plsim.ini {PLSiMCpp}

Initialize coefficients

Description

Xia et al.'s MAVE method is used to obtain initialized coefficients \alpha_0 and \beta_0 for PLSiM

Y = \eta(Z^T\alpha) + X^T\beta + \epsilon

.

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 \alpha_0, and zeta_i[(ncol(z)+1):(ncol(z)+ncol(x))] is the initial coefficient vector \beta_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)