So Sánh Các Phản Hồi Khảo Sát Không Thể So Sánh: Đánh Giá và Chọn Lựa Các Vignettes Neo Định Hướng
Tóm tắt
Khi các đối tượng khảo sát sử dụng các loại hình phản hồi thứ bậc trong các câu hỏi khảo sát tiêu chuẩn theo những cách khác nhau, độ tin cậy của các phân tích dựa trên dữ liệu thu được có thể bị thiên lệch. Các vignette neo định hướng là một kỹ thuật thiết kế khảo sát, được giới thiệu bởi King và cộng sự (2004, Nâng cao độ tin cậy và khả năng so sánh liên văn hóa của phép đo trong nghiên cứu khảo sát.
Từ khóa
Tài liệu tham khảo
Shannon, 1949, The mathematical theory of communication
King, 2001, Analyzing incomplete political science data: An alternative algorithm for multiple imputation, American Political Science Review, 95, 49, 10.1017/S0003055401000235
King, 1997, A solution to the ecological inference problem: Reconstructing individual behavior from aggregate data
Grendar M. Jr. , and Grendar M. 2003. Maximum probability/entropy translating of contiguous categorical observations into frequencies. Working paper, Institute of Mathematics and Computer Science, Mathematical Institute of Slovak Academy of Sciences, Banska Bystrica.
Paradoxically, entropy was developed as a measure of randomness or the lack of information in a communications signal and was used even earlier in physics as a measure of the disorder, or the amount of thermal energy not available to do work, in a closed system. In contrast, in our context, entropy is roughly the opposite, a measure of the amount of information in our survey responses. What unites the examples is that, in both cases, entropy is a measure of equality.
The plotted proportions are the conditional fitted probabilities from a censored probit model with covariates age, years of education, male dummy, and a China dummy. The cutpoints for the censored ordered probit are assumed constant for all observations.
A library of anchoring vignette examples used in these and other surveys, and other materials, can be found at http://gking.harvard.edu/vign/. Our software for analyzing anchoring vignettes is at http://wand.stanford.edu; see Wand, King, and Lau (forthcoming). Gary King and Jonathan Wand
The estimated entropy for the sleep questions are calculated from the conditional fitted probabilities of a censored probit model with covariates sex, age, weight, years of schooling, and marital status. The same holds for self-care ability, subsequently, except that height is excluded from the set of covariates since it's inclusion leads to an unidentified cutpoint. No country dummy is included because figures are for China only.
We wondered whether it might be possible to determine analytically the minimum entropy without going through the intermediate step of estimating the frequency distribution. We thus posed this question to some experts in the field and soon received very helpful suggestions from Amos Golan, George Judge, and Doug Miller for how to do this in several interesting special cases. We have even received a working paper on the subject generated by our question Grendar and Grendar (2003), and it seems that research on the question continues. Since our needs are more general than current results, we compute the minimum value of entropy, in the presence of a vector-valued C, via a genetic algorithm optimizer, GENOUD (Sekhon and Mebane 1998).
Wand Jonathan , King Gary , and Lau Olivia . Forthcoming. Anchors: Software for anchoring vignettes data. Journal of Statistical Software.
Golan, 1996, Maximum entropy econometrics: Robust estimation with limited data
If two response categories are observed as part of the vector-valued C for the same set of observations and for no others, some of the threshold parameters are not identified. The nonidentification in this unusual special case is partial in the sense that the likelihood still indicates the mass in the sum of the two categories. The problem can be easily addressed by combining the two categories or by using information to construct a prior for the τ's.
The ordering of vignettes is normally chosen by the researchers, but it is also possible to draw upon a consensus ordering by the respondents, so long as only one ordering is used for all respondents for the analysis. Differences between hypothesized ordering of the researchers and the consensus ordering may fruitfully be used for diagnosing problems in the survey instruments, particularly when translating the questions for use in different languages.
Although the optimization procedure produces estimates of the q's, they are ancillary parameters and are of no particular interest in and of themselves. Because our criteria indicate that we are indifferent among all histograms with the same entropy, the only relevant quantity produced by this procedure is the value of the minimum entropy. We would be interested in differences between two densities with the same level of entropy if, for example, we had preferences for measures that provided more precision at a certain portion of the scale or if we only wished to identify some specific percentile or fraction of respondents. In these situations, alternative formal criteria would probably lead to a measure of weighted or relative entropy, such as that computed from the Kullback and Leibler (1951) distance,