3. A Partial Independence Item Response Model for Surveys with Filter Questions

@article{Reardon20063AP,
  title={3. A Partial Independence Item Response Model for Surveys with Filter Questions},
  author={Sean F. Reardon and Stephen Raudenbush},
  journal={Sociological Methodology},
  year={2006},
  volume={36},
  pages={257 - 300}
}
In many surveys, responses to earlier questions determine whether later questions are asked. The probability of an affirmative response to a given item is therefore nonzero only if the participant responded affirmatively to some set of logically prior items, known as “filter items.” In such surveys, the usual conditional independence assumption of standard item response models fails. A weaker “partial independence” assumption may hold, however, if an individual's responses to different items… 

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