semTools (version 0.5-3)

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 $$\lambda = (N - 1)d\varepsilon^2 / K,$$ where \(N\) is sample size, \(d\) is the model degree of freedom, \(K\) is the number of group, and \(\varepsilon\) 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 (\(\hat{\varepsilon}\)) by $$\hat{\varepsilon} = \sqrt{K}\sqrt{\frac{\chi^2 - d}{(N - 1)d}},$$ 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)

# }