In this paper, an introduction to some existing Item Response Theory (IRT)
models for Local Item Dependencies (LIDs) is presented together with an app
lication. First, four LID models introduced by Hoskens and De Boeck (1997)
are discussed and a more general model is derived. Second, it is described
in broad outline how these models can be estimated and tested statistically
via a loglinear approach. Third, responses are examined on questions that
cannot be understood by the respondents. For this purpose a Polish Question
naire was used in which there was no clear indication in the items of which
response (yes or no) had to be chosen. An interpretable dependency structu
re was found for the first part of the test, but it could not be validated
for the entire test. In conclusion, the problems are discussed that are inh
erent to the classical estimation and testing procedure when dealing with l
ocal item dependencies and some solutions are offered.