RMFM (version 1.1.0)

RMFM: Fit the high-dimensional robust matrix factor model

Description

Fit the high-dimensional robust matrix factor model via variational inference.

Usage

RMFM(
  X,
  r1 = 10,
  r2 = 10,
  epsELBO = 1e-09,
  maxIter = 30,
  verbose = TRUE,
  seed = 1,
  cal_eigs = FALSE
)

Value

return a list including the following components:

• hF - a r1* r2*T array, which is the estimated factor matrix for each individual, where T is the sample size.

• hmu - a p1-by-p2 matrix, the estimated mean matrix.

• hR - the estimated row loading matrix.

• hC - the estimated column loading matrix.

• hnu - the estimated degree of freedom for the error term.

• hLambda1 - a p1 vector, the estimated row scatter matrix for error.

• hLambda2 - a p2 vector, the estimated column scatter matrix for error.

• dR - NULL if cal_eigs=FALSE; a group of eigenvalues of the sample covariance across rows if cal_eigs=TRUE.

• dC - NULL if cal_eigs=FALSE; a group of eigenvalues of the sample covariance across columns if cal_eigs=TRUE.

• ELBO - the ELBO value when algorithm stops;

• ELBO_seq - the sequence of ELBO values.

• time_use - the running time in model fitting of RMFM;

Arguments

X

a p1* p2*T array, which is the observed matrix from each individual, where T is the sample size.

r1

an optional positive integer, specify the number of row factors; default as 10.

r2

an optional positive integer, specify the number of column factors; default as 10.

epsELBO

an optional positive value, tolerance of relative variation rate of the variational lower bound value, default as '1e-9'.

maxIter

the maximum iteration of the VEM algorithm. The default is 30.

verbose

a logical value, whether output the information in iteration.

seed

an optional integer, specify the random seed for reproducibility in initialization.

cal_eigs

an optional logical value, specify whether calculate the eigenvalues of covariance matrix, default as FALSE.

Details

None

References

None

See Also

None

Examples

r1 <- 4; r2 <- 3;
Tt <- 100; type <- 'MatrixT'
p1 <- 50; p2 <- 50
datlist <- gendata_rmfm(Tt = Tt,p1 =p1, p2=p2, r1=r1, r2=r2,
                        rho=1, type= 'MatrixT', nu=1)
str(datlist)
reslist <- RMFM(X=datlist$X, r1=r1, r2=r2,  verbose = TRUE, maxIter = 6)