Students who got answers correct scoring lower than ones that missed all questions

[Eduardo Bonet]

Hello,

I am trying to implement scoring using TRI for a dicotomous 3PL model, but I am running into a very strange behavior. There are 45 questions in the exam, and the following plot represents Theta x (Number of correct answers).

What I expected was to have the lowest possible score to the person who did not get any question correct, but I'm seeing that there are people who scored as much as 14 questions that got lower scores than him, in some cases more than 1 sd lower. Here's my code:

m <- mirt(patterns,1, itemtype = "3PL")
theta <- fscores(m, method = "EAP", full.scores = T)

Is this something expected to happen, or there's something wrong with my code?

Thanks in advance

[Phil Chalmers]

Point estimates may not be the only piece of information you want to look at here. Consider the precision of each estimate as well, which will provide information about why this is likely to occur (respondents who answered very few questions will be pulled closer to the population mean, but will have considerably less precision, and therefore will be less reliable overall).

Phil 

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