Item Response Theory (IRT) models are a popular analytic method for self report data. We show how traditional IRT models can be vulnerable to specific kinds of asymmetric measurement error (AME) in self-report data, because the models spread the error to all estimates -- even those of items that do not contribute error. We quantify the impact of this misestimation on traditional IRT models through simulation. Then, we evaluate 3PL and 4PL multiprocess models that allow detailed modeling of response behaviors indicative of AME, which gives the analyst a more informed basis for interpreting traditional IRT models. The 3PL and 4PL multiprocess models are easy to estimate with commonly used statistical software and easy to interpret, making them more likely to be used by non-methodologists. Finally, we conduct simulations and real-data analyses to evaluate these models under different plausible scenarios. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]