00FAiR-package: Factor Analysis in R
In FAiR: Factor Analysis in R

Description Details Author(s) Examples

This package estimates exploratory, confirmatory, and semi-exploratory factor analysis models via a genetic algorithm, namely genoud. This use of a genetic algorithm is tantamount to restricted optimization with virtually unlimited possibilities for restrictions. In particular, semi-exploratory factor analysis, which is new to the literature, minimizes a discrepancy function subject to a restriction on the number of exact zeros in each column of the primary pattern matrix but does not require that the locations of the zeros be specified in advance (as in confirmatory factor analysis). FAiR encourages the use of inequality restrictions on functions of multiple parameters to characterize testable hypotheses.

Package:	FAiR
Type:	Package
URL:	http://wiki.r-project.org/rwiki/doku.php?id=packages:cran:fair
Version:	0.4-7
Date:	2010-02-24
License:	AGPL (>= 3.0) but see the LICENSE file for details

Let the factor analysis model in the population be

Sigma = Omega(beta Phi beta' + Theta)Omega

where Sigma is the covariance matrix among outcome variables, Omega is a diagonal matrix of standard deviations of the manifest variables, beta is the primary pattern matrix (calibrated to standardized variables) with one column per factor, Phi is the correlation matrix among the primary factors, and Theta is the diagonal matrix of uniquenesses, which is fully determined by beta, Phi, and the requirement that the matrix within parentheses has ones down its diagonal. Hence, beta Phi beta' + Theta is the model's purported correlation matrix among outcome variables as a function of the factors.

Each of the matrices on the right-hand side is a parameter to be estimated, and unlike many structural equation modeling programs, there is no mechanism for “translating” the model from a path diagram or otherwise avoiding the matrix algebra representation of the model. On a technical programming note, each of these matrices is represented by a parameter-class in FAiR, which includes a slot for the (proposed) estimate but also includes slots for ancillary information.

The usual steps to estimate and interpret a factor analysis model are as follows:

0. Get your data into R somehow. It is best to load the raw data in one of the usual fashions (e.g. read.table, read.spss, etc.) and the read.cefa function can also be used if your data are saved in the format used by CEFA 2.0. If you only have a covariance matrix, then read.triangular can be used to load it into R.

1. Call make_manifest to construct the left-hand side of the factor analysis model, namely an S4 object to house the sample estimate of Sigma and some other information (e.g. number of observations).

2. Call make_restrictions to establish the additional restrictions to be imposed on the right-hand side of factor analysis model, inclusive of whether the model is exploratory, semi-exploratory, or confirmatory and what discrepancy function to use. There is an extensive GUI that pops up when make_restrictions is called to guide you through this step. FAiR differs fundamentally from other factor analysis software in that it permits you to impose inequality restrictions on functions of beta and Phi. Hence, the restrictions-class is critical to the way FAiR is programmed internally and houses S4 objects representing each of the matrices to be estimated.

3. Call Factanal to estimate the model and thereby produce estimates of Omega, beta, Phi, and Theta.

4. (exploratory factor analysis only) Call Rotate to choose a transformation matrix (T) for the factors. There is an extensive GUI that pops up when Rotate is called to guide you through this step. Again, Rotate differs fundamentally from other approaches to factor rotation in that it permits you to impose inequality restrictions on functions of parameters when searching for T.

5. Call the usual post-estimation methods to interpret the estimates, like summary, pairs,FA-method, etc., and call model_comparison to see the test statistics and fit indices.

The vignette has additional information regarding the pop-up menus produced in step 2 by
make_restrictions and in step 4 by Rotate; execute vignette("FAiR") to read it. The primary examples are in Factanal and Rotate.

Ben Goodrich