Approaches for dealing with item omission include incorrect scoring, ignoring missing values, and approaches for nonignorable missing values and have only been evaluated for certain forms of nonignorability. In this paper we investigate the performance of these approaches for various conditions of nonignorability, that is, when the missing response depends on i) the item response, ii) a latent missing propensity, or iii) both. No approach results in unbiased parameter estimates of the Rasch model under all missing data mechanisms. Incorrect scoring only results in unbiased estimates under very specific data constellations of missing mechanisms i) and iii). The approach for nonignorable missing values only results in unbiased estimates under condition ii). Ignoring results in slightly more biased estimates than the approach for nonignorable missing values, while the latter also indicates the presence of nonignorablity under all simulated conditions. We illustrate the results in an empirical example on PISA data.