semTools (version 0.4-11)

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, group=1)

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.

group

The number of group that is used to calculate RMSEA.

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 (Steiger, 1998; Dudgeon, 2004) by $$\lambda = (N - 1)d\varepsilon^2 / K,$$ where $N$ is sample size, $d$ is the model degree of freedom, $K$ is the number of groupand $\varepsilon$ 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 $$\hat{\varepsilon} = \sqrt{K}\sqrt{\frac{\chi^2 - d}{(N - 1)d}},$$ where $\chi^2$ is the chi-square value obtained from the noncentral chi-square distribution.

References

Dudgeon, P. (2004). A note on extending Steiger's (1998) multiple sample RMSEA adjustment to other noncentrality parameter-based statistic. Structural Equation Modeling, 11, 305-319. 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. Steiger, J. H. (1998). A note on multiple sample extensions of the RMSEA fit index. Structural Equation Modeling, 5, 411-419.

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

Examples

plotRMSEAdist(rmsea=c(.05, .08), n=200, df=20, ptile=0.95, rmseaScale = TRUE)
plotRMSEAdist(rmsea=c(.05, .01), n=200, df=20, ptile=0.05, rmseaScale = FALSE)