olkin_beta1_2 {r2redux}

olkin_beta1_2 function

Description

This function derives Information matrix for beta1^2 and beta2^2 where beta1 and 2 are regression coefficients from a multiple regression model, i.e. y = x1 * beta1 + x2 * beta2 + e, where y, x1 and x2 are column-standardised, (i.e. in the context of correlation coefficients,see Olkin and Finn 1995).

Usage

olkin_beta1_2(omat, nv)

Arguments

omat

3 by 3 matrix having the correlation coefficients between y, x1 and x2, i.e. omat=cor(dat) where dat is N by 3 matrix having variables in the order of cbind (y,x1,x2)

nv

Sample size

Value

This function will give information (variance-covariance) matrix of beta1^2 and beta2^2.To get information (variance-covariance) matrix of beta1^2 and beta2^2. Where beta1 and beta2 are regression coefficients from a multiple regression model. The outputs are listed as follows.

info

2x2 information (variance-covariance) matrix

var1

Variance of beta1_2

var2

Variance of beta2_2

var1_2

Variance of difference between beta1_2 and beta2_2

References

Olkin, I. and Finn, J.D. Correlations redux. Psychological Bulletin, 1995. 118(1): p. 155.

Examples

#To get information (variance-covariance) matrix of beta1_2 and beta2_2 where 
#beta1 and 2 are regression coefficients from a multiple regression model.
dat=dat1
omat=cor(dat)[1:3,1:3]
#omat
#1.0000000 0.1958636 0.1970060
#0.1958636 1.0000000 0.9981003
#0.1970060 0.9981003 1.0000000

nv=length(dat$V1)
output=olkin_beta1_2(omat,nv) 
output

#output$info (2x2 information (variance-covariance) matrix)
#0.04146276 0.08158261
#0.08158261 0.16111124             

#output$var1 (variance of beta1_2)
#0.04146276 
            
#output$var2 (variance of beta2_2)
#0.1611112

#output$var1_2 (variance of difference between beta1_2 and beta2_2)
#0.03940878