The Personality Test Item Response Model Containing The Time Variable Based On The Information Function-response Difficulty Assumption

In the field of educational statistics and psychometrics, the response time istreated as a kind of important auxiliary information resources, it can be used todistinguish the bad behavior of participants in the test, improved the design ofcomputer adaptive test, improved the accuracy of measurements and so on. But themodel that contains response time of the personality measurement is rare, so that toestablish a model combined with response time data to measure personality is verymeaningful.In the personality test, it is considered that the response time and responsedifficulties are positively correlated. The famous "distance-difficult" hypothesisbelieved the item-person distance as a standards to measure response difficulties, butthis kind of linear measurement standards exists some defects. This paper proposes anew theory that “information function-difficult distance”hypothesis. Aims to use theinformation function instead of the item-person distance to measure the responsedifficulties. And the information function itself is the monotonic function of theitem-person distance, so the hypothesis is more general.Under the framework of item response theory, for the binary scored personalitytest, we have combined with the information function to set up a joint measurementmodel which contains the response time, the joint model is composed of two submodels, one is the two parameters Logistic model, the other is a logarithm linearmodel about response time variable, and correspondingly have given a two-stepmethod of parameter estimation. Then through the model simulation,we can knowthat: when assess the characteristics of a person, the model combined with theresponse time compared to the model just using the item response data is moreaccuracy in the measurement of the person, it can also indicates the usefulness andthe effectiveness of this new model. And through practical examples,we can achievethe conclusion that the information function and response time were positivelycorrelated.And Illustrated the rationality and applicability of this new theory.Finally,we puts forward some deficiencies of this article in our opinions.