SSpower {semTools}

Power for model parameters

Description

Apply Satorra & Saris (1985) method for chi-squared power analysis.

Usage

SSpower(powerModel, n, nparam, popModel, mu, Sigma, fun = "sem",
  alpha = 0.05, ...)

Arguments

powerModel

lavaan model.syntax for the model to be analyzed. This syntax should constrain at least one nonzero parameter to 0 (or another number).

n

integer. Sample size used in power calculation, or a vector of sample sizes if analyzing a multigroup model. If length(n) < length(Sigma) when Sigma is a list, n will be recycled. If popModel is used instead of Sigma, n must specify a sample size for each group, because that is used to infer the number of groups.

nparam

integer. Number of invalid constraints in powerModel.

popModel

lavaan model.syntax specifying the data-generating model. This syntax should specify values for all nonzero parameters in the model. If length(n) > 1, the same population values will be used for each group, unless different population values are specified per group, either in the lavaan model.syntax or by utilizing a list of Sigma (and optionally mu).

mu

numeric or list. For a single-group model, a vector of population means. For a multigroup model, a list of vectors (one per group). If mu and popModel are missing, mean structure will be excluded from the analysis.

Sigma

matrix or list. For a single-group model, a population covariance matrix. For a multigroup model, a list of matrices (one per group). If missing, popModel will be used to generate a model-implied Sigma.

fun

character. Name of lavaan function used to fit powerModel (i.e., "cfa", "sem", "growth", or "lavaan").

alpha

Type I error rate used to set a criterion for rejecting H0.

...

additional arguments to pass to lavaan. See also lavOptions.

Details

Specify all non-zero parameters in a population model, either by using lavaan syntax (popModel) or by submitting a population covariance matrix (Sigma) and optional mean vector (mu) implied by the population model. Then specify an analysis model that places at least one invalid constraint (note the number in the nparam argument).

There is also a Shiny app called "power4SEM" that provides a graphical user interface for this functionality (Jak et al., in press). It can be accessed at https://sjak.shinyapps.io/power4SEM/.

Author(s)

Alexander M. Schoemann (East Carolina University; [e-mail])

Terrence D. Jorgensen (University of Amsterdam; [e-mail])

References

Satorra, A., & Saris, W. E. (1985). Power of the likelihood ratio test in covariance structure analysis. Psychometrika, 50(1), 83–90. doi:10.1007/BF02294150

Jak, S., Jorgensen, T. D., Verdam, M. G., Oort, F. J., & Elffers, L. (2021). Analytical power calculations for structural equation modeling: A tutorial and Shiny app. Behavior Research Methods, 53, 1385–1406. doi:10.3758/s13428-020-01479-0

Examples

## Specify population values. Note every parameter has a fixed value.
modelP <- '
  f1 =~ .7*V1 + .7*V2 + .7*V3 + .7*V4
  f2 =~ .7*V5 + .7*V6 + .7*V7 + .7*V8
  f1 ~~ .3*f2
  f1 ~~ 1*f1
  f2 ~~ 1*f2
  V1 ~~ .51*V1
  V2 ~~ .51*V2
  V3 ~~ .51*V3
  V4 ~~ .51*V4
  V5 ~~ .51*V5
  V6 ~~ .51*V6
  V7 ~~ .51*V7
  V8 ~~ .51*V8
'
## Specify analysis model. Note parameter of interest f1~~f2 is fixed to 0.
modelA <- '
  f1 =~ V1 + V2 + V3 + V4
  f2 =~ V5 + V6 + V7 + V8
  f1 ~~ 0*f2
'
## Calculate power
SSpower(powerModel = modelA, popModel = modelP, n = 150, nparam = 1,
        std.lv = TRUE)

## Get power for a range of sample sizes
Ns <- seq(100, 500, 40)
Power <- rep(NA, length(Ns))
for(i in 1:length(Ns)) {
  Power[i] <- SSpower(powerModel = modelA, popModel = modelP,
                      n = Ns[i], nparam = 1, std.lv = TRUE)
}
plot(x = Ns, y = Power, type = "l", xlab = "Sample Size")


## Optionally specify different values for multiple populations

modelP2 <- '
  f1 =~ .7*V1 + .7*V2 + .7*V3 + .7*V4
  f2 =~ .7*V5 + .7*V6 + .7*V7 + .7*V8
  f1 ~~ c(-.3, .3)*f2                  # DIFFERENT ACROSS GROUPS
  f1 ~~ 1*f1
  f2 ~~ 1*f2
  V1 ~~ .51*V1
  V2 ~~ .51*V2
  V3 ~~ .51*V3
  V4 ~~ .51*V4
  V5 ~~ .51*V5
  V6 ~~ .51*V6
  V7 ~~ .51*V7
  V8 ~~ .51*V8
'
modelA2 <- '
  f1 =~ V1 + V2 + V3 + V4
  f2 =~ V5 + V6 + V7 + V8
  f1 ~~ c(psi21, psi21)*f2        # EQUALITY CONSTRAINT ACROSS GROUPS
'
## Calculate power
SSpower(powerModel = modelA2, popModel = modelP2, n = c(100, 100), nparam = 1,
        std.lv = TRUE)
## Get power for a range of sample sizes
Ns2 <- cbind(Group1 = seq(10, 100, 10), Group2 = seq(10, 100, 10))
Power2 <- apply(Ns2, MARGIN = 1, FUN = function(nn) {
  SSpower(powerModel = modelA2, popModel = modelP2, n = nn,
          nparam = 1, std.lv = TRUE)
})
plot(x = rowSums(Ns2), y = Power2, type = "l", xlab = "Total Sample Size",
     ylim = 0:1)
abline(h = c(.8, .9), lty = c("dotted","dashed"))
legend("bottomright", c("80% Power","90% Power"), lty = c("dotted","dashed"))