Maximum Likelihood Score Estimation Method With Fences for Short-Length Tests and Computerized Adaptive Tests

A critical shortcoming of the maximum likelihood estimation (MLE) method for test score estimation is that it does not work with certain response patterns, including ones consisting only of all 0s or all 1s. This can be problematic in the early stages of computerized adaptive testing (CAT) administration and for tests short in length. To overcome this challenge, test practitioners often set lower and upper bounds of theta estimation and truncate the score estimation to be one of those bounds when the log likelihood function fails to yield a peak due to responses consisting only of 0s or 1s. Even so, this MLE with truncation (MLET) method still cannot handle response patterns in which all harder items are correct and all easy items are incorrect. Bayesian-based estimation methods such as the modal a posteriori (MAP) method or the expected a posteriori (EAP) method can be viable alternatives to MLE. The MAP or EAP methods, however, are known to result in estimates biased toward the center of a prior distribution, resulting in a shrunken score scale. This study introduces an alternative approach to MLE, called MLE with fences (MLEF). In MLEF, several imaginary "fence" items with fixed responses are introduced to form a workable log likelihood function even with abnormal response patterns. The findings of this study suggest that, unlike MLET, the MLEF can handle any response patterns and, unlike both MAP and EAP, results in score estimates that do not cause shrinkage of the theta scale.