CCA {GrFA}

Canonical Correlation Estimation

Description

Canonical Correlation Estimation

Usage

CCA(y, rmax = 8, r0 = NULL, r = NULL, method = "CCD", 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).

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 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 = "MCC".

References

Choi, I., Kim, D., Kim, Y. J., & Kwark, N. S. (2018). A multilevel factor model: Identification, asymptotic theory and applications. Journal of Applied Econometrics, 33(3), 355-377.

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$y, method = "CCD")
CCA(dat$y, method = "MCC")