stepwise.PIC {NPRED}

Calculate stepwise PIC

Description

Calculate stepwise PIC

Usage

stepwise.PIC(x, py, nvarmax = 100, alpha = 0.1)

Arguments

x

A vector of response.

py

A matrix containing possible predictors of x.

nvarmax

The maximum number of variables to be selected.

alpha

The significance level used to judge whether the sample estimate in Equation

\hat{PIC} = sqrt(1-exp(-2\hat{PI})

is significant or not. A default alpha value is 0.1.

Value

A list of 2 elements: the column numbers of the meaningful predictors (cpy), and partial informational correlation (cpyPIC).

References

Sharma, A., Mehrotra, R., 2014. An information theoretic alternative to model a natural system using observational information alone. Water Resources Research, 50(1): 650-660.

Examples

data(data1) # AR9 model   x(i)=0.3*x(i-1)-0.6*x(i-4)-0.5*x(i-9)+eps
x <- data1[, 1] # response
py <- data1[, -1] # possible predictors
stepwise.PIC(x, py)

data(data2) # AR4 model:  x(i)=0.6*x(i-1)-0.4*x(i-4)+eps
x <- data2[, 1] # response
py <- data2[, -1] # possible predictors
stepwise.PIC(x, py)

data(data3) # AR1 model  x(i)=0.9*x(i-1)+0.866*eps
x <- data3[, 1] # response
py <- data3[, -1] # possible predictors
stepwise.PIC(x, py)