CCA: Canonical Correlation Estimation

In GrFA: Group Factor Analysis

Canonical Correlation Estimation

Description

Canonical Correlation Estimation

Usage

CCA(y, rmax = 8, r0 = NULL, r = NULL, localfactor = FALSE, method = "CCD", type = "IC3")

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).
localfactor	if localfactor = FALSE, then we would not estimate the local factors; if localfactor = TRUE, then we will further estimate the local factors.
method	the method used in the algorithm, default is CCD, it can also be MCC.
type	the method used in estimating the factor numbers in each group initially, default is 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 = "MCC".

References

Choi, I., Lin, R., & Shin, Y. (2021). Canonical correlation-based model selection for the multilevel factors. Journal of Econometrics.

Examples

dat = gendata()
dat
CCA(dat$y, rmax = 8, localfactor = TRUE, method = "CCD")
CCA(dat$y, rmax = 8, localfactor = TRUE, method = "MCC")

GrFA documentation built on April 4, 2025, 2:09 a.m.