Reordering and Reflecting Factors for Simulation Studies With Exploratory Factor Analysis

Nicholas D. Myers, Soyeon Ahn, Min Lu, Seniz Celimli, Cengiz Zopluoglu

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)112-128
Number of pages17
JournalStructural Equation Modeling
Issue number1
StatePublished - Jan 2 2017


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

ASJC Scopus subject areas

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


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