As the computer technology progress, the reaction-time can be automatically recorded by computer-based testing. Thus, response times can be an additional source for describing or gaining information for examinees. An import notion of reaction-time research with a special impact on the current modeling of response times on test items is that of a speed-accuracy tradeoff. Many models were proposed to account for response times (Roskam, 1997; Thissen, 1983; Verhelst, Verstralen & jasnsen, 1997). This paper proposed a new idea for modeling speed and accuracy on test items that is a hierarchical framework.
This model was based on three important points: (1) the within-person level, at which the value of the person parameters is allowed to change over time; (2) the fixed-person level, at which the parameters remain constant; and (3) the level of a population of fixed persons, for which we have a distribution of parameter values across persons. And it contains five key assumptions: (1) a test taker operating at a fixed level of speed; (2) for a fixed test taker, both the response and the time on an item are assumed to be random variables; (3) assume separate item and person parameters both for the distributions of the responses on the items and the time required to produce them; (4) conditional independence between the responses and the response times given the levels of ability and speed at which the test taker operates; and (5) model the relations between speed and accuracy for a population of test takers separately from the impact of these parameters on the responses and times of the individual test takers. The model includes two levels, both a response model and a response-time model were used in the first level, and two different models used in the second level were used for represented the parameters which were specified in the first level models. An empirical data analysis was used for demonstrating the performance of the new model.