Incorporate new information into admissions prediction model?

Question

I am at a small college and we are doing basic admissions predictions for who will attend.

We have built a basic logistic regression model that aims to predict the probability of students who we have offered admissions to actually attend. This model is based upon several years of past admissions data for students and likelihood of attending given various features(e.g. SAT, grades, scholarship).

For instance, say in October we may offer 1000 people admission, but we won't know until the following May (our firm deadline) whether they will come. So before May, we just have to estimate which students will come at what probability.

My question is, how do we incorporate additional positive or negative signals from individual students into our model? For instance, say we admit 1000 students in October, and our estimated overall attendance rate for those 1000 students will be 20% based upon our model. Then, in between October and May, a few things happen:

1. Say in December, 200 of those 1000 students tell us they are definitely not coming. That leaves 800 students remaining who still may come. Surely that 800 remaining pool now has a different probability of coming from the 20% rate that applied to the entire 1000 pool. How do I incorporate the information that 200 of 1000 students have definitely told us they are not coming into the probabilities of the remaining 800 students?

2. Imagine that in January 100 of the remaining 800 students call us and say, "We are almost definitely coming." How do I reflect that positive attendance signal for those 100 students?

3. Imagine that in February 200 other of the remaining 800 students don't bother even checking their admission status online, which is a signal that they are very unlikely to come. How do I incorporate that negative signal into my model?

My essential thinking is that if I get a positive signal, somehow I have to slightly reduce the probability of the remaining folks for which I got no signal (and vice-versa), but I don't know how to do that. The logistic regression model is built on past data where we definitively know the outcome of past students.

Answer 1

Some comments:

Say in December, 200 of those 1000 students tell us they are definitely not coming. That leaves 800 students remaining who still may come. Surely that 800 remaining pool now has a different probability of coming from the 20% rate that applied to the entire 1000 pool. How do I incorporate the information that 200 of 1000 students have definitely told us they are not coming into the probabilities of the remaining 800 students?

No modification should be necessary. The logistic regression model gives individual attendance probabilities for each of those 1000 students. That some of them (unknown probably to the others) say they will definitely not come should not influence probabilities for others.

Imagine that in January 100 of the remaining 800 students call us and say, "We are almost definitely coming." How do I reflect that positive attendance signal for those 100 students?

Use historical data about students calling in January saying they will definitely come. How many of then did appear?

Imagine that in February 200 other of the remaining 800 students don't bother even checking their admission status online, which is a signal that they are very unlikely to come. How do I incorporate that negative signal into my model?

Same as former point, use historical data. And, if you don't have them, plan to record them for the future!