Explanation about difference in original and bootstrap value - r

Question

I have the following function; (1) to calculate the deviance difference for each variable I have and (2) to do bootstrap for the deviance difference that I calculated in the first step
set.seed(1001)
xfunction <- function(d,i)
{
glm.snp1 <- glm(PHENOTYPE~d[i], family="binomial", data=training1)
null <- glm.snp1$null.deviance
residual <- glm.snp1$deviance
dDeviance <- null-residual
return(dDeviance)
}
myboot <- function(d)
{
boot(d,xfunction, R=1000)
}
result <- lapply(training1,function(x)myboot(x))
So basically from the result I got the values for original dDeviance (without bootstrap) and I can calculate the mean(dDeviance) from the bootstrap. I need help in explaining why the original and the mean bootstrap values are too different? For example for one of the variable, the original value of dDeviance is 0.024 while the bootstrap mean of dDeviance is 0.000412.

Answer 1

As pointed out in the comments, it's is better to subset the data.frame indices, to make it compatible with boot. If you want to iterate through different variables, and apply this function, it's better to do it within the iterate.
For every bootstrap, you fit the different models and extract the values.
So we re-write the function, and it takes in an extra formula parameter, indep_var which specifies the columns to regress PHENOTYPE against:
xfunction <- function(d,ind,indep_var){
dDeviance = sapply(indep_var,function(V){
f = reformulate(V,response="PHENOTYPE")
glm.snp1 <- glm(f, family="binomial", data=d[ind,])
glm.snp1$null.deviance-glm.snp1$deviance
})
return(dDeviance)
}
We can set up an example dataset:
set.seed(111)
training1 = data.frame(PHENOTYPE=rbinom(100,1,0.5),matrix(rnorm(500),ncol=5))
head(training1)
PHENOTYPE X1 X2 X3 X4 X5
1 1 0.1916634 -0.09152026 -0.9685094 -1.0503824 -0.9137690
2 1 1.5525443 -1.87430581 0.9119331 0.3251424 0.1126909
3 0 0.9142423 -0.66416202 0.0928326 -2.1048716 -2.3597249
4 1 0.3586254 0.20341282 -0.5329309 -0.9551027 -1.5693983
5 0 0.1750956 -2.59444339 -1.6669055 -0.5306399 1.2274569
6 0 -0.8472678 -0.09373393 -0.5743455 0.8274405 0.7620480
And try this on data:
xfunction(training1,1:nrow(training1),indep_var=c("X1","X2","X3"))
X1 X2 X3
0.1189847 0.2512539 0.2684927
Then using bootstrap:
library(boot)
boot(training1,xfunction,R=1000,indep_var=c("X1","X2","X3"))
ORDINARY NONPARAMETRIC BOOTSTRAP
Call:
boot(data = training1, statistic = xfunction, R = 1000, indep_var = c("X1",
"X2", "X3"))
Bootstrap Statistics :
original bias std. error
t1* 0.1189847 1.033286 1.564971
t2* 0.2512539 1.047503 1.863012
t3* 0.2684927 1.005062 1.747959