wp.sem.rmsea {WebPower}

Statistical Power Analysis for Structural Equation Modeling based on RMSEA

Description

Structural equation modeling (SEM) is a multivariate technique used to analyze relationships among observed and latent variables. It can be viewed as a combination of factor analysis and multivariate regression analysis. Two methods are widely used in power analysis for SEM. One is based on the likelihood ratio test proposed by Satorra and Saris (1985). The other is based on RMSEA proposed by MacCallum et al. (1996). This function is for SEM power analysis based on RMSEA.

Usage

wp.sem.rmsea(n = NULL, df = NULL, rmsea0 = NULL, rmsea1 = NULL,
  power = NULL, alpha = 0.05, type = c("close", "notclose"))

Arguments

n

Sample size.

df

Degrees of freedom. The degrees of freedom of the chi-squared test.

rmsea0

RMSEA for H0. It usually euquals zero.

rmsea1

RMSEA for H1.

power

Statistical power.

alpha

significance level chosed for the test. It equals 0.05 by default.

type

Close fit or non-clase fit ('close' or 'notclose'). It is 'close' by default.

Value

An object of the power analysis.

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(2), 130.

Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.

Examples

#To calculate the statistical power given sample size and effect size:
wp.sem.rmsea (n = 100, df = 4, rmsea0 = 0,
               rmsea1 = 0.116,  power = NULL, alpha = 0.05)
#    Power for SEM based on RMSEA
#  
#        n df rmsea0 rmsea1     power alpha
#      100  4      0  0.116 0.4208173  0.05
#  
#    URL: http://psychstat.org/rmsea

#To generate a power curve given a sequence of sample sizes:
res <- wp.sem.rmsea (n = seq(100,600,100), df = 4, rmsea0 = 0,
                        rmsea1 = 0.116,  power = NULL, alpha = 0.05)
res
#    Power for SEM based on RMSEA
#  
#        n df rmsea0 rmsea1     power alpha
#      100  4      0  0.116 0.4208173  0.05
#      200  4      0  0.116 0.7494932  0.05
#      300  4      0  0.116 0.9135968  0.05
#      400  4      0  0.116 0.9746240  0.05
#      500  4      0  0.116 0.9933963  0.05
#      600  4      0  0.116 0.9984373  0.05
#  
#    URL: http://psychstat.org/rmsea

#To plot the power curve:
plot(res) 

#To calculate the required sample size given power and effect size:
wp.sem.rmsea (n = NULL, df = 4, rmsea0 = 0,
              rmsea1 = 0.116,  power = 0.8, alpha = 0.05)
#    Power for SEM based on RMSEA
#  
#             n df rmsea0 rmsea1 power alpha
#      222.7465  4      0  0.116   0.8  0.05
#  
#    URL: http://psychstat.org/rmsea

#  #To calculate the minimum detectable effect size of rmsea1 given power and sample size:
wp.sem.rmsea (n = 100, df = 4, rmsea0 = 0,
             rmsea1 = NULL,  power = 0.8, alpha = 0.05)
#    Power for SEM based on RMSEA
#  
#        n df rmsea0    rmsea1 power alpha
#      100  4      0 0.1736082   0.8  0.05
#  
#    URL: http://psychstat.org/rmsea