APM: Aggregated Projection Method

In GrFA: Group Factor Analysis

Aggregated Projection Method

Description

Aggregated Projection Method for Group Factor Model.

Usage

APM(
  y,
  rmax = 8,
  r0 = NULL,
  r = NULL,
  localfactor = FALSE,
  weight = TRUE,
  method = "ic",
  type = "IC3"
)

Arguments

y	A list of the observation data, each element is a data matrix of each group with dimension T \times N_m.
rmax	The maximum factor numbers of all groups. Default is 8.
r0	The number of global factors. Default is NULL, the algorithm will automatically estimate the number of global factors. If you have prior information about the true number of global factors, you can set it manually.
r	The number of local factors in each group. Default is NULL, the algorithm will automatically estimate the number of local factors. If you have prior information, set it manually as an integer vector of length M (the number of groups).
localfactor	Logical. If FALSE (default), local factors are not estimated. If TRUE, local factors will be estimated.
weight	The weight of each projection matrix. If TRUE (default), weights are w_m = N_m/N. If FALSE, the mean of all projection matrices is calculated (equal weights). Can also be a numeric vector of length M specifying custom weights.
method	The method used in the algorithm. Default is "ic", can also be "gap".
type	The method used in estimating the factor numbers in each group initially. Default is "IC3".

Value

An object of class "GFA" containing:

r0hat	The estimated number of global factors.
rhat	The estimated number of local factors (if localfactor = TRUE).
rho	The first rmax eigenvalues of the weighted projection matrix.
Ghat	The estimated global factors.
loading_G	A list consisting of the estimated global factor loadings.
Fhat	The estimated local factors (if localfactor = TRUE).
loading_F	A list consisting of the estimated local factor loadings (if localfactor = TRUE).
residual	A list consisting of the residuals (if localfactor = TRUE).
threshold	The threshold used in determining the number of global factors (only for method = "ic").

References

Aggregated Projection Method: A New Approach for Group Factor Model. Jiaqi Hu, Ting Li, Xueqin Wang (2025). Journal of the American Statistical Association, doi:10.1080/01621459.2025.2491154

Examples

## Not run: 
dat <- GrFA::gendata()
APM(dat$y, rmax = 8, localfactor = TRUE, method = "ic")
APM(dat$y, rmax = 8, localfactor = TRUE, method = "gap")

## End(Not run)

GrFA documentation built on Dec. 7, 2025, 1:07 a.m.