regZIC.test {ConfZIC}

Test whether two ZIC values differ significantly based on minimum ZIC for regression data

Description

Test whether two ZIC values differ significantly based on minimum ZIC for regression data.

Usage

regZIC.test(model1,model2,model_ZIC="AIC",data,alpha=0.05)

Arguments

model1

an object of class “lm".

model2

an object of class “lm".

model_ZIC

type of the information criterion, it can be "AIC", "BIC", or "AICc" (Default is the "AIC").

data

a matrix of n by (m+1) where m is the number of independent variables.First column should be the dependent variable and the rest of the m columns should be the independent variables of the dataset. Maximum of m should be 10.

alpha

significance level \alpha for the hypothesis testing (Default is 0.05).

Details

Consider the hypothesis: Under the null hypothesis that the two expected discrepancies are equal.

H_0: ZIC_i=ZIC_j , H_1: ZIC_i\neq ZIC_j

Z_0=\frac{(\hat{ZIC_i}-\hat{ZIC_j})-0}{\sqrt{SD(ZIC_i,ZIC_j)}}\sim N(0,1)

is calculated empirically.

Value

p-value with significance status.

References

Linhart, H. (1988). A test whether two AIC's differ significantly. South African Statistical Journal, 22(2), 153-161.

Examples

library(ConfZIC)
data(Concrete)
x=Concrete
Y=x[,9] #dependent variable
#independent variables
X1=x[,1];X2=x[,2];X3=x[,3];X4=x[,4];
X5=x[,5];X6=x[,6];X7=x[,7];X8=x[,8];
mydata=cbind(Y,X1,X2,X3,X4,X5,X6,X7,X8) #data matrix
model1=lm(Y~X1); model2=lm(Y~X1+X2)
regZIC.test(model1,model2,model_ZIC="BIC",data=mydata,alpha=0.05)