help rrreg                                                   also see:  regress
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Title

    rrreg -- Linear probability model for randomized response data


Syntax

        rrreg depvar [indepvars] [if] [in] [weight] [, options]


    options                     Description
    -------------------------------------------------------------------------
      pwarner(#|varname)        probability of the non-negated question in
                                  Warner's model; default is pwarner(1)
      pyes(#|varname)           probability of a surrogate "yes"; default is
                                  pyes(0)
      pno(#|varname)            probability of a surrogate "no"; default is
                                  pno(0)
      regress_options           options as described in help regress
    -------------------------------------------------------------------------
    Prefix commands allowed as described in help regress.
    aweights, fweights, iweights, and pweights are allowed; see weight.


Description

    rrreg fits a linear probability model to data collected using the
    randomized response technique (RRT). depvar=0 indicates a negative
    outcome (a "no" answer); depvar!=0 & depvar<. (typically depvar=1)
    indicates a positive outcome (a "yes" answer).

    rrreg is suited for the analysis of data from Warner's RRT scheme, the
    forced-response RRT, or the unrelated-question RRT with a known
    distribution for the non-sensitive question (see, e.g., Fox and Tracy
    1986).


Options

    pwarner(#|varname) specifies the probability of the non-negated question
        in Warner's RRT scheme. # must be in [0,1] and may not be 0.5. The
        default is pwarner(1). Individually varying probabilities may be
        specified by pwarner(varname), where varname holds the individual
        probabilities.

    pyes(#|varname) specifies the probability of a surrogate "yes" answer. #
        must be in [0,1]. The default is pyes(0). Individually varying
        probabilities may be specified by pyes(varname), where varname holds
        the individual probabilities.

    pno(#|varname) specifies the probability of a surrogate "no" answer. #
        must be in [0,1]. The default is pno(0). Individually varying
        probabilities may be specified by pno(varname), where varname holds
        the individual probabilities.

    regress_options are options as described in help regress.


Examples

        . rrreg infidelity male age, pyes(0.5)


Methods and formulas

    The randomized response regression model is estimated by fitting a linear
    regression to a transformed dependent variable

            depvar - (1 - pyes - pno)*(1 - pwarner) - pyes 
        y = ----------------------------------------------
                 (2*pwarner - 1) * (1 - pyes - pno)
        
    where pwarner is the probability of the negated question in Warner's
    scheme and pyes and pno are the probabilities of a surrogate "yes" and a
    surrogate "no".

    pyes and pno are unconditional (overall) probabilities. For example, in
    an unrelated-question RRT where the probability to be directed to the
    non-sensitive question is 0.4 (i.e. the probability to answer the
    sensitive question is 60%) and the probability to answer "yes" to the
    non-sensitive question is known to be, say, 0.75, the overall probability
    of a surrogate "yes" is pyes = 0.4*0.75 = 0.3. Likewise, the overall
    probability of a surrogate "no" is pno = 0.4*(1-0.75) = 0.1.

    pwarner, however, is conditional, i.e. it only applies to respondents
    that are not instructed to give a surrogate "yes" or "no". That is,
    overall (1-pyes-pno)*pwarner percent of respondents answer the original
    sensitive question, (1-pyes-pno)*(1-pwarner) percent answer the negated
    question.

    In the unrelated question design, if the distribution of the answers to
    the non-sensitive question is unknown, an estimate has to be used to
    determine the probabilities. rrreg, however, assumes pyes and pno to be
    non-stochastic. To account for the additional variance induced by
    stochastic pyes and pno you can, for example, apply bootstrap to the
    combined procedure of estimating pyes and pno and fitting rrreg.


References

    Fox, James Alan, and Paul E. Tracy. 1986. Randomized response: A method
        for sensitive surveys. London: Sage.


Author

    Ben Jann, Institute of Sociology, University of Bern, jann@soz.unibe.ch


Also see

    Online:  regress, bootstrap; rrlogit (if installed)