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There is a growing need to use response time data to improve measurement quality with the increasing popularity of computerized testing. This work simultaneously models item response and response time to improve on current IRT models that do not account for response time when there is a time limit in real testing. The joint distribution for item response and response time is presented in this work. It is specified as the product of the conditional distribution of response accuracy given response time and the marginal distribution of response time based on the lognormal distribution. A modified version of Thissen's (1983) log linear model is used to fit the response time. Marginal maximum likelihood estimation is developed and employed to estimate the item parameters. In addition, a maximum a posteriori procedure is developed and implemented to estimate person parameters. Three different simulation studies were conducted to evaluate the precision of estimation procedures. The results of item and person parameter estimates based on MML and MAP procedures were found to be consistent and accurate.