Saturday, November 8, 2008

Bayesian Estimation

Dr Yeoh is just finishing his presentation on item response theory. The audience is quiet, so the moderator asks a question.


 Dr Yeoh: So in summary, computer adaptive testing works like this: the computer analyzes responses of a student, if the student gets it right, a slightly more difficult question is put up next on the screen, and so on until it gets a reading on the proficiency level of the student.

Moderator: Does the computer know if the student is guessing?

Dr Yeoh: That can be screened for by analyzing previous student responses. After that, this stochastic approach comes in. We can use a Bayesian Estimation if we know something about the background or history of the test-takers. Or we can use a Maximum Likelihood Estimation if we don’t know anything about the test-taking population.

Moderator: Can you give us an example?

Dr Yeoh: OK, like this. If the sky is already cloudy it will help make a prediction on whether it will rain or not. That’s Bayesian. But if we are remote, we don’t know whether the sky is cloudy or not, and we make a prediction based on previous cases, the history of the area, assuming a normal distribution, that’s Maximum Likelihood Estimation.

Moderator: That’s all we have time for. Please remember there are two discussion rooms. There is this fantastic room, E1, with hi-tech presentations, but the other one is, the other room, E2, is ah, wonderful too.



One of the moderator’s tasks is to make a presentation conclude smoothly. Clarifying questions such as “Can you give us an example?” are a reliable standby.

Note the moderator’s dropped guard, flagged by the contrastive conjunction “but”, in expressing unconscious preference for Room E1 over E2.



Matt Barney, Ph.D. said...

Rasch measurement has many benefits in CAT over IRT - was this covered as well:

a) Smaller sample sizes required
b) Because all slopes are the same, with a large enough item bank, item over exposure is not a concern

Barry Natusch said...

Very stimulating questions. Thank you Matt. Moderator dozed off at one point in the presentation, and he says, Rasch could have slipped in unnoticed.

However, presenter claims (a) sample sizes between 10 and a thousand were discussed, as was (b) advantage of a large item bank.

Just a question: Is it so that accommodating test-taker guessing is difficult in the Rasch approach as the left asymptote always approaches a zero probability?