# Estimating how quickly people submit their answers

In a contest for solving a problem, a person submits his/her answer for the problem at any time during the contest. The contest system provides the person with feedback on the submitted answer. The person can resubmit a modified answer based on the feedback at any time during the contest. This process is repeated until the end of the contest.

I have a dataset for the contest as follows:

Table 1
person feedback submission_time
A     50             20
A     80             50
A     90             60
B     10             35
B     11             80
...


My interest is to estimate how quickly people submitted their answers based on feedback. In other words, how does feedback at the previous time affect the probability of submitting a revised answer? For this purpose, I first considered a survival model and modified the above model as follows:

Table 2
person feedback time0 time1 submission
A      .        0    20      1
A     50        20   50      1
A     80        50   60      1
A     90        60           0
...


As seen in the above table, every submission is present except for the final submission. In this case, does a survival model such as the Cox proportional hazard model provide the proper estimates for my research objectivw? Secondly, are there more suitable statistical models to address my objective than a survival model?

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The main advantage of survival models such as Cox (as opposed to OLS regression) is that survival models deal well with censored data. I am not clear enough on what exactly you are trying to model. Is it something like "time to correct answer"? If so, and if some people never get the answer right, then survival analysis is likely what you want. If it is something else, please elucidate. –  Peter Flom Sep 8 '12 at 12:12
Sorry for my poor explanation.In short, based on the Table 1, I want to estimate the effect of feedback on submission at submission time t on the duration until next submission. For example, in the Table 1, my purpose is to estimate the effect of the feedback 50 at submission time 20 on the duration 30 until next submission time 50, to estimate the effect of the feedback 80 at submission time 80 at submission time 50 on the duration 10 until next submission time 60, and so on. –  siren99 Sep 9 '12 at 4:36
It sounds like you want some form of survival analysis that allows for multiple events. These get complicated. –  Peter Flom Sep 9 '12 at 11:42