Bootstrap with one measurement per individual

Question

Hello,

I have a database with measurements taken repeatedly on individuals. For each new measurement on an individual the measurements differ except for the structural size measurements which were taken once and therefore remain the same.

I want to do a bootstrap but with only one measurement per individual taken randomly at each re-sampling, is it possible to do this with JMP?

Thank you in advance for your help!

Mark_Bailey · Answer

The bootstrap function in JMP Pro does not provide a way to stratify the bootstrap samples. It is intended for the simple, common situation where the individual observations represent the experimental unit and errors. The randomization is intended to develop the empirical sampling distribution under the null hypothesis. This would work if you were to eliminate all but one of the with-in subject responses, for example, the last measurement or the mean measurement, before performing the analysis. The question comes down to the errors: do you believe that the experimental unit is the measurement or the subject? Do you need to model one error or two errors?

Another way to include the individual measurements is to use 'fractional weights' (i.e., non-integer frequency value) in the bootstrap. Instead of trying to include one response at a time, you would give each response a chance to be included. An appropriate weight might be reciprocal local frequency. If you had 5 measurements for the same subject, then use 1/5 = 0.2 for the frequency of all 5 responses. A column formula using 1/Col Number( Y, Subject ) would do the trick.

Also, I want to be clear about your intention. Bootstrapping uses sample with replacement, so even if you had only one measurement per subject, some subjects might not be selected while other subjects might be selected more than once in each bootstrap sample. Is that result your intention?

Jeanne · Answer

Thank you for your response.

In fact, my objective is to obtain an equation that will allow me to predict the amount of fat (in g) in individuals captured in the wild based on several parameters that can be taken in the field (body mass, structural size and visual fat score).

To find my prediction equation, I use a database that includes repeated measurements in captive individuals (measured at different periods of time). For these individuals, I have the amount of fat (in g), body mass and fat score at each measurement.

On the other hand, the structural size remains the same for an individual at each measurement because the structural size was taken only once (at the 1st measurement).

I would therefore like to make a "stratified" bootstrap by selecting only one measurement per individual at each re-sampling, is this possible?

I don't see how to proceed in the JMP help.

Thank you for your feedback.

P_Bartell · Answer

It's not clear to me based on your original post which of the attributes you want to perform bootstrapping on? The attributes measured repeatedly or only once? Also, some more context of the practical problem and sampling strategy and tactics would also be very helpful. I assume the measurements are all of a continuous variable type vs. nominal or some other type of data? In general I suggest reading the JMP documentation surrounding bootstrapping to see what's possible in JMP Pro.

https://www.jmp.com/support/help/en/15.1/index.shtml#page/jmp/overview-of-bootstrapping.shtml