plsim.ini: Initialize coefficients

In PLSiMCpp: Methods for Partial Linear Single Index Model

Initialize coefficients

Description

Xia et al.'s MAVE method is used to obtain initialized coefficients α_0 and β_0 for PLSiM

Y = η(Z^Tα) + X^Tβ + ε

.

Usage

plsim.ini(...)

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

## Default S3 method:
plsim.ini(xdat, zdat, ydat, Method="MAVE_ini", verbose = TRUE, ...)

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).
Method	string, optional (default="MAVE_ini").
verbose	bool, default: TRUE. Enable verbose output.

Value

zeta_i

initial coefficients. zeta_i[1:ncol(z)] is the initial coefficient vector α_0, and zeta_i[(ncol(z)+1):(ncol(z)+ncol(x))] is the initial coefficient vector β_0.

References

Y. Xia, W. Härdle. Semi-parametric estimation of partially linear single-index models. Journal of Multivariate Analysis, 2006, 97(5): 1162-1184.

Examples

# EXAMPLE 1 (INTERFACE=FORMULA)
# To obtain initial values by using MAVE methods for partially
# linear single-index model.

n = 50
sigma = 0.1

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

beta = matrix(4,1,1)

# Case1: Matrix Input
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)

zeta_i = plsim.ini(y~x|z)

# Case 2: Vector Input
x = rep(1,n)
z1 = runif(n)
z2 = runif(n) 
y = 4*((z%*%alpha-1/sqrt(2))^2) + x%*%beta + sigma*matrix(rnorm(n),n,1)

zeta_i = plsim.ini(y~x|z1+z2)


# EXAMPLE 2 (INTERFACE=DATA FRAME)
# To obtain initial values by using MAVE methods for partially
# linear single-index model.

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)

zeta_i = plsim.ini(xdat=X, zdat=Z, ydat=y)

PLSiMCpp documentation built on Sept. 24, 2022, 5:05 p.m.