The person-response function (PRF) relates the probability of an individual's correct answer to the difficulty of items measuring the same latent trait. Local deviations of the observed PRF from the expected PRF indicate person misfit. We discuss two new approaches to investigate person fit. The first approach uses kernel smoothing to estimate continuous PRF estimates. Graphical displays of PRFs were used to localize and diagnose misfit. The second approach approximates the PRF by a logistic regression model. Hypothesis tests on the regression parameters were used to detect certain types of misfit. A simulation study was conducted to investigate the Type I error rates and the detection rates of the regression approach.