Educational tests often have a cluster of items linked by a common stimulus ("testlet"). In such a design, the dependencies caused between items are called "testlet effects." In particular, the directional testlet effect (DTE) refers to a recursive influence whereby responses to earlier items can positively or negatively affect the scores on later items. This study aims to introduce an innovative measurement model to describe DTEs among multiple polytomouslyscored open-ended items. Through simulations, we found that (1) item and DTE parameters can be accurately recovered in Latent GOLD®, (2) ignoring positive (or negative) DTEs by fitting a standard item response theory model can result in the overestimation (or underestimation) of test reliability, (3) collapsing multiple items of a testlet into a super item is still effective in eliminating DTEs, (4) the popular multidimensional strategy of adding nuisance factors to describe item dependencies fails to account for DTE adequately, and (5) fitting the proposed model for DTE to testlet data involving nuisance factors will observe positive DTEs but will not have a better fit. Moreover, using the proposed model, we demonstrated the coexistence of positive and negative DTEs in a real history exam.