Bootstrapping size option

[Henry Strawforrd]

In the bootstrap help file, the size option is described as "size(#) ... draw samples of size #; default is _N".

How does this make any sense? If we draw a sample of all observations, then every sample will be the same. We have to use leave-one-out or something.. What am I missing?

[Rich Goldstein]

bootstrap sampling is done WITH replacement so, yes, each sample by default is the same size but differs because of the with replacement re-sampling

[Henry Strawforrd]

How can it be different if in each sample we draw the whole dataset?

[Leonardo Guizzetti]

How can it be different if in each sample we draw the whole dataset?

because of the replacement. Take one observation at random into your new sample, then put it back, meaning you allow it to be possibly selected again. Repeat.

[Felix Bittmann]

Imagine you have 5 individuals in your sample with the IDs

1 2 3 4 5

A bootstrapped sample can look like

1 2 2 3 3 5

So IDs 2 and 3 were drawn twice, 4 not at all. As you can imagine, as soon as samples get larger, the combinatorial possibilities are immense.

[Rich Goldstein]

Felix Bittmann there is a typo in #4 (there are 5 numbers in the first block but 6 in the seance) but that should not detract from the point; sorry for not explaining more fully in #2

[Felix Bittmann]

Thanks for the comment you are absolutely right. The example should be:

IDs

 
 1 2 3 4 5 6

Random bootstrap sample

 
 1 2 2 3 3 5

[Henry Strawforrd]

Ah because Stata's Bootstrap does pairwise bootstrap by default?

[Leonardo Guizzetti]

Ah because Stata's Bootstrap does pairwise bootstrap by default?

I don’t know what that means, but that’s not what we’re demonstrating in this thread.