studySim {nFactors}

Simulation Study from Given Factor Structure Matrices and Conditions

Description

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).

Usage

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

Value

values

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

Author(s)

Gilles Raiche
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
[e-mail]

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

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)