r2_var {r2redux}

r2_var function

Description

This function estimates var(R2(y~x[,v1])) where R2 is the R squared value of the model, where R2 is the R squared value of the model, y is N by 1 matrix having the dependent variable, and x is N by M matrix having M explanatory variables. v1 indicates the ith column in the x matrix (v1 can be multiple values between 1 - M, see Arguments below)

Usage

r2_var(dat, v1, nv)

Arguments

dat

N by (M+1) matrix having variables in the order of cbind(y,x)

v1

This can be set as v1=c(1), v1=c(1,2) or possibly with more values

nv

Sample size

Value

This function will test the null hypothesis for R2. To get the test statistics for R2(y~x[,v1]). The outputs are listed as follows.

rsq

R2

var

Variance of R2

r2_based_p

P-value under the null hypothesis, i.e. R2=0

upper_r2

Upper limit of 95% CI for R2

lower_r2

Lower limit of 95% CI for R2

Examples

#To get the test statistics for R2(y~x[,1])
dat=dat1
nv=length(dat$V1)
v1=c(1)
output=r2_var(dat,v1,nv)
output

#r2redux output

#output$rsq (R2)
#0.03836254

#output$var (variance of R2) 
#0.0001436128

#output$r2_based_p (P-value under the null hypothesis, i.e. R2=0)
#1.188162e-10

#output$upper_r2 (upper limit of 95% CI for R2)
#0.06433782

#output$lower_r2 (lower limit of 95% CI for R2)
#0.01764252


#To get the test statistic for R2(y~x[,1]+x[,2]+x[,3])

dat=dat1
nv=length(dat$V1)
v1=c(1,2,3) 
r2_var(dat,v1,nv)

#r2redux output

#output$rsq (R2)
#0.03836254

#output$var (variance of R2)
#0.0001436128

#output$r2_based_p (R2 based P-value)
#1.188162e-10

#output$upper_r2 (upper limit of 95% CI for R2)
#0.06433782

#output$lower_r2 (lower limit of 95% CI for R2)
#0.0176425


#When comparing two independent sets of PGSs 
#Let’s assume dat1$V1 and dat2$V2 are independent for this example
#(e.g. male PGS vs. female PGS)

nv=length(dat1$V1)
v1=c(1)
output1=r2_var(dat1,v1,nv)
nv=length(dat2$V1)
v1=c(1)
output2=r2_var(dat2,v1,nv)

#To get the difference between two independent sets of PGSs 
r2_diff_independent=abs(output1$rsq-output2$rsq)

#To get the variance of the difference between two independent sets of PGSs 
var_r2_diff_independent= output1$var+output2$var
sd_r2_diff_independent=sqrt(var_r2_diff_independent)

#To get p-value (following eq. 15 in the paper)
chi=r2_diff_independent^2/var_r2_diff_independent
p_value=pchisq(chi,1,lower.tail=FALSE)
#to get 95% CI (following eq. 15 in the paper)
uci=r2_diff_independent+1.96*sd_r2_diff_independent
lci=r2_diff_independent-1.96*sd_r2_diff_independent