Fit the high-dimensional multi-study multi-modality covariate-augmented generalized factor model

Fit the high-dimensional multi-study multi-modality covariate-augmented generalized factor model via variational inference.

MMGFM(
  XList,
  ZList,
  numvarmat,
  tauList = NULL,
  q = 15,
  qsvec = rep(2, length(XList)),
  init = c("MSFRVI", "random", "LFM"),
  epsELBO = 1e-12,
  maxIter = 30,
  verbose = TRUE,
  seed = 1
)

Arguments

XList: a S-length list with each component a m-length list composed by a combined modality matrix of the same type modalities, which is the observed matrix from each source/study and each modality, where m is the number of modality types.
ZList: a S-length list with each component a matrix that is the covariate matrix from each study.
numvarmat: a m-by-T matrix with rownames modality types that specifies the variable number for each modality of each modality type, where m is the number of modality types, T is the maximum number of modalities for one of modality types .
tauList: an optional S-length list with each component a m-length list correponding the offset term for each combined modality of each study; default as full-zero matrix.
q: an optional string, specify the number of study-shared factors; default as 15.
qsvec: a integer vector with length S, specify the number of study-specifed factors; default as 2.
init: an optional string, specify the initialization method, supporting "MSFRVI", "random" and "LFM", default as "MSFRVI".
epsELBO: an optional positive vlaue, tolerance of relative variation rate of the envidence lower bound value, defualt as '1e-5'.
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.

Value

return a list including the following components:

hbeta - a M-length list composed by the estimated regression coefficient matrix for each modality;
hA - a M-length list composed by the loading matrix corresponding to study-shared factors for each modality;
hB - a S-length list composed by a M-length loading matrix list corresponding to study-specified factors for each study;
hF - a S-length list composed by the posterior estimation of study-shared factor matrix for each study;
hH - a S-length list composed by the posterior estimation of study-specified factor matrix for each study;
hSigma - a S-length list composed by the estimated posterior variance of the study-shared factor;
hPhi - a S-length list composed by the estimated posterior variance of study-specified factor;
hv - a S-length list composed by a M-length vector list corresponding to the posterior estimation of study-specified and modality variable-shared factor for each study and modality;
hzeta - the estimated posterior variance for study-specified and modality variable-shared factor;
hsigma2 - the estimated variance for study-specified and modality variable-shared factor;
hinvLambda - a S-length list composed by a M-length vector list corresponding to the inverse of the estimated variances of error;
S - the approximated posterior covariance for each row of F;
ELBO - the ELBO value when algorithm stops;
ELBO_seq - the sequence of ELBO values.
time_use - the running time in model fitting of SpaCOAP;

Details

If init="MSFRVI", it will use the results from multi-study linear factor model in MultiCOAP package as initial values; If init="LFM", it will use the results from linear factor model by combing data from all studies as initials.

References

None

Examples