### Abstract

This article describes the REREFACT R package, which provides a postrotation algorithm that reorders or reflects factors for each replication of a simulation study with exploratory factor analysis (EFA). The purpose of REREFACT is to provide a general algorithm written in freely available software, R, dedicated to addressing the possibility that a nonuniform order or sign pattern of the factors could be observed across replications. The algorithm implemented in REREFACT proceeds in 4 steps. Step 1 determines the total number of equivalent forms, I, of the vector of factors, η. Step 2 indexes, i = 1, 2 … I, each equivalent form of η (i.e., η^{i}) via a unique permutation matrix, P (i.e., P^{i}). Step 3 determines which η^{i} each replication follows. Step 4 uses the appropriate P^{i} to reorder or re-sign parameter estimates within each replication so that all replications uniformly follow the order and sign pattern defined by the population values. Results from two simulation studies provided evidence for the efficacy of the REREFACT to identify and remediate equivalent forms of η in models with EFA only (i.e., Example 1) and in fuller parameterizations of exploratory structural equation modeling (i.e., Example 2). How to use REREFACT is briefly demonstrated prior to the Discussion section by providing annotations for key commands and condensed output using a subset of simulated data from Example 1.

Original language | English (US) |
---|---|

Pages (from-to) | 1-17 |

Number of pages | 17 |

Journal | Structural Equation Modeling |

DOIs | |

State | Accepted/In press - Sep 26 2016 |

### Fingerprint

### Keywords

- exploratory structural equation modeling
- factor order
- Monte Carlo
- negative factor
- permutation matrices
- simulation

### ASJC Scopus subject areas

- Decision Sciences(all)
- Modeling and Simulation
- Sociology and Political Science
- Economics, Econometrics and Finance(all)

### Cite this

*Structural Equation Modeling*, 1-17. https://doi.org/10.1080/10705511.2016.1230721

**Reordering and Reflecting Factors for Simulation Studies With Exploratory Factor Analysis.** / Myers, Nicholas; Ahn, Soyeon; Lu, Min; Celimli, Seniz; Zopluoglu, Cengiz.

Research output: Contribution to journal › Article

*Structural Equation Modeling*, pp. 1-17. https://doi.org/10.1080/10705511.2016.1230721

}

TY - JOUR

T1 - Reordering and Reflecting Factors for Simulation Studies With Exploratory Factor Analysis

AU - Myers, Nicholas

AU - Ahn, Soyeon

AU - Lu, Min

AU - Celimli, Seniz

AU - Zopluoglu, Cengiz

PY - 2016/9/26

Y1 - 2016/9/26

N2 - This article describes the REREFACT R package, which provides a postrotation algorithm that reorders or reflects factors for each replication of a simulation study with exploratory factor analysis (EFA). The purpose of REREFACT is to provide a general algorithm written in freely available software, R, dedicated to addressing the possibility that a nonuniform order or sign pattern of the factors could be observed across replications. The algorithm implemented in REREFACT proceeds in 4 steps. Step 1 determines the total number of equivalent forms, I, of the vector of factors, η. Step 2 indexes, i = 1, 2 … I, each equivalent form of η (i.e., ηi) via a unique permutation matrix, P (i.e., Pi). Step 3 determines which ηi each replication follows. Step 4 uses the appropriate Pi to reorder or re-sign parameter estimates within each replication so that all replications uniformly follow the order and sign pattern defined by the population values. Results from two simulation studies provided evidence for the efficacy of the REREFACT to identify and remediate equivalent forms of η in models with EFA only (i.e., Example 1) and in fuller parameterizations of exploratory structural equation modeling (i.e., Example 2). How to use REREFACT is briefly demonstrated prior to the Discussion section by providing annotations for key commands and condensed output using a subset of simulated data from Example 1.

AB - This article describes the REREFACT R package, which provides a postrotation algorithm that reorders or reflects factors for each replication of a simulation study with exploratory factor analysis (EFA). The purpose of REREFACT is to provide a general algorithm written in freely available software, R, dedicated to addressing the possibility that a nonuniform order or sign pattern of the factors could be observed across replications. The algorithm implemented in REREFACT proceeds in 4 steps. Step 1 determines the total number of equivalent forms, I, of the vector of factors, η. Step 2 indexes, i = 1, 2 … I, each equivalent form of η (i.e., ηi) via a unique permutation matrix, P (i.e., Pi). Step 3 determines which ηi each replication follows. Step 4 uses the appropriate Pi to reorder or re-sign parameter estimates within each replication so that all replications uniformly follow the order and sign pattern defined by the population values. Results from two simulation studies provided evidence for the efficacy of the REREFACT to identify and remediate equivalent forms of η in models with EFA only (i.e., Example 1) and in fuller parameterizations of exploratory structural equation modeling (i.e., Example 2). How to use REREFACT is briefly demonstrated prior to the Discussion section by providing annotations for key commands and condensed output using a subset of simulated data from Example 1.

KW - exploratory structural equation modeling

KW - factor order

KW - Monte Carlo

KW - negative factor

KW - permutation matrices

KW - simulation

UR - http://www.scopus.com/inward/record.url?scp=84991208119&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84991208119&partnerID=8YFLogxK

U2 - 10.1080/10705511.2016.1230721

DO - 10.1080/10705511.2016.1230721

M3 - Article

AN - SCOPUS:84991208119

SP - 1

EP - 17

JO - Structural Equation Modeling

JF - Structural Equation Modeling

SN - 1070-5511

ER -