Repository Mirror for your Cloud Server and Webhosting

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:

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