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 Jim Yocom posted on Friday, December 26, 2003 - 5:13 pm
I am developing a research proposal and am wondering how to model the following strategy, if it is possible to do so.

When using surveys to elicit sensitive information (such as criminal history), a "list technique" is sometimes used to protect respondents' anonymity. A respondent is asked something like:

"Please tell me how many of the following apply to you, but do not tell me which ones -- only the total number.

(a) Won over $1,000 in the lottery in the last year
(b) Had a spouse die in the last year
(c) Spent more than a year in a foreign country in the last ten years
(d) Spent more than two days in jail or prison in the last ten years."

Now, suppose I had a good estimate of the probability of a respondent answering (a), (b), or (c), say a 0.005 probability each. These three options are chosen a priori to have very low probabilities, even relative to (d), which is what I'm really interested in.

I want to model the effect of being in prison on some outcome, say earned income:
PRISON --------------> INCOME
(latent class) (continuous observed)

Fox and Tracy (1986) [ISBN#0803923090] suggest that randomized response models, very closely related to this strategy, can be modeled using SEM, but they do not give any hints as to how. I am ashamed to admit that I'm somewhat baffled.

How might I use the total number reported by the respondent and the estimated probabilities of answering (a), (b), and (c) to estimate a model like this?
 bmuthen posted on Friday, December 26, 2003 - 5:22 pm
Will get back to you with some randomized response modeling information related to Mplus.
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