r2_enrich_beta {r2redux}

r2_enrich_beta

Description

This function estimates var(beta1^2/R^2), beta1 and R^2 are regression coefficient and the coefficient of determination 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). y is N by 1 matrix having the dependent variable, and x1 is N by 1 matrix having the ith explanatory variables. x2 is N by 1 matrix having the jth explanatory variables. v1 and v2 indicates the ith and jth column in the data (v1 or v2 should be a single interger between 1 - M, see Arguments below).

Usage

r2_enrich_beta(dat, v1, v2, nv, exp1)

Arguments

dat

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

v1

These can be set as v1=1, v1=2, v1=3 or any value between 1 - M based on combination

v2

These can be set as v2=1, v2=2, v2=3, or any value between 1 - M based on combination

nv

Sample size

exp1

The expectation of the ratio (e.g. ratio of # SNPs in genomic partitioning)

Value

This function will estimate var(beta1^2/R^2), beta1 and R^2 are regression coefficient and the coefficient of determination from a multiple regression model, i.e. y = x1 * beta1 + x2 * beta2 +e, where y, x1 and x2 are column-standardised. The outputs are listed as follows.

beta1_sq

beta1_sq

beta2_sq

beta2_sq

ratio1

beta1_sq/R^2

ratio2

beta2_sq/R^2

ratio_var1

variance of ratio 1

ratio_var2

variance of ratio 2

upper_ratio1

upper limit of 95% CI for ratio 1

lower_ratio1

lower limit of 95% CI for ratio 1

upper_ratio2

upper limit of 95% CI for ratio 2

lower_ratio2

lower limit of 95% CI for ratio 2

enrich_p1

two tailed P-value for beta1_sq/R^2 is significantly different from exp1

enrich_p1_one_tail

one tailed P-value for beta1_sq/R^2 is significantly different from exp1

enrich_p2

P-value for beta2_sq/R2 is significantly different from (1-exp1)

enrich_p2_one_tail

one tailed P-value for beta2_sq/R2 is significantly different from (1-exp1)

References

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

Examples

#To get the test statistic for the ratio which is significantly
#different from the expectation, this function estiamtes 
#var (beta1^2/R^2), where 
#beta1^2 and R^2 are regression coefficients and the 
#coefficient of dterminationfrom a multiple regression model,
#i.e. y = x1 * beta1 + x2 * beta2 +e, where y, x1 and x2 are 
#column-standardised.

dat=dat2
nv=length(dat$V1)
v1=c(1)
v2=c(2)
expected_ratio=0.04
output=r2_enrich_beta(dat,v1,v2,nv,expected_ratio)
output

#r2redux output

#output$beta1_sq (beta1_sq)
#0.01118301

#output$beta2_sq (beta2_sq)
#0.004980285

#output$ratio1 (beta1_sq/R^2)
#0.4392572

#output$ratio2 (beta2_sq/R^2)
#0.1956205

#output$ratio_var1 (variance of ratio 1)
#0.08042288

#output$ratio_var2 (variance of ratio 2)
#0.0431134

#output$upper_ratio1 (upper limit of 95% CI for ratio 1)
#0.9950922

#output$lower_ratio1 (lower limit of 95% CI for ratio 1)
#-0.1165778

#output$upper_ratio2 upper limit of 95% CI for ratio 2)
#0.6025904

#output$lower_ratio2 (lower limit of 95% CI for ratio 2)
#-0.2113493

#output$enrich_p1 (two tailed P-value for beta1_sq/R^2 is 
#significantly different from exp1)
#0.1591692

#output$enrich_p1_one_tail (one tailed P-value for beta1_sq/R^2 
#is significantly different from exp1)
#0.07958459

#output$enrich_p2 (two tailed P-value for beta2_sq/R2 is 
#significantly different from (1-exp1))
#0.000232035

#output$enrich_p2_one_tail (one tailed P-value for beta2_sq/R2  
#is significantly different from (1-exp1))
#0.0001160175