The research reported here was funded by grants from the National Institute of Alcohol and Alcohol Use (grant R01-AA13814) and the William T. Grant Foundation. We thank Stephen Buka and Scott Novak for helpful comments and Richard Congdon for applications programming to implement the statistical methods reported herein.
A PARTIAL INDEPENDENCE ITEM RESPONSE MODEL FOR SURVEYS WITH FILTER QUESTIONS
Article first published online: 17 NOV 2006
Volume 36, Issue 1, pages 257–300, December 2006
How to Cite
Reardon, S. F. and Raudenbush, S. W. (2006), A PARTIAL INDEPENDENCE ITEM RESPONSE MODEL FOR SURVEYS WITH FILTER QUESTIONS. Sociological Methodology, 36: 257–300. doi: 10.1111/j.1467-9531.2006.00181.x
- Issue published online: 17 NOV 2006
- Article first published online: 17 NOV 2006
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 are independent conditional on the item parameters, the individual's latent trait, and the participant's affirmative responses to each of a set of filter items. In this paper, we propose an item response model for such “partially independent” item response data. We model such item response patterns as a function of a person-specific latent trait and a set of item parameters. Our model can be seen as a generalized hybrid of a discrete-time hazard model and a Rasch model. The proposed procedure yields estimates of (1) person-specific, interval-scale measures of a latent trait (or traits), along with person-specific standard errors of measurement; (2) conditional and marginal item severities for each item in a protocol; (3) person-specific conditional and marginal probabilities of an affirmative response to each item in a protocol; and (4) item information and total survey information. In addition, we show here how to investigate and test alternative conceptions of the dimensionality of the latent trait(s) being measured. Finally, we compare our procedure with a simpler alternative approach to summarizing data of this type.