semTools (version 0.5-0)

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 ${\chi }^2$ distribution (MacCallum, Browne, & Suguwara, 1996). First, the noncentrality parameter ($\lambda$) is calculated from RMSEA (Steiger, 1998; Dudgeon, 2004) by $$\lambda =(N-1)d{\epsilon }^2/K,$$ where $N$ is sample size, $d$ is the model degree of freedom, $K$ is the number of group, and $\epsilon$ is the population RMSEA. Next, the noncentral ${\chi }^2$ distribution with a specified df and noncentrality parameter is plotted. Thus, the x-axis represents the sample ${\chi }^2$ value. The sample ${\chi }^2$ value can be transformed to the sample RMSEA scale ($\hat{\epsilon }$) by $$\hat{\epsilon }=\sqrt{K}\sqrt{\frac{{\chi }^2-d}{(N-1)d}},$$ where ${\chi }^2$ is the ${\chi }^2$ value obtained from the noncentral ${\chi }^2$ 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(3), 305--319. doi:10.1207/s15328007sem1103_1

MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130--149. doi:10.1037/1082-989X.1.2.130

Steiger, J. H. (1998). A note on multiple sample extensions of the RMSEA fit index. Structural Equation Modeling, 5(4), 411--419. doi:10.1080/10705519809540115

See Also

• plotRMSEApower to plot the statistical power based on population RMSEA given the sample size

• findRMSEApower to find the statistical power based on population RMSEA given a sample size

• findRMSEAsamplesize to find the minium sample size for a given statistical power based on population RMSEA

Examples

# NOT RUN {
plotRMSEAdist(c(.05, .08), n = 200, df = 20, ptile = .95, rmseaScale = TRUE)
plotRMSEAdist(c(.05, .01), n = 200, df = 20, ptile = .05, rmseaScale = FALSE)

# }