olkin_beta_ratio {r2redux}

olkin_beta_ratio function

Description

This function derives variance of beta1^2 / R^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 (see Olkin and Finn 1995).

Usage

olkin_beta_ratio(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

sampel size

Value

This function will generate the variance of the proportion, i.e. beta1_2/R^2.The outputs are listed as follows.

ratio_var

Variance of ratio

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=dat2
omat=cor(dat)[1:3,1:3]
#omat
#1.0000000 0.1497007 0.136431
#0.1497007 1.0000000 0.622790
#0.1364310 0.6227900 1.000000

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

#r2redux output

#output$ratio_var (Variance of ratio)
#0.08042288