semPower (version 1.0.0)

semPower: semPower: Power analyses for structural equation models (SEM).

Description

semPower allows for performing a-priori, post-hoc, and compromise power-analyses for structural equation models (SEM).

Details

• A-priori power analysis semPower.aPriori computes the required N, given an effect, alpha, power, and the model df

• Post-hoc power analysis semPower.postHoc computes the achieved power, given an effect, alpha, N, and the model df

• Compromise power analysis semPower.compromise computes the implied alpha and power, given an effect, the alpha/beta ratio, N, and the model df

In SEM, the discrepancy between H0 and H1 (the magnitude of effect) refers to the difference in fit between two models. If only one model is defined (which is the default), power refers to the global chi-square test. If both models are explicitly defined, power is computed for nested model tests. semPower allows for expressing the magnitude of effect by one of the following measures: F0, RMSEA, Mc, GFI, or AGFI.

Alternatively, the implied effect can also be computed from the discrepancy between the population (or a certain model-implied) covariance matrix defining H0 and the hypothesized (model-implied) covariance matrix from a nested model defining H1. See the examples below how to use this feature in conjunction with lavaan.

References

Moshagen, M., & Erdfelder, E. (2016). A new strategy for testing structural equation models. Structural Equation Modeling, 23, 54-60. doi: 10.1080/10705511.2014.950896

Examples

# NOT RUN {
# a-priori power analyses using rmsea = .05 a target power (1-beta) of .80
ap1 <- semPower.aPriori(0.05, 'RMSEA', alpha = .05, beta = .20, df = 200)
summary(ap1)
# a-priori power analyses using f0 = .75 and a target power of .95
ap2 <- semPower.aPriori(0.75, 'F0', alpha = .05, power = .95, df = 200)
summary(ap2)
# create a plot showing how power varies by N (given a certain effect)
semPower.powerPlot.byN(.05, 'RMSEA', alpha=.05, df=200, power.min=.05, power.max=.99)
# post-hoc power analyses using rmsea = .08
ph <- semPower.postHoc(.08, 'RMSEA', alpha = .05, N = 250, df = 50)
summary(ph)
# create a plot showing how power varies by the magnitude of effect (given a certain N)
semPower.powerPlot.byEffect('RMSEA', alpha=.05, N = 100, df=200, effect.min=.001, effect.max=.10)
# compromise power analyses using rmsea = .08 and an abratio of 2
cp <- semPower.compromise(.08, 'RMSEA', abratio = 2, N = 1000, df = 200)
summary(cp)

# use lavaan to define effect through covariance matrices:
# }
# NOT RUN {
library(lavaan)

# define population model (= H0)
model.pop <- '
f1 =~ .8*x1 + .7*x2 + .6*x3
f2 =~ .7*x4 + .6*x5 + .5*x6
f1 ~~ 1*f1
f2 ~~ 1*f2
f1 ~~ 0.5*f2
'
# define (wrong) H1 model
model.h1 <- '
f1 =~ x1 + x2 + x3
f2 =~ x4 + x5 + x6
f1 ~~ 0*f2
'

# get population covariance matrix; equivalent to a perfectly fitting H0 model
cov.h0 <- fitted(sem(model.pop))$cov
# get covariance matrix as implied by H1 model
res.h1 <- sem(model.h1, sample.cov = cov.h0, sample.nobs = 1000, likelihood='wishart')
df <- res.h1@test[[1]]$df
cov.h1 <- fitted(res.h1)$cov

## do power analyses

# post-hoc
ph <- semPower.postHoc(SigmaHat = cov.h1, Sigma = cov.h0, alpha = .05, N = 1000, df = df)
summary(ph)
# => Power to reject the H1 model is > .9999 (1-beta = 1-1.347826e-08) with N = 1000 at alpha=.05

# compare:
ph$fmin * (ph$N-1)
fitmeasures(res.h1, 'chisq')
# => expected chi-square matches empirical chi-square

# a-priori
ap <- semPower.aPriori(SigmaHat = cov.h1, Sigma = cov.h0, alpha = .05, power = .80, df = df)
summary(ap)
# => N = 194 gives a power of ~80% to reject the H1 model at alpha = .05

# compromise
cp <- semPower.compromise(SigmaHat = cov.h1, Sigma = cov.h0, abratio = 1, N = 1000, df = df)
summary(cp)
# => A critical Chi-Squared of 33.999 gives balanced alpha-beta
#    error probabilities of alpha=beta=0.000089 with N = 1000.

# }
# NOT RUN {
# }