Publication Details

Two stage randomized response schemes for estimating a multinomial

Type: article

Author(s): Hochberg, Yosef

Pages: 1021-1032

Url: http://www.tandfonline.com/doi/abs/10.1080/03610927508827310

Publication Date: Jan-1975

Journal: Communications in Statistics

Volume: 4

Issue: 11

Issn: 0090-3272

Doi: 10.1080/03610927508827310

Abstract: Warner's (1965) original randomized response technique for dichotomous data was extended by Abul-Ela, et al. (1967) to the case of a multinomial with t ≥ 3 groups, r of which are stigmatizing. A competing approach for estimating a multinomial via the randomized response technique is discussed by Warner (1971). Yet a third approach for the multinomial is considered by Greenberg, et al. (1969) and is based on using an alternate independent question. Here we outline some alternative schemes for estimating the t group proportions when r < t −1, using only one sample. Their realizations for any sampled individual, constitute two-stage schemes. The second stage is conditional on the random individual's response in the first stage. In Section 1 we briefly summarize the three existing methods. Section 2 describes the new procedures and the resulting estimators. In Section 3 we identify the new schemes as special cases of Warner's (1971) general linear randomized response model thereby obtaining alternative estimators based on modified generalized least squares method due to Zellner (1962).