studySim function

Simulation Study from Given Factor Structure Matrices and Conditions

The structureSim function returns statistical results from simulations from predefined congeneric factor structures. The main ideas come from the methodology applied by Zwick and Velicer (1986).

studySim(var, nFactors, pmjc, loadings, unique, N, repsim, reppar,
  stats = 1, quantile = 0.5, model = "components", r2limen = 0.75,
  all = FALSE, dir = NA, trace = TRUE)

Arguments

• var: numeric: vector of the number of variables
• nFactors: numeric: vector of the number of components/factors
• pmjc: numeric: vector of the number of major loadings on each component/factor
• loadings: numeric: vector of the major loadings on each component/factor
• unique: numeric: vector of the unique loadings on each component/factor
• N: numeric: vector of the number of subjects/observations
• repsim: numeric: number of replications of the matrix correlation simulation
• reppar: numeric: number of replications for the parallel and permutation analysis
• stats: numeric: vector of the statistics to return: mean(1), median(2), sd(3), quantile(4), min(5), max(6)
• quantile: numeric: quantile for the parallel and permutation analysis
• model: character: "components" or "factors"
• r2limen: numeric: R2 limen value for the R2 Nelson index
• all: logical: if TRUE computes the Bentler and Yuan index (very long computing time to consider)
• dir: character: directory where to save output. Default to NA
• trace: logical: if TRUE outputs details of the status of the simulations

Returns

• values: Returns selected statistics about the number of components/factors to retain: mean, median, quantile, standard deviation, minimum and maximum.

Examples

## Not run:

# ....................................................................
# Example inspired from Zwick and Velicer (1986)
# Very long computimg time
# ...................................................................

# 1. Initialisation
# reppar    <- 30
# repsim    <- 5
# quantile  <- 0.50

# 2. Simulations
# X         <- studySim(var=36,nFactors=3, pmjc=c(6,12), loadings=c(0.5,0.8),
#                       unique=c(0,0.2), quantile=quantile,
#                       N=c(72,180), repsim=repsim, reppar=reppar,
#                       stats=c(1:6))

# 3. Results (first 10 results)
# print(X[1:10,1:14],2)
# names(X)

# 4. Study of the error done in the determination of the number
#    of components/factors. A positive value is associated to over
#    determination.
# results   <- X[X$stats=="mean",]
# residuals <- results[,c(11:25)] - X$nfactors
# BY        <- c("nsubjects","var","loadings")
# round(aggregate(residuals, by=results[BY], mean),0)
## End(Not run)

References

Raiche, G., Walls, T. A., Magis, D., Riopel, M. and Blais, J.-G. (2013). Non-graphical solutions for Cattell's scree test. Methodology, 9(1), 23-29.

Zwick, W. R. and Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432-442.

See Also

generateStructure, structureSim

Author(s)

Gilles Raiche

Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)

Universite du Quebec a Montreal

raiche.gilles@uqam.ca