Package 'TPCselect'

A function to generate toy partial linear model data

Description

A function to generate toy partial linear model data

Usage

generate_toy_pldata()

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Variable Selection via Thresholded Partial Correlation

Description

These are the main selection functions with fixed significance level s and constant. The function TPC implements the thresholded partial correlation (TPC) approach to selecting important variables in linear models of Li et al. (2017). The function TPC_pl implements the thresholded partial correlation approach to selecting important variables in partial linear models of Liu et al. (2018). This function also extends the PC-simple algorithm of Bühlmann et al. (2010) to partial linear models.

Usage

TPC(y, x, s = 0.05, constant = 1, method = "threshold")

TPCselect(y, x, s = 0.05, constant = 1, method = "threshold")

Arguments

y	response vector;
x	covariate matrix;
s	a numeric value that used as significance level(s) for partial correlation test.
constant	a value that used as the tuning constant for partial correlation test. constant is treated as 1 when method is "simple".
method	the method to be used; default set as method = "threshold"; "simple" is also available.

Value

TPC.object a TPC object, which extends the lm object. New attributes are:

• beta - the fitted coefficients

• selected_index - the selected coefficients indices

Examples

#generate sample data
p = 200
n = 200
truebeta <- c(c(3,1.5,0,0,2),rep(0,p-5))
rho = 0.3
sigma =  matrix(0,p+1,p+1)
for(i in 1:(p+1)){
  for(j in 1:(p+1)){
    sigma[i,j] = rho^(abs(i-j))
  }
}
x_error = 0.9*MASS::mvrnorm(n,rep(0,p+1),sigma) + 0.1*MASS::mvrnorm(n,rep(0,p+1),9*sigma)
x = x_error[,1:p]
error = x_error[,p+1]
y = x%*%truebeta + error

#perform variable selection via partial correlation
TPC.fit = TPC(y,x,0.05,1,method="threshold")
TPC.fit$beta

---

Variable Selection via Thresholded Partial Correlation

Description

Use BIC to select the best s and constant over grids.

Usage

TPC_BIC(y, x, s = 0.05, constant = 1, method = "threshold")

Arguments

y	response vector;
x	covariate matrix;
s	a value or a vector that used as significance level(s) for partial correlation test. BIC will be used to select the best s.
constant	a value or a vector that used as the tuning constant for partial correlation test. BIC will be used to select the best constant. constant is treated as 1 when method is "simple".
method	the method to be used; default set as method = "threshold"; "simple" is also available.

Value

TPC.object a TPC object, which extends the lm object. New attributes are:

• beta - the fitted coefficients

• selected_index - the selected coefficients indices

Examples

#generate sample data
p = 200
n = 200
truebeta <- c(c(3,1.5,0,0,2),rep(0,p-5))
rho = 0.3
sigma =  matrix(0,p+1,p+1)
for(i in 1:(p+1)){
  for(j in 1:(p+1)){
    sigma[i,j] = rho^(abs(i-j))
  }
}
x_error = 0.9*MASS::mvrnorm(n,rep(0,p+1),sigma) + 0.1*MASS::mvrnorm(n,rep(0,p+1),9*sigma)
x = x_error[,1:p]
error = x_error[,p+1]
y = x%*%truebeta + error

#perform variable selection via partial correlation
TPC.fit = TPC_BIC(y,x,0.05,c(1,1.5),method="threshold")
TPC.fit$beta

---

Variable Selection via Thresholded Partial Correlation

Description

These are the main selection functions with fixed significance level s and constant. The function TPC implements the thresholded partial correlation (TPC) approach to selecting important variables in linear models of Li et al. (2017). The function TPC_pl implements the thresholded partial correlation approach to selecting important variables in partial linear models of Liu et al. (2018). This function also extends the PC-simple algorithm of Bühlmann et al. (2010) to partial linear models.

Usage

TPC_pl(y, x, u = NULL, s = 0.05, constant = 1, method = "threshold", ...)

Arguments

y	response vector;
x	covariate matrix;
u	non-parametric variable, should be a vector;
s	s is a numeric value or vector that used as the significance level(s) for the partial correlation tests
constant	a value that used as the tuning constant for partial correlation test. constant is treated as 1 when method is "simple".
method	the method to be used; default set as method = "threshold"; "simple" is also available.
...	smoothing parameters and functions: kernel, degree, and bandwidth h.

Value

TPC.object a TPC object, which extends the lm object. New attributes are:

• beta - the fitted coefficients

• selected_index - the selected coefficients indices

Examples

#generate partial linear data
samples <- generate_toy_pldata()
y <- samples[[1]]
x <- samples[[2]]
times <- samples[[3]]

#perform variable selection via partial correlation
TPC.fit = TPC_pl(y,x,times,0.05,1,method="threshold")
TPC.fit$beta

---

Variable Selection via Thresholded Partial Correlation

Description

Use BIC to select the best s and constant over grids.

Usage

TPC_pl_BIC(y, x, u = NULL, s = 0.05, constant = 1, method = "threshold", ...)

Arguments

y	response vector;
x	covariate matrix;
u	non-parametric variable, should be a vector;
s	a value or a vector that used as significance level(s) for partial correlation test. BIC will be used to select the best s.
constant	a value or a vector that used as the tuning constant for partial correlation test. BIC will be used to select the best constant. constant is treated as 1 when method is "simple".
method	the method to be used; default set as method = "threshold"; "simple" is also available.
...	smoothing parameters and functions: kernel, degree, and bandwidth h.

Value

TPC.object a TPC object, which extends the lm object. New attributes are:

• beta - the fitted coefficients

• selected_index - the selected coefficients indices

Examples

#generate partial linear data
samples <- generate_toy_pldata()
y <- samples[[1]]
x <- samples[[2]]
times <- samples[[3]]

#perform variable selection via partial correlation
TPC.fit = TPC_pl_BIC(y,x,times,0.05,c(1,1.5),method="threshold")
TPC.fit$beta

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