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I am analyzing self-reported delinquency (SRD) data in a school sample of juveniles (sample size = 3406). As expected, most of the juveniles in my sample (approximately 66%) have not shown any of the 15 studied behaviors. The 15 indicators are binary, that means the answers only differ between "not offended" (code=0) and "offended" (code=1) for each offense. Some single SRD behaviors are reported only very rarely. Offending proportions for the 15 SRD items range from 0.8 percent (n = 27) to 15.9 percent (n = 540).

Here are my questions:

  1. Is there some kind of "threshold" for the amount of rare event data (be it a percentage or total number of cases) where it seems not reasonable to analyze this data with the help of IRT?
  2. The second question concerns the estimation of mixture IRT models. I found a paper (Wall et al., 2015) that recommends to estimate mixture IRT models with rare event data (zero-inflation). Despite from fitting better to the model (what it should), is there again a problem with the amount of zero-inflation also in these kind of models?
  3. Is there a different "event threshold" between IRT and mixture IRT models?

If it is not reasonable to analyze data below a specific threshold, what are the best options to deal with this issue?

Would it be, for example, sensible to delete items below this "threshold" to estimate IRT models?

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    $\begingroup$ Good question. If you strongly believe all 15 items measure the same underlying trait, I don't think the rarer events will be a problem. Your numbers are almost equivalent to Osgood et al. (2002). They had graded responses and were able to estimate very good fit. (I don't think the 0-1 responses will result in that big of differences.) $\endgroup$ – Andy W Aug 14 '16 at 15:04
  • $\begingroup$ @AndyW: Thanks for your comment and reference! There have been more researchers, who also computed IRT models with similar rare self-reported delinquency behavior (e.g., Piquero et al., 2002, Raudenbush et al., 2003). But I think that they never mention, if IRT/Rasch models are really suitable for this sort of data. I wondered if there is no (general) reference in which this issue is discussed. $\endgroup$ – FloK Aug 14 '16 at 15:27
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1). I am not aware of any threshold established in the literature or other 'best practice' with regards to this issue although one has to consider their sample size (yours is fairly large) in relation to item response frequency patterns. All else being equal, sparse response patterns with a smaller sample size present estimation difficulties/challenges and standard errors of IRT parameters which are not at all precise or reliable. See also this post 2PLM IRT modeling of rare event behavioral data: Why changing discrimination and difficulty values? which discusses the issue.

2). I am working with the Wall et al. (2015) method (from the paper) at this very moment and had the same question as you. Note that in the Wall et al. method, the structural zero latent class is not part of the estimation or scaling of theta (see the supplementary Mplus syntax they provide). This is the class where all items are zero. So you essentially are extracting the structural zero class from the data and setting that aside while you estimate theta on those with item probabilities > 0. See also this paper: http://www.statmodel.com/download/Muthen_tobacco_2006.pdf which provides additional insight into the Wall et al. (2015) approach.

3). See answer to #2. In addition, if you note in the Wall et al. (2015) supplementary syntax, the mean of theta for the structural zero latent class is set to -100, virtually ensuring 'practically zero probability of endorsement to each item' (i.e., high item thresholds). In contrast, in the class where the latent trait is estimated, probabilities for all items will, by and large, be > 0. This means that item thresholds should be lower (i.e., lower threshold for item endorsement).

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