simulate: simulate

In semPower: Power Analyses for SEM

simulate

Description

Estimates empirical power using a simulation approach.

Usage

simulate(
  modelH0 = NULL,
  modelH1 = NULL,
  Sigma = NULL,
  mu = NULL,
  N = NULL,
  alpha = NULL,
  simOptions = list(nReplications = 500, minConvergenceRate = 0.75, type = "normal",
    missingVars = NULL, missingVarProp = 0, missingProp = 0, missingMechanism = "MCAR",
    nCores = 1),
  lavOptions = NULL,
  lavOptionsH1 = lavOptions,
  returnFmin = TRUE
)

Arguments

modelH0	lavaan model string defining the (incorrect) analysis model.
modelH1	lavaan model string defining the comparison model. If omitted, the saturated model is the comparison model.
Sigma	population covariance matrix.
mu	population means.
N	sample size
alpha	alpha error probability
simOptions	a list of additional options specifying simulation details, see details.
lavOptions	a list of additional options passed to lavaan, e. g., list(estimator = 'mlm') to request robust ML estimation
lavOptionsH1	lavoptions when fitting modelH1. If NULL, the same as lavOptions.
returnFmin	whether to return the mean unbiased Fmin over replications (i. e., fmin_0 = fmin_hat - df/N)

Details

The details of the simulation are specified in simOptions, which is a list that may have the following components:

• nReplications: The targeted number of valid simulation runs, defaults to 500.

• minConvergenceRate: The minimum convergence rate required, defaults to .75. The maximum actual simulation runs are increased by a factor of 1/minConvergenceRate.

• type: specifies whether the data should be generated from a population assuming multivariate normality ('normal'; the default), or based on an approach generating non-normal data ('IG', 'mnonr', 'RK', or 'VM'). The approaches generating non-normal data require additional arguments detailed below.

• missingVars: vector specifying the variables containing missing data (defaults to NULL).

• missingVarProp: can be used instead of missingVars: The proportion of variables containing missing data (defaults to zero).

• missingProp: The proportion of missingness for variables containing missing data (defaults to zero), either a single value or a vector giving the probabilities for each variable.

• missingMechanism: The missing data mechanism, one of 'MCAR' (the default), 'MAR', or 'NMAR'.

• nCores: The number of cores to use for parallel processing. Defaults to 1 (= no parallel processing). This requires the doFuture package.

type = 'IG' implements the independent generator approach (IG, Foldnes & Olsson, 2016) approach specifying third and fourth moments of the marginals, and thus requires that skewness (skewness) and excess kurtosis (kurtosis) for each variable are provided as vectors. This requires the covsim package.

type = 'mnonr' implements the approach suggested by Qu, Liu, & Zhang (2020) and requires provision of Mardia's multivariate skewness (skewness) and kurtosis (kurtosis), where skewness must be non-negative and kurtosis must be at least 1.641 skewness + p (p + 0.774), where p is the number of variables. This requires the mnonr package.

type = 'RK' implements the approach suggested by Ruscio & Kaczetow (2008) and requires provision of the population distributions of each variable (distributions). distributions must be a list (if all variables shall be based on the same population distribution) or a list of lists. Each component must specify the population distribution (e.g. rchisq) and additional arguments (list(df = 2)).

type = 'VM' implements the third-order polynomial method (Vale & Maurelli, 1983) specifying third and fourth moments of the marginals, and thus requires that skewness (skewness) and excess kurtosis (kurtosis) for each variable are provided as vectors.

Foldnes, N. & Olsson, U. H. (2016) A Simple Simulation Technique for Nonnormal Data with Prespecified Skewness, Kurtosis, and Covariance Matrix. Multivariate Behavioral Research, 51, 207-219. doi: 10.1080/00273171.2015.1133274

Qu, W., Liu, H., & Zhang, Z. (2020). A method of generating multivariate non-normal random numbers with desired multivariate skewness and kurtosis. Behavior Research Methods, 52, 939-946. doi: 10.3758/s13428-019-01291-5

Ruscio, J., & Kaczetow, W. (2008). Simulating multivariate nonnormal data using an iterative algorithm. Multivariate Behavioral Research, 43, 355-381. doi: 10.1080/00273170802285693

Vale, C. & Maurelli, V. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48, 465-471.

Value

Returns empirical power: sum(p < alpha) / nReplications or a list (if returnFmin = TRUE) with the following components:

ePower	the empirical power.
meanFmin	the estimated mean unbiased Fmin over replications (i. e., fmin_0 = fmin_hat - df/N).
meanFminGroups	the estimated mean unbiased Fmin by groups given as a vector, assuming the df spread equally over groups. Therefore, meanFmin != sum(meanFminGroups)
df	the model df.
nrep	the number of successful replications.
convergenceRate	the convergence rate of the H0 model.
bChiSq	median chi-square bias of the H1 model
bLambda	average median bias in lambda in the H1 model
bPhi	average median bias in phi in the H1 model
bPsi	average median bias in psi in the H1 model
bBeta	average median bias in beta in the H1 model

Examples

## Not run: 
# create Sigma and modelH0 using powerCFA
powerCFA <- semPower.powerCFA(type = 'a-priori', alpha = .05, beta = .05,
                              comparison = 'saturated',
                              Phi = .2, loadings = list(rep(.5, 3), rep(.7, 3)))
                              
# perform simulated power analysis using defaults       
simulate(modelH0 = powerCFA$modelH0, 
         Sigma = powerCFA$Sigma,
         N = powerCFA$requiredN,
         alpha = .05,
         simulatedPower = TRUE)
         

# same with additional options       
simulate(modelH0 = powerCFA$modelH0, 
         Sigma = powerCFA$Sigma,
         N = powerCFA$requiredN,
         alpha = .05,
         simulatedPower = TRUE, 
         simOptions = list(nReplications = 500, 
                           minConvergenceRate = .80, 
                           nCores = 8))


# same with IG as data generation routine
simulate(modelH0 = powerCFA$modelH0, 
         Sigma = powerCFA$Sigma,
         N = powerCFA$requiredN,
         alpha = .05,
         simulatedPower = TRUE, 
         simOptions = list(type = 'IG', 
                           skewness = c(0, 1, -2, 6, 5, 4), 
                           kurtosis = c(-3, 6, 9, 0, 2, -2)))
                           
                           
# same with mnonr as data generation routine
simulate(modelH0 = powerCFA$modelH0, 
         Sigma = powerCFA$Sigma,
         N = powerCFA$requiredN,
         alpha = .05,
         simulatedPower = TRUE, 
         simOptions = list(type = 'mnonr', 
                           skewness = 1, 
                           kurtosis = 50))
                           
                           
# same with RK as data generation routine
distributions <- list(
  list('rnorm', list(mean = 0, sd = 10)),
  list('runif', list(min = 0, max = 1)),
  list('rbeta', list(shape1 = 1, shape2 = 2)),
  list('rexp', list(rate = 1)),
  list('rpois', list(lambda = 4)),
  list('rbinom', list(size = 1, prob = .5))
)
simulate(modelH0 = powerCFA$modelH0, 
         Sigma = powerCFA$Sigma,
         N = powerCFA$requiredN,
         alpha = .05,
         simulatedPower = TRUE, 
         simOptions = list(type = 'RK', 
                           distributions = distributions))

## End(Not run)

semPower documentation built on Sept. 30, 2024, 9:24 a.m.