plotRMSEAdist: Plot the sampling distributions of RMSEA
Description
Plots the sampling distributions of RMSEA based on the noncentral chi-square distributions
Usage
plotRMSEAdist(rmsea, n, df, ptile=NULL, caption=NULL, rmseaScale = TRUE)
Arguments
rmsea
The vector of RMSEA values to be plotted
n
Sample size of a dataset
df
Model degrees of freedom
ptile
The percentile rank of the distribution of the first RMSEA that users wish to plot a vertical line in the resulting graph
caption
The name vector of each element of rmsea
rmseaScale
If TRUE, the RMSEA scale is used in the x-axis. If FALSE, the chi-square scale is used in the x-axis.
Details
This function creates overlappling plots of the sampling distribution of RMSEA based on noncentral chi-square distribution (MacCallum, Browne, & Suguwara, 1996). First, the noncentrality parameter ($\lambda$) is calculated from RMSEA by
$$\lambda = (N - 1)d\varepsilon^2,$$
where $N$ is sample size, $d$ is the model degree of freedom, and $\varepsilon$ is the population RMSEA. Next, the noncentral chi-square distribution with a specified degree of freedom and noncentrality parameter is plotted. Thus, the x-axis represent the sample chi-square value. The sample chi-square value can be transformed to the sample RMSEA scale ($\hat{\varepsilon}$) by
$$\hat{\varepsilon} = \sqrt{\frac{\chi^2 - d}{(N - 1)d}},$$
where $\chi^2$ is the chi-square value obtained from the noncentral chi-square distribution.
References
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.
See Also
plotRMSEApowerto plot the statistical power based on population RMSEA given the sample size
findRMSEApowerto find the statistical power based on population RMSEA given a sample size
findRMSEAsamplesizeto find the minium sample size for a given statistical power based on population RMSEA