How to conduct parametric bootstrapping in R? - r

Question

I am working with the orings data set in the faraway package in R. I have written the following grouped binomial model:
orings_model <- glm(cbind(damage, 6-damage) ~ temp, family = binomial, data = orings)
summary(orings_model)
I then constructed the Chi-Square test statistic and calculated the p-value:
pchisq(orings_model$null.deviance, orings_model$df.null,lower=FALSE)
First, I would like to generate data under the null distribution for this test statistic using rbinom with the average proportion of damaged o-rings (i.e., the variable "damage"). Second, I would like to recompute the above test statistic with this new data. I am not sure how to do this.
And second, I want to the process above 1000 times, saving the test statistic
each time. I am also not sure how to do this. My inclination is to use a for loop, but I am not sure how to set it up. Any help would be really appreciated!

Answer 1

It is not completely clear what you're looking to do here, but we can at least show some quick principles of how we can achieve this, and then hopefully you can get to your goal.
1) Simulating the null model
It is not entirely clear that you would like to simulate the null model here. It seems more like you're interested in simulating the actual model fit. Note that the null model is the model with form cbind(damage, 6-damage) ~ 1, and the null deviance and df are from this model. Either way, we can simulate data from the model using the simulate function in base R.
sims <- simulate(orings_model, 1000)
If you want to go the manual way estimate the mean vector of your model and use this for the probabilities in your call to rbinom
nsim <- 1000 * nrow(orings)
probs <- predict(orings_model, type = 'response')
sims_man <- matrix(rbinom(nsim, 6, probs),
ncol = 1000)
# Check they are equal:
# rowMeans(sims_man) - probs
In the first version we get a data.frame with 1000 columns each with a n times 2 matrix (damage vs not damage). In the latter we just summon the damage outcome.
2) Perform the bootstrapping
You could do this manually with the data above.
# Data from simulate
statfun <- function(x){
data <- orings_model$data
data$damage <- if(length(dim(x)) > 1)
x[, 1]
else
x
newmod <- update(orings_model, data = data)
pchisq(newmod$null.deviance, newmod$df.null, lower=FALSE)
}
sapply(sims, statfun)
# data from manual method
apply(sims_man, 2, statfun)
or alternatively one could take a bit of time with the boot function, allowing for a standardized way to perform the bootstrap:
library(boot)
# See help("boot")
ran_gen <- function(data, mle){
data$damage <- simulate(orings_model)[[1]][,1]
data
}
boot_metric <- function(data, w){
model <- glm(cbind(damage = damage, not_damage = 6 - damage) ~ temp,
family = binomial, data = data)
pchisq(model$null.deviance,
model$df.null,
lower=FALSE)
}
boots <- boot(orings, boot_metric,
R = 1000,
sim = 'parametric',
ran.gen = ran_gen,
mle = pchisq(orings_model$null.deviance,
orings_model$df.null,
lower=FALSE))
At which point we have the statistic in boots$t and the null statistic in boots$t0, so a simple statistic can be estimated using sum(boots$t > boots$t0) / boots$R (R being the number of replication).