modeling, 17, 23-41.
Preacher, K. J., Cai, L., & MacCallum, R. C. (2007). Alternatives to traditional model comparison strategies for covariance structure models. In T. D. Little, J. A. Bovaird, & N. A. Card (Eds.), Modeling contextual effects in longitudinal studies (pp. 33-62). Mahwah, NJ: Lawrence Erlbaum Associates.
Steiger, J. H. (1998). A note on multiple sample extensions of the RMSEA fit index. Structural Equation Modeling, 5, 411-419.
Steiger, J. H., & Lind, J. C. (1980, June). Statistically based tests for the number of factors. Paper presented at the annual meeting of the Psychometric Society, Iowa City, IA.
Original version posted May, 2006.