single categorical DV, single countinuous IV

Question

Background:

I have a set of student answers to some questions and also their scores, whether the answer is correct or not (1 - not correct, 2 - somewhat correct, 3 - correct). I also have for each question a gold answer so I've tried to predict their correctness based on the similarity of the answers to the correct answer.

I've used LSA (latent semantic analysis), and built the semantic space for each question separately, using all of their answers and the gold standard answer. Then I calculated the cosine similarity between the student answers and the gold standard answer.

Problem:

Which classification meethod would be appropriate for predicting the correctness of student answers based on the similarity to the correct answer?

The problem is a bit weird as I have only one continuous predictor (similarity to the gold standard) and one outcome variable (correctness: 1,2 or 3) so all more complex methods like SVM (support vector machines), decision trees etc don't sense. I was thinking of using LDA (Linear Discriminant Analysis) but wanted to check would it be a good approach.

Answer 1

One possibility you might consider is a form of regression model suitable for ordered categorical response (IV), with cosine similarity as a predictor.

There are many such forms of potentially suitable model for that case

Some extend logistic regression - such as

ordered logistic regression (ordered logit, proportional odds)

Another suitable model is the stereotype model which is related to multinomial logistic regression (which itself is suitable for nominal data but is also at least sometimes used with ordered data)

There's a little more discussion (and links) here