Package 'GrFA' reference manual

Title:	Group Factor Analysis
Description:	Several group factor analysis algorithms are implemented, including Canonical Correlation-based Estimation by Choi et al. (2021) <doi:10.1016/j.jeconom.2021.09.008> , Generalised Canonical Correlation Estimation by Lin and Shin (2023) <doi:10.2139/ssrn.4295429>, Circularly Projected Estimation by Chen (2022) <doi:10.1080/07350015.2022.2051520>, and Aggregated projection method.
Authors:	Jiaqi Hu [cre, aut], Ting Li [aut], Xueqin Wang [aut]
Maintainer:	Jiaqi Hu <[email protected]>
License:	GPL-3
Version:	0.2
Built:	2024-11-23 03:15:43 UTC
Source:	https://github.com/cran/GrFA

Aggregated Projection Method

Description

Aggregated Projection Method

Usage

APM(y, rmax = 8, r0 = NULL, r = NULL, localfactor = FALSE, weight = TRUE,
      method = "ic", type = "IC3")
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 $T * N_m$ .
`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.
`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 `ic`, it can also be `gap`.
`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.
`loading_G`	a list consisting of the estimated global factor loadings.
`Fhat`	the estimated local factors.
`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 = ic`.

Examples

dat = gendata()
dat
APM(dat$y, rmax = 8, localfactor = TRUE, method = "ic")
APM(dat$y, rmax = 8, localfactor = TRUE, method = "gap")
dat = gendata()
dat
APM(dat$y, rmax = 8, localfactor = TRUE, method = "ic")
APM(dat$y, rmax = 8, localfactor = TRUE, method = "gap")

Canonical Correlation Estimation

Description

Canonical Correlation Estimation

Usage

CCA(y, rmax = 8, r0 = NULL, r = NULL, localfactor = FALSE, method = "CCD", type = "IC3")
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")
dat = gendata()
dat
CCA(dat$y, rmax = 8, localfactor = TRUE, method = "CCD")
CCA(dat$y, rmax = 8, localfactor = TRUE, method = "MCC")

Circularly Projected Estimation

Description

Circularly Projected Estimation

Usage

CP(y, rmax = 8, r0 = NULL, r = NULL, localfactor = FALSE, type = "IC3")
CP(y, rmax = 8, r0 = NULL, r = NULL, localfactor = FALSE, 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.
`type`	the method used in estimating the local factor numbers in each group after projecting out the global factors, 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.

References

Chen, M. (2023). Circularly Projected Common Factors for Grouped Data. Journal of Business & Economic Statistics, 41(2), 636-649.

Examples

dat = gendata()
dat
CP(dat$y, rmax = 8, localfactor = TRUE)
dat = gendata()
dat
CP(dat$y, rmax = 8, localfactor = TRUE)

Estimate factor numbers

Description

Estimate factor numbers.

Usage

est_num(X, kmax = 8, type = "BIC3")
est_num(X, kmax = 8, type = "BIC3")

Arguments

`X`	the observation data matrix of dimension $T\times N$ .
`kmax`	the maximum number of factors.
`type`	the criterion used in determining the number of factors, default is `type = "BIC3"`, it can also be `"PC1", "PC2", "PC3", "IC1", "IC2","IC3", "AIC3", "BIC3", "ER", "GR"`.

Value

rhat

the estimated number of factors.

References

Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191-221.

Ahn, S. C., & Horenstein, A. R. (2013). Eigenvalue ratio test for the number of factors. Econometrica, 81(3), 1203-1227.

Factor analysis

Description

Factor analysis.

Usage

FA(X, r)
FA(X, r)

Arguments

`X`	the observation data matrix of dimension $T\times N$ .
`r`	the factor numbers need to estimated.

Value

`F`	the estimated factors.
`L`	the estimated factor loadings.

Author(s)

Jiaqi Hu

References

Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191-221.

Generalised Canonical Correlation

Description

Generalised Canonical Correlation

Usage

GCC(y, rmax = 8, r0 = NULL, r = NULL, localfactor = FALSE, type = "IC3")
GCC(y, rmax = 8, r0 = NULL, r = NULL, localfactor = FALSE, 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.
`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.

References

Lin, R., & Shin, Y. (2023). Generalised Canonical Correlation Estimation of the Multilevel Factor Model. Available at SSRN 4295429.

Examples

dat = gendata()
dat
GCC(dat$y, rmax = 8, localfactor = TRUE)
dat = gendata()
dat
GCC(dat$y, rmax = 8, localfactor = TRUE)

Generate the grouped data.

Description

Generate the grouped data.

Usage

gendata(seed = 1, T = 50, N = rep(30, 5), r0 = 2, r = rep(2, 5),
        Phi_G = 0.5, Phi_F = 0.5, Phi_e = 0.5, W_F = 0.5, beta = 0.2,
        kappa = 1, case = 1)
gendata(seed = 1, T = 50, N = rep(30, 5), r0 = 2, r = rep(2, 5),
        Phi_G = 0.5, Phi_F = 0.5, Phi_e = 0.5, W_F = 0.5, beta = 0.2,
        kappa = 1, case = 1)

Arguments

`seed`	the seed used in `set.seed`.
`T`	the number of time points.
`N`	a vector representing the number of variables in each group.
`r0`	the number of global factors.
`r`	a vector representing the number of the local factors. Notice, the length of $r$ is the same as $N$ .
`Phi_G`	hyperparameter of the global factors, default is 0.5, the value should between 0 and 1.
`Phi_F`	hyperparameter of the local factors, default is 0.5, the value should between 0 and 1.
`Phi_e`	hyperparameter of the errors, default is 0.5, the value should between 0 and 1.
`W_F`	hyperparameter of the correlation of local factors, only applicable in `case = 3`, the value should between 0 and 1.
`beta`	hyperparameter of the errors, default is 0.2.
`kappa`	hyperparameter of signal to noise ratio, default is 1.
`case`	the case of the data-generating process, default is 1, it can also be 2 and 3.

Value

`y`	a list of the data.
`G`	the global factors.
`F`	a list of the local factors.
`loading_G`	the global factor loadings.
`loading_F`	the local factor loadings.
`T`	the number of time points.
`N`	a vector representing the number of variables in each group.
`M`	the number of groups.
`r0`	the number of global factors.
`r`	a vector representing the number of the local factors.
`case`	the case of the data-generating process.

Examples

dat = gendata()
dat
dat = gendata()
dat

Print

Description

Print the summarized results of the estimated group factor model, such as the estimated global and local factors.

Usage

## S3 method for class 'GFA'
print(x, ...)
## S3 method for class 'GFA'
print(x, ...)

Arguments

`x`	the `GFA` object returned from the algorithm.
`...`	additional print arguments.

Value

No return value, called for side effects

Trace ratio

Description

Evaluation of the estimated factors by trace ratios, the values is between 0 and 1, higher values means better estimation.

Usage

TraceRatio(G, Ghat)
TraceRatio(G, Ghat)

Arguments

`G`	the true factors.
`Ghat`	the estimated factors.

Value

trace ratio

defined as $\mathrm{TR} = \mathrm{tr} ( \mathbf{G}' \widehat{\mathbf{G}} (\widehat{\mathbf{G}}'\widehat{\mathbf{G}})^{-1} \widehat{\mathbf{G}}'\mathbf{G})/\mathrm{tr}(\mathbf{G'G})$ .

Housing price data for 16 states in the U.S.

Description

Housing price data for 16 states in the U.S over the period Jan 2000 to April 2023.

Usage

data("UShouseprice")data("UShouseprice")

Format

A list with a length of 16. Each element is a matrix of dimension $T*N_m$ .

Source

The original data is downloaded from the website of Zillow.

Examples

data(UShouseprice)
log_diff = function(x){
  T = nrow(x)
  res = log(x[2:T,]/x[1:(T-1),])*100
  scale(res, center = TRUE, scale = TRUE)
}
UShouseprice1 = lapply(UShouseprice, log_diff)
data(UShouseprice)
log_diff = function(x){
  T = nrow(x)
  res = log(x[2:T,]/x[1:(T-1),])*100
  scale(res, center = TRUE, scale = TRUE)
}
UShouseprice1 = lapply(UShouseprice, log_diff)

Package 'GrFA'

Help Index

Aggregated Projection Method

Description

Usage

Arguments

Value

Examples

Canonical Correlation Estimation

Description

Usage

Arguments

Value

References

Examples

Circularly Projected Estimation

Description

Usage

Arguments

Value

References

Examples

Estimate factor numbers

Description

Usage

Arguments

Value

References

Factor analysis

Description

Usage

Arguments

Value

Author(s)

References

Generalised Canonical Correlation

Description

Usage

Arguments

Value

References

Examples

Generate the grouped data.

Description

Usage

Arguments

Value

Examples

Print

Description

Usage

Arguments

Value

Trace ratio

Description

Usage

Arguments

Value

Housing price data for 16 states in the U.S.

Description

Usage

Format

Source

Examples