Conditional Logistic Regression? Firstly, I am new to all of this.
I am currently trying to predict the chance of different students finishing top of their class. Students will be separated into different groups depending on the class they are in (class id), and obviously only one student can finish top of each class (top of class=1, not top of class=0). I have 5 potential variables based on previous scores in past exams, the student's attendance etc
From the basic research I have done, this seems like it would be a conditional logisitic regression, is that correct?
Is it possible to run a conditional logistic regression when there are a different number of students in each class? For example, class 1 has 35 students, class 2 has 18 students, class 3 has 26 students etc.
If so, what would be the best approach for doing this moving forward, what is the best software/package for using conditional logistic regression? I have found lots of support for logistic regression online but not for conditional logistic regression.
Thanks

As discussed in the comments, you have a dataset of exam scores from previous years. It makes more sense to build a model for predicting a student's final exam score based on various covariates (previous exam scores, attendance, etc.), then use this to predict the probability each student finishes top of their current class.
For simplicity, suppose that you're using a linear regression model for the exam scores. You can estimate the desired probabilities with a simple simulation scheme.
Consider the 35 students from Class 1. If $\hat{y}_i$ is the predicted score for the $i$th student and $\hat{\sigma}_{y_i}$ the associated standard error, you can draw a sample $\tilde{Y}_i^{(1)}\sim\mathcal{N}(\hat{y}_i, \hat{\sigma}_{y_i})$, $i=1,\ldots,35$, from the forecast distribution.
Now repeat the process $N$ times (some large number) and look at how many times each student finishes top of the class.
