Description Usage Arguments Details Value References See Also Examples
Find out the best number of factors using BiCrossValidation (BCV) with EarlyStoppingAlternation (ESA) and then estimate the factor matrix.
1 2 
Y 
observed data matrix. p is the number of variables and
n is the sample size. Dimension is 
X 
the known predictors of size 
r.limit 
the maximum number of factor to try. Default is 20. Can be set to Inf. 
niter 
the number of iterations for ESA. Default is 3. 
nRepeat 
number of repeats of BCV. In other words, the random partition of Y
will be repeated for 
only.r 
whether only to estimate and return the number of factors. 
svd.method 
either "fast", "propack" or "standard".
"fast" is using the 
center 
logical, whether to add an intercept term in the model. Default is False. 
The model is
Y = 1 μ' + X β + n^{1/2}U D V' + E Σ^{1/2}
where D and Σ are diagonal matrices, U and V
are orthogonal and mu'
and V' represent _mu transposed_ and _V transposed_ respectively.
The entries of E are assumed to be i.i.d. standard Gaussian.
The model assumes heteroscedastic noises and especially works well for
highdimensional data. The method is based on Owen and Wang (2015). Notice that
when nonnull X
is given or centering the data is required (which is essentially
adding a known covariate with all 1), for identifiability, it's required that
<X, U> = 0 or <1, U> = 0 respectively. Then the method will first make a rotation
of the data matrix to remove the known predictors or centers, and then use
the latter n  k
(or n  k  1
if centering is required) samples to
estimate the latent factors. The rotation idea first appears in Sun et.al. (2012).
EsaBcv
returns an obejct of class
"esabcv"
The function plot
plots the crossvalidation results and points out the
number of factors estimated
An object of class "esabcv" is a list containing the following components:
best.r 
the best number of factor estimated 
estSigma 
the diagonal entries of estimated Σ
which is a vector of length 
estU 
the estimated U. Dimension is 
estD 
the estimated diagonal entries of D
which is a vector of length 
estV 
the estimated V. Dimension is 
beta 
the estimated β which is a matrix of size 
estS 
the estimated signal(factor) matrix S where S = 1 μ' + X β + n^{1/2}U D V' 
mu 
the sample centers of each variable which is a vector of length

max.r 
the actual maximum number of factors used. For the details of how this is decided, please refer to Owen and Wang (2015) 
result.list 
a matrix with dimension 
Art B. Owen and Jingshu Wang(2015), Bicrossvalidation for factor analysis, http://arxiv.org/abs/1503.03515
Yunting Sun, Nancy R. Zhang and Art B. Owen, Multiple hypothesis testing adjusted for latent variables, with an application to the AGEMAP gene expression data. The Annuals of Applied Statistics, 6(4): 16641688, 2012
1 2 
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.