alfa: Alpha Factor Analysis

In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description

Alpha factor analysis (AFA) is a method proposed by Kaiser and Caffrey (1965) which is motivated by considering as a source of error that only a portion of possibly relevant variables have been collected and submitted to the analysis. As such the objective function is minimizing the L1 norm of communalities, rather than the L2 norm of uniquenesses. Furthermore, the eigenvalues of the latent variables are taken as measures of the generalizability of the latent variables.

Usage

alfa(
  Y,
  nfac = min(nrow(Y) - 3, ncol(Y) - 2),
  rotate = Varimax,
  scale = T,
  screen = F,
  corr = c("pearson", "robust", "spearman"),
  max.iter = 4000,
  tol = 1e-24
)

Arguments

Y	a numeric matrix or data frame of only numeric variables.
nfac	the number of factors to attempt to extract.
rotate	a rotation function from the GPArotation package. Defaults to Varimax.
scale	should the variables be scaled prior to analysis? Defaults to TRUE.
screen	Kaiser and Caffrey suggested that only latent variables with eigenvalues greater than 1 are retained. If TRUE, if the initial fit with the user-chosen number of factors fails to satisfy the criterion the model is iteratively refit with a smaller number of factors until all factor eigenvalues are greater than 1. However, such criteria have fallen out of favor thus the default is FALSE.
corr	one of "pearson", "robust", or "spearman".
max.iter	maximum number of iterations. defaults to 4000.
tol	a tolerance value for convergence. defaults to 1e-9.

References

Kaiser, H. F., & Caffrey, J. (1965). Alpha factor analysis. Psychometrika, 30(1), 1–14. doi:10.1007/bf02289743

Kaiser, H. F., & Derflinger, G. (1990). Some Contrasts Between Maximum Likelihood Factor Analysis and Alpha Factor Analysis. Applied Psychological Measurement, 14(1), 29–32. doi:10.1177/014662169001400103

abnormally-distributed/cvreg documentation built on May 3, 2020, 3:45 p.m.