olkin_beta_inf {r2redux}

olkin_beta_inf function

Description

This function derives Information matrix for beta1 and beta2 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 (see Olkin and Finn 1995).

Usage

olkin_beta_inf(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 generate information (variance-covariance) matrix of beta1 and beta2.The outputs are listed as follows.

info

2x2 information (variance-covariance) matrix

var1

Variance of beta1

var2

Variance of beta2

var1_2

Variance of difference between beta1 and beta2

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 and beta2 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_beta_inf(omat,nv)
output 

#output$info (2x2 information (variance-covariance) matrix)
#0.2531406 -0.2526212
#-0.2526212  0.2530269            

#output$var1 (variance of beta1)
#0.2531406
            
#output$var2 (variance of beta2)
#0.2530269

#output$var1_2 (variance of difference between beta1 and beta2)
#1.01141