```help rrreg                                                   also see:  regress
-------------------------------------------------------------------------------

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)

```