Description Usage Arguments Details Value References Examples
Estimate the latent factor matrix and noise variance using early stopping alternation (ESA) given the number of factors.
1 
Y 
observed data matrix. p is the number of variables and
n is the sample size. Dimension is 
r 
The number of factors to use 
X 
the known predictors of size 
center 
logical, whether to add an intercept term in the model. Default is False. 
niter 
the number of iterations for ESA. Default is 3. 
svd.method 
either "fast", "propack" or "standard".
"fast" is using the 
The model used 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 μ'
and V' mean _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 returned value is a list with components
estSigma 
the diagonal entries of estimated Σ
which is a vector of length 
estU 
the estimated U. Dimension 
estD 
the estimated diagonal entries of D
which is a vector of length 
estV 
the estimated V. Dimension is 
beta 
the estimated beta 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

Art B. Owen and Jingshu Wang(2015), Bicrossvalidation for factor analysis, http://arxiv.org/abs/1503.03515
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