APM {GrFA}

Weighted Projection Estimation

Description

Weighted Projection Estimation

Usage

APM(y, rmax = 8, r0 = NULL, r = NULL, weight = TRUE, method = "ic1", type = "BIC3")

Arguments

y

a list of the observation data, each element is a data matrix of each group with dimension T * N_m.

rmax

the maximum factor numbers of all groups.

r0

the number of global factors, default is NULL, the algorithm will automatically estimate the number of global factors. If you have the prior information about the true number of global factors, you can set it by your own.

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 the prior information about the true number of local factors, you can set it by your own, notice it should be an integer vector of length M (the number of groups).

weight

the weight of each projection matrix, default is TRUE, means w_m = N_m/N, if weight = FALSE, then simply calculate the mean of all projection matrices.

method

the method used in the algorithm, default is ic1, it can also be ic2 and gap.

type

the method used in estimating the factor numbers in each group initially, default is BIC3, it can also be IC3

Value

r0hat

the estimated number of the global factors.

rho

the estimated number of the local factors.

Ghat

the estimated global factors.

Fhat

the estimated local factors.

loading_G

a list consisting of the estimated global factor loadings.

loading_F

a list consisting of the estimated local factor loadings.

e

a list consisting of the residuals.

threshold

the threshold used in determining the number of global factors, only for method = ic1 and method = ic2.

Author(s)

Jiaqi Hu

Examples

dat = gendata()
dat
APM(dat$y, method = "ic1")
APM(dat$y, method = "ic2")
APM(dat$y, method = "gap")