Multi-Battery Factor Analysis in R

Description

Inter-battery factor analysis (IBFA) is a multivariate technique for evaluating the stability of common factors across two test batteries that have been administered to the same individuals. Tucker (1958) introduced the model in the late 1950s and derived the least squares solution for estimating model parameters. Two decades later, Browne (1979) extended Tucker’s work by (a) deriving the maximum-likelihood (ML) model estimates and (b) enabling the model to accommodate two or more test batteries (Browne, 1980). Browne’s extended model is called multiple-battery factor analysis (MBFA). Influenced by Browne’s ideas, Cudeck (1980) produced a FORTRAN program for MBFA (Cudeck, 1982) and a readable account of the method’s underlying logic. For many years, this program was the primary vehicle for conducting MBFA in a Window’s environment (Brown, 2007; Finch & West, 1997; Finch et al., 1999, Waller et al., 1991). Unfortunately, until now, open-source software for conducting IBFA and MBFA on Windows, Mac OS, Linux, and Unix operating systems was not available.

To introduce the ideas of Tucker (1958) and Browne (1979, 1980) to the broader research community, two open-source programs were developed in R (R Core Team, 2021) for obtaining ML estimates for the inter-battery and MBFA models. The programs are called faIB and faMB. Both programs are included in the R fungible (Waller, 2021) library and can be freely downloaded from the Comprehensive R Archive Network (CRAN; https://cran.r-project.org/package=fungible).

faIB and faMB include a number of features that make them attractive choices for extracting common factors from two or more batteries. For instance, both programs include a wide range of rotation options by building upon functionality from the GPArotation package (Bernaards & Jennrich, 2005). This package provides routines for rotating factors by oblimin, geomin (orthogonal and oblique), infomax, simplimax, varimax, promax, and many other rotation algorithms. Both programs also allow users to initiate factor rotations from random starting configurations to facilitate the location of global and local solutions (for a discussion of why feature this is important, see Rozeboom, 1992). Prior to rotation, factors can be preconditioned (i.e., row standardized) by methods described by Kaiser (1958) or Cureton and Mulaik (1975). After rotation, factor loadings can be sorted within batteries to elucidate the structure of the battery-specific tests. faMB also includes a summary function to help locate global and local solutions for rotated factors.

faIB and faMB include numerous options for evaluating model fit at both the global and local levels. For instance, at the global level, both programs report the likelihood-based ${\chi }^2$ (and associated degrees of freedom and p-value), the Akaike Information Criterion (AIC; Akaike et al., 1973), the Bayesian Information Criterion (Schwarz, 1978), the Root Mean Squared Error of Approximation (Steiger & Lind, 1980), and factor indeterminacy values (Guttman, 1955). For local model evaluation, both programs can compute non-parametric bootstrap standard errors and confidence intervals (at user-defined levels) for all model parameters. Finally, to help researchers implement these and other options included in faIB and faMB, the associated R programs include extensive help files that include fully worked examples from the IBFA and MBFA literatures (e.g., Browne, 1979; 1980; Cudeck, 1982).

ORCID iD

Niels Waller https://orcid.org/0000-0003-1877-7232