help rrregalso see:regress-------------------------------------------------------------------------------

Title

rrreg-- Linear probability model for randomized response data

Syntax

rrregdepvar[indepvars] [if] [in] [weight] [,options]

optionsDescription -------------------------------------------------------------------------pwarner(#|varname)probability of the non-negated question in Warner's model; default ispwarner(1)pyes(#|varname)probability of a surrogate "yes"; default ispyes(0)pno(#|varname)probability of a surrogate "no"; default ispno(0)regress_optionsoptions as described in helpregress------------------------------------------------------------------------- Prefix commands allowed as described in helpregress.aweights,fweights,iweights, andpweights are allowed; see weight.

Description

rrregfits 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<. (typicallydepvar=1) indicates a positive outcome (a "yes" answer).

rrregis 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 ispwarner(1). Individually varying probabilities may be specified bypwarner(varname), wherevarnameholds the individual probabilities.

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

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

regress_optionsare options as described in helpregress.

Examples. rrreg infidelity male age, pyes(0.5)

Methods and formulasThe randomized response regression model is estimated by fitting a linear regression to a transformed dependent variable

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

pyesandpnoare 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" ispyes= 0.4*0.75 = 0.3. Likewise, the overall probability of a surrogate "no" ispno= 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)*pwarnerpercent 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, assumespyesandpnoto be non-stochastic. To account for the additional variance induced by stochasticpyesandpnoyou can, for example, applybootstrapto the combined procedure of estimatingpyesandpnoand fittingrrreg.

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

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

Also seeOnline:

regress,bootstrap;rrlogit(if installed)