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

This is similar to the factor model fitting method in the facanal function, but the variant of the EM algorithm by Rubin & Thayer (1982) is implemented instead of the Bai & Li (2012) EM algorithm uesd in facanal. This is due to more easily accomodating a change in objective function; here the median absolute deviation of the errors is used as the criteria to be minimized.

The algorithm is also initialized with an eigendecomposition of a robust correlation/covariance matrix. The minimum regularized covariance determinant (cov.mrcd) will be used in the case of n < p. Otherwise, if p <= 10 the smoothed-hard-rejection estimator (cov.shr) will be used, and if p > 10 Rocke's S-estimator will be used.

In the case of Likert scale type data, univariate outliers in the sense of a data point far from its mean are rarely an issue save for data entry errors. This is due to the fact that likert scales take on values from a small set of integers. However, if the data being analyzed are continuous measurements without hard bounds on the possible values the robust estimator will assist in ensuring results are not compromised. However, multivariate outliers, which are unusual combinations of values across the rows of a data matrix, could still potentially obscure the latent factor structure. If the data are suspected to be 'dirty', or one wishes to validate the results of a standard factor fitting method, the robust factor model can be useful.

robfa(
  Y,
  nfac = min(nrow(Y) - 3, ncol(Y) - 2),
  rotate = GPArotation::Varimax,
  scale = T,
  max.iter = 4000,
  tol = 1e-12
)

`Y`	a numeric matrix or data frame of only numeric variables.
`nfac`	the number of factors 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.
`max.iter`	maximum number of iterations. defaults to 4000.
`tol`	a tolerance value for convergence. defaults to 1e-12.

Rubin, D. B., and Thayer, D. T. (1982), EM Algorithms for ML Factor Analysis, Psychometrika, 47 (1), 69-76.

Bai, J. and Li, K. (2012). Statistical analysis of factor models of high dimension. The Annals of Statistics 40, 436-465.

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