REREFACT (version 1.0)

rerefact: Identifies an appropriate permutation matrix for each replication

Description

The rerefact function accomplishes Step 1 thru Step 3 of the algorithm and creates the P that is used in the correct_alpha, correct_beta, correct_gamma, correct_lambda and correct_psi functions to accomplish Step 4 of the algorithm.

Usage

rerefact(n.factor, n.eta, n.var, pop_lambda, sample_lambda)

Arguments

n.factor

the number of latent variables within eta that may be affected by indeterminacies within eta.

n.eta

the total number of latent variables within eta.

n.var

the number of observed endogenous variables with regard to n.factor.

pop_lambda

the population pattern coefficient matrix.

sample_lambda

a list containing replications of the estimated pattern coefficient matrix.

Value

n.perm

the total number of equivalent forms of eta that can result from indeterminacies within eta (i.e., I) and provides the result for Step 1 of the algorithm.

permutation

a matrix that indexes within I via a unique, orthogonal permutation matrix for each equivalent form of eta and provides the result for Step 2 of the algorithm.

correct.permutation

a matrix that provides the specific equivalent form of eta (within the set indexed in Step 2) that each replication follows and provides the result for Step 3 of the algorithm.

replication.permutation

a table that provides the specific equivalent form of eta (within the set indexed in Step 2) that each replication follows.

summary.permutation

a table that provides a count of the number of replications observed within each specific equivalent form of eta (within the set indexed in Step 2).

Details

The rerefact function accomplishes Step 1 thru Step 3 of the algorithm. Step 1 determines the total number of equivalent forms of eta that can result from indeterminacies within eta (i.e., I) and provides the result with the n.perm value. Step 2 indexes, i=1,2,..., I, each equivalent form of eta (i.e.,eta_i) via a unique permutation matrix, P (i.e., P_i) and provides the result with the permutation value. Step 3 determines which eta_i each replication follows and provides the result with the correct.permutation value. At the conclusion of Step 3 P is automatically returned and saved as a text file to the designated working directory.

References

Myers, N. D., Ahn, S., Lu, M., Celimli, S., Zopluoglu, C. (2016). REREFACT: An R package for reordering and reflecting factors for simulation studies with Exploratory Factor Analysis. Manuscript submitted for publication.

See Also

correct_alpha, correct_beta, correct_lambda, correct_psi, correct_gamma

Examples

# Dependent packages

require(Matrix)
require(psych)
require(gdata)
require(combinat)

# Load the population pattern coefficient matrix for Example 1 from 
# Myers, Ahn, Lu, Celimli, and Zopluoglu (2016).

data(pop_L_efa)

# Load 200 replications of the estimated pattern coefficient matrix provided by 
# replication numbers 1 through 100 and 4701 through 4800
# in Example 1 from Myers, Ahn, Lu, Celimli, and Zopluoglu (2016). 

data(sample_lambda_efa)

# Specify the following arguments within the rerefact function for Example 1 from 
# Myers, Ahn, Lu, Celimli, and Zopluoglu (2016).

rerefact(n.factor=3, n.eta=3, n.var=10, pop_lambda=pop_L_efa, sample_lambda=sample_lambda_efa)

# Load the population pattern coefficient matrix for Example 2 from 
# Myers, Ahn, Lu, Celimli, and Zopluoglu (2016).

data(pop_L_esem)

# Load 200 replications of the estimated pattern coefficient matrix provided by 
# replication numbers 1 through 100 and 4701 through 4800
# in Example 2 from Myers, Ahn, Lu, Celimli, and Zopluoglu (2016).

data(sample_lambda_esem)

rerefact(n.factor=3, n.eta=4, n.var=10, pop_lambda=pop_L_esem, sample_lambda=sample_lambda_esem)