| Type: | Package |
| Title: | Variable Selection in a Specific Regression Time Series of Counts |
| Version: | 1.0 |
| Date: | 2023-07-17 |
| Description: | Performs variable selection in sparse negative binomial GLARMA (Generalised Linear Autoregressive Moving Average) models. For further details we refer the reader to the paper Gomtsyan (2023), <doi:10.48550/arXiv.2307.00929>. |
| License: | GPL-2 |
| Depends: | R (≥ 3.5.0), Matrix, glmnet, stats, MASS, mpath, ggplot2 |
| VignetteBuilder: | knitr |
| Suggests: | knitr, markdown, formatR |
| NeedsCompilation: | no |
| Packaged: | 2023-07-17 06:58:36 UTC; marina |
| Author: | Marina Gomtsyan [aut, cre] |
| Maintainer: | Marina Gomtsyan <mgomtsian@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2023-07-17 17:40:02 UTC |
Variable Selection in a Specific Regression Time Series of Counts
Description
NBtsVarSel consists of four functions: "variable_selection.R", "grad_hess_beta.R", "grad_hess_gamma.R" and "NR_gamma.R" For further information on how to use these functions, we refer the reader to the vignette of the package.
Details
This package consists of four functions: "variable_selection.R", "grad_hess_beta.R", "grad_hess_gamma.R" and "NR_gamma.R" For further information on how to use these functions, we refer the reader to the vignette of the package.
Author(s)
Marina Gomtsyan
Maintainer: Marina Gomtsyan <mgomtsian@gmail.com>
References
M. Gomtsyan "Variable selection in a specific regression time series of counts.", arXiv:2307.00929
Examples
n = 50
p = 30
X = matrix(NA,(p+1),n)
f = 1/0.7
for(t in 1:n){X[,t] = c(1,cos(2*pi*(1:(p/2))*t*f/n),sin(2*pi*(1:(p/2))*t*f/n))}
gamma0 = c(0)
data(Y)
result = variable_selection(Y, X, gamma.init=gamma0, alpha.init=NULL, k.max=1, method="cv",
tr=0.3, n.iter=100, n.rep=1000)
beta_est = result$beta_est
Estim_active = result$estim_active
gamma_est = result$gamma_est
alpha_est = result$alpha_est
Newton-Raphson method for estimation of gamma
Description
This function estimates gamma with Newton-Raphson method
Usage
NR_gamma(Y, X, beta, gamma, alpha, n.iter)
Arguments
Y |
Observation matrix |
X |
Design matrix |
beta |
Initial beta vector |
gamma |
Initial gamma vector |
alpha |
Initial overdispertion parameter |
n.iter |
Number of iterations of the algorithm. Default=100 |
Value
gamma |
Estimated gamma vector |
Author(s)
Marina Gomtsyan
Maintainer: Marina Gomtsyan <mgomtsian@gmail.com>
References
M. Gomtsyan "Variable selection in a specific regression time series of counts.", arXiv:2307.00929
Examples
n = 50
p = 30
X = matrix(NA,(p+1),n)
f = 1/0.7
for(t in 1:n){X[,t] = c(1,cos(2*pi*(1:(p/2))*t*f/n),sin(2*pi*(1:(p/2))*t*f/n))}
gamma0 = c(0)
data(Y)
glm_nb = glm.nb(Y~t(X)[,2:(p+1)])
beta0 = as.numeric(glm_nb$coefficients)
alpha0 = glm_nb$theta
gamma_est = NR_gamma(Y, X, beta0, gamma0, alpha0, n.iter=100)
Observation matrix Y
Description
An example of observation matrix
Usage
data("Y")Format
The format is: num [1:50] 9 2 11 14 18 17 1 0 1 0 ...
References
M. Gomtsyan "Variable selection in a specific regression time series of counts.", arXiv:2307.00929
Examples
data(Y)
Gradient and Hessian of the log-likelihood with respect to beta
Description
This function calculates the gradient and Hessian of the log-likelihood with respect to beta.
Usage
grad_hess_beta(Y, X, beta, gamma, alpha)
Arguments
Y |
Observation matrix |
X |
Design matrix |
beta |
Initial beta vector |
gamma |
Initial gamma vector |
alpha |
Initial overdispertion parameter |
Value
grad_L_beta |
Vector of the gradient of L with respect to beta |
hess_L_beta |
Matrix of the Hessian of L with respect to beta |
Author(s)
Marina Gomtsyan
Maintainer: Marina Gomtsyan <mgomtsian@gmail.com>
References
M. Gomtsyan "Variable selection in a specific regression time series of counts.", arXiv:2307.00929
Examples
n = 50
p = 30
X = matrix(NA,(p+1),n)
f = 1/0.7
for(t in 1:n){X[,t] = c(1,cos(2*pi*(1:(p/2))*t*f/n),sin(2*pi*(1:(p/2))*t*f/n))}
gamma0 = c(0)
data(Y)
glm_nb = glm.nb(Y~t(X)[,2:(p+1)])
beta0 = as.numeric(glm_nb$coefficients)
alpha0 = glm_nb$theta
result = grad_hess_beta(Y, X, beta0, gamma0, alpha0)
grad = result$grad_L_beta
Hessian = result$hess_L_beta
Gradient and Hessian of the log-likelihood with respect to gamma
Description
This function calculates the gradient and Hessian of the log-likelihood with respect to gamma
Usage
grad_hess_gamma(Y, X, beta, gamma, alpha)
Arguments
Y |
Observation matrix |
X |
Design matrix |
beta |
Initial beta vector |
gamma |
Initial gamma vector |
alpha |
Initial overdispertion parameter |
Value
grad_L_gamma |
Vector of the gradient of L with respect to gamma |
hess_L_gamma |
Matrix of the Hessian of L with respect to gamma |
Author(s)
Marina Gomtsyan
Maintainer: Marina Gomtsyan <mgomtsian@gmail.com>
References
M. Gomtsyan "Variable selection in a specific regression time series of counts.", arXiv:2307.00929
Examples
n = 50
p = 30
X = matrix(NA,(p+1),n)
f = 1/0.7
for(t in 1:n){X[,t] = c(1,cos(2*pi*(1:(p/2))*t*f/n),sin(2*pi*(1:(p/2))*t*f/n))}
gamma0 = c(0)
data(Y)
glm_nb = glm.nb(Y~t(X)[,2:(p+1)])
beta0 = as.numeric(glm_nb$coefficients)
alpha0 = glm_nb$theta
result = grad_hess_gamma(Y, X, beta0, gamma0, alpha0)
grad = result$grad_L_gamma
Hessian = result$hess_L_gamma
Variable selection
Description
This function performs variable selection, estimates new vectors of beta and gamma and a new alpha
Usage
variable_selection(Y, X, gamma.init, alpha.init = NULL, k.max = 1, method = "cv",
tr = 0.3, n.iter = 100, n.rep = 1000)
Arguments
Y |
Observation matrix |
X |
Design matrix |
gamma.init |
Initial gamma vector |
alpha.init |
Optional initial alpha value. The default is NULL |
k.max |
Number of iteration to repeat the whole algorithm |
method |
Stability selection method: "min" or "cv". In "min" the smallest lambda is chosen, in "cv" cross-validation lambda is chosen for stability selection. The default is "cv" |
tr |
Threshold for stability selection. The default is 0.3 |
n.iter |
Number of iteration for Newton-Raphson algorithm. The default is 100 |
n.rep |
Number of replications in stability selection step. The default is 1000 |
Value
estim_active |
Estimated active coefficients |
beta_est |
Vector of estimated beta values |
gamma_est |
Vector of estimated gamma values |
alpha_est |
Estimation of alpha |
Author(s)
Marina Gomtsyan
Maintainer: Marina Gomtsyan <mgomtsian@gmail.com>
References
M. Gomtsyan "Variable selection in a specific regression time series of counts.", arXiv:2307.00929
Examples
n = 50
p = 30
X = matrix(NA,(p+1),n)
f = 1/0.7
for(t in 1:n){X[,t] = c(1,cos(2*pi*(1:(p/2))*t*f/n),sin(2*pi*(1:(p/2))*t*f/n))}
gamma0 = c(0)
data(Y)
result = variable_selection(Y, X, gamma.init=gamma0, alpha.init=NULL, k.max=1, method="cv",
tr=0.3, n.iter=100, n.rep=1000)
beta_est = result$beta_est
Estim_active = result$estim_active
gamma_est = result$gamma_est
alpha_est = result$alpha_est