Conduct a priori Monte Carlo simulation to empirically study the effects of (mis)specifications of input information on the calculated sample size. The sample size is planned so that the expected width of a confidence interval for the population RMSEA is no larger than desired. Random data are generated from the true covariance matrix but fit to the proposed model, whereas sample size is calculated based on the input covariance matrix and proposed model.
ss.aipe.rmsea.sensitivity(width, model, Sigma, N=NULL,
conf.level=0.95, G=200, save.file="sim.results.txt", ...)the number of successful replications
the G random confidence interval widths
the G estimated RMSEA values based on the G random samples
the sample size calculated
degrees of freedom of the proposed model
the input RMSEA value that is used to calculated the necessary sample size
desired confidence interval width
mean of the random confidence interval widths
median of the random confidence interval widths
the proportion of confidence interval widths narrower than desired
99, 97, 95, 90, 80, 70, and 60 percentiles of the random confidence interval widths
the upper empirical Type I error rate
the lower empirical Type I error rate
total empirical Type I error rate
confidence level
a text file that saves the simulation results; it updates after each replication. 'sim.results.txt' is the default file name
desired confidence interval width for the model parameter of interest
the model the researcher proposes, may or may not be the true model. This argument should be an RAM (reticular action model; e.g., McArdle & McDonald, 1984) specification of a structural equation model, and should be of class mod. The model is specified in the same manner as does the sem package; see sem and specify.model for detailed documentation about model specifications in the RAM notation.
the true population covariance matrix, which will be used to generate random data for the simulation study. The row names and column names of Sigma should be the same as the manifest variables in model.
if N is specified, random sample of the specified N size will be generated. Otherwise the sample size is calculated with the sample size planning method with the goal that the expected width of a confidence interval for population RMSEA is no larger than desired.
confidence level (i.e., 1- Type I error rate)
number of replications in the Monte Carlo simulation
the name of the file that simulation results will be saved to
allows one to potentially include parameter values for inner functions
Keke Lai (University of California -- Merced) and Ken Kelley (University of Notre Dame; KKelley@ND.Edu)
This function implements the sample size planning methods proposed in Kelley and Lai (2010). It depends on the
function sem in the sem package to fit the proposed model to random data, and uses the same notation to specify SEM
models as does sem. Please refer to sem for more detailed documentation
about model specifications, the RAM notation, and model fitting techniques. For technical discussion
on how to obtain the model implied covariance matrix in the RAM notation given model parameters, see McArdle and McDonald (1984)
Cudeck, R., & Browne, M. W. (1992). Constructing a covariance matrix that yields a specified minimizer and a specified minimum discrepancy function value. Psychometrika, 57, 357--369.
Fox, J. (2006). Structural equation modeling with the sem package in R. Structural Equation Modeling, 13, 465--486.
Kelley, K., & Lai, K. (2010). Accuracy in parameter estimation for the root mean square of approximation: Sample size planning for narrow confidence intervals. Manuscript under review.
McArdle, J. J., & McDonald, R. P. (1984). Some algebraic properties of the reticular action model. British Journal of Mathematical and Statistical Psychology, 37, 234--251.
sem; specify.model; ss.aipe.rmsea; theta.2.Sigma.theta; Sigma.2.SigmaStar