plsim.lam {PLSiMCpp}

Select lambda for Penalized Profile Least Squares Estimator

Description

Use AIC or BIC to choose the regularization parameters for Penalized Profile least squares (PPLS) estimation.

Usage

plsim.lam(...)

## S3 method for class 'formula'
plsim.lam(formula, data, ...)

## Default S3 method:
plsim.lam(xdat=NULL, ydat, zdat, h, zetaini=NULL, penalty="SCAD", 
lambdaList=NULL, l1_ratio_List=NULL, lambda_selector="BIC", verbose=TRUE, seed=0, ...)

Arguments

...

additional arguments.

formula

a symbolic description of the model to be fitted.

data

an optional data frame, list or environment containing the variables in the model.

xdat

input matrix (linear covariates). The model reduces to a single index model when x is NULL.

zdat

input matrix (nonlinear covariates). z should not be NULL.

ydat

input vector (response variable).

h

bandwidth.

zetaini

initial coefficients, optional (default: NULL). It could be obtained by the function plsim.ini. zetaini[1:ncol(z)] is the initial coefficient vector \alpha_0, and zetaini[(ncol(z)+1):(ncol(z)+ncol(x))] is the initial coefficient vector \beta_0.

penalty

string, optional (default="SCAD"). It could be "SCAD", "LASSO" or "ElasticNet".

lambdaList

candidates for lambda selection. lambda is a constant that multiplies the penalty term. If lambdaList is NULL, function plsim.lam will automatically set it.

l1_ratio_List

candidates for l1_ratio selection. l1_ratio is a constant that balances the importances of L1 norm and L2 norm for "ElasticNet". If l1_ratio_List is NULL, function plsim.lam ranges from 0 to 1 with an increment 0.1.

lambda_selector

the criterion to select lambda (and l1_ratio), default: "BIC".

verbose

bool, default: TRUE. Enable verbose output.

seed

int, default: 0.

Value

goodness_best

the AIC (or BIC) statistics with lambda_best.

lambda_best

lambda selected by AIC or BIC.

l1_ratio_best

l1_ratio selected by AIC or BIC.

lambdaList

lambdaList automatically selected when inputting NULL.

References

H. Liang, X. Liu, R. Li, C. L. Tsai. Estimation and testing for partially linear single-index models. Annals of statistics, 2010, 38(6): 3811.

Examples

# EXAMPLE 1 (INTERFACE=FORMULA)
# To select the regularization parameters based on AIC.

n = 50
sigma = 0.1

alpha = matrix(1,2,1)
alpha = alpha/norm(alpha,"2")
beta = matrix(4,1,1)

x = matrix(1,n,1)
z = matrix(runif(n*2),n,2)
y = 4*((z%*%alpha-1/sqrt(2))^2) + x%*%beta + sigma*matrix(rnorm(n),n,1)


fit_plsimest = plsim.est(y~x|z)

# Select the regularization parameters by AIC
res = plsim.lam(y~x|z,h=fit_plsimest$data$h,zetaini = fit_plsimest$zeta,
             lambda_selector='AIC')


# EXAMPLE 2 (INTERFACE=DATA FRAME)
# To select the regularization parameters based on AIC.

n = 50
sigma = 0.1

alpha = matrix(1,2,1)
alpha = alpha/norm(alpha,"2")
beta = matrix(4,1,1)

x = rep(1,n)
z1 = runif(n)
z2 = runif(n) 
X = data.frame(x)
Z = data.frame(z1,z2)

x = data.matrix(X)
z = data.matrix(Z)
y = 4*((z%*%alpha-1/sqrt(2))^2) + x%*%beta + sigma*matrix(rnorm(n),n,1)

fit_plsimest = plsim.est(xdat=X,zdat=Z,ydat=y)

# Select the regularization parameters by AIC
res2 = plsim.lam(xdat=X,ydat=y,zdat=Z,h=fit_plsimest$data$h,
              zetaini = fit_plsimest$zeta, lambda_selector='AIC')