Multi-choice stratified randomized response model with two-stage classification. (English) Zbl 07498016
Summary: Generally, stratification gives a small error and greater precision than the simple random sampling method in estimating the sample for the study. This paper aims to formulate the sampling problem as a multi-choice programming problem for determining the optimum allocation in the presence of non-response and considering a two-stage stratified Warner’s randomized response model with cost constraint. But, mostly in real-life situations, the cost is not certain. Therefore, in cost constraint, the right-hand side parameter, i.e. total available budget, has been considered as multi-choice in nature. Multiple choices may exist for the fixed cost in the constraint, out of which exactly one has to be selected. The selection should make so that the combination of each choice should provide the best compromise optimum solution. The problem has been formulated as a multi-choice integer nonlinear programming problem, and an illustrative numerical example has been presented to demonstrate the proposed model.
MSC:
| 62-XX | Statistics |
Keywords:
two-stage randomized response model; stratified sampling; optimum allocation; multi-choice programming; non-linear programming; integer programming; sensitive characteristicsReferences:
| [1] | Ravindran, A.; Phillips, DT; Solberg, J., Operations research principles & practice (1987), New York: John Wiley, New York |
| [2] | Hiller, F.; Lieberman, G., Introduction to operations research (1990), New York: McGraw-Hill, New York |
| [3] | Chang, CT., Revised multi-choice goal programming, Appl Math Model, 32, 2587-2595 (2008) · Zbl 1167.90637 |
| [4] | Chang, CT., Multi-choice goal programming, Omega, 35, 389-396 (2007) |
| [5] | Biswal, MP; Acharya, S., Multi-choice multi-objective linear programming problem, J Interdiscip Math, 12, 5, 607-637 (2009) · Zbl 1192.90187 |
| [6] | Biswal, MP; Acharya, S., Transformation of a multi-choice linear programming problem, Appl Math Comput, 210, 182-188 (2009) · Zbl 1180.90182 |
| [7] | Dutta, D.; Murthy, S., Multi-choice goal programming approach for a fuzzy transportation problem, IJRRAS, 2, 2, 132-139 (2010) · Zbl 1191.90099 |
| [8] | Biswal, MP; Acharya, S., Solving multi-choice linear programming problems by interpolating polynomials, Math Comput Model, 54, 1405-1412 (2011) · Zbl 1228.90051 |
| [9] | Roy, SK; Mahapatra, DR; Biswal, MP., Multi-choice stochastic transportation problem with exponential distribution, J Uncertain Syst, 6, 3, 200-213 (2012) |
| [10] | Mahapatra, DR; Roy, SK; Biswal, MP., Multi-choice stochastic transportation problem involving extreme value distribution, Appl Math Model, 37, 4, 2230-2240 (2013) · Zbl 1349.90626 |
| [11] | Gupta, N.; Bari, A., Multi-choice goal programming with trapezoidal fuzzy numbers, Int J Oper Res, 11, 3, 82-90 (2014) |
| [12] | Roy, SK., Multi-choice stochastic transportation problem involving Weibull distribution, Int J Oper Res, 21, 1, 38-58 (2014) · Zbl 1308.90102 |
| [13] | Roy, SK., Transportation problem with multi-choice cost and demand and stochastic supply, J Oper Res Soc China, 4, 2, 193-204 (2016) · Zbl 1342.90026 |
| [14] | Maity, G.; Roy, SK., Solving multi-choice multi-objective transportation problem: a utility function approach, J Uncertain Anal Appl, 2, 1, 11 (2014) |
| [15] | Maity, G.; Roy, SK., Solving a multi-objective transportation problem with nonlinear cost and multi-choice demand, Int J Manag Sci Eng Manag, 11, 1, 62-70 (2016) |
| [16] | Acharya, S.; Biswal, MP., Solving multi-choice multi-objective transportation problem, Int J Math Oper Res, 8, 4, 509-527 (2016) · Zbl 1452.90054 |
| [17] | Khalil, TA; Raghav, YS; Badra, N., Optimal solution of multi-choice mathematical programming problem using a new technique, Am J Oper Res, 6, 1, 167-172 (2016) |
| [18] | Gupta, S.; Ali, I.; Ahmed, A., Multi-choice multi-objective capacitated transportation problem – a case study of uncertain demand and supply, J Stat Manag Syst, 21, 3, 467-491 (2018) |
| [19] | Kamal, M.; Gupta, S.; Chatterjee, P., Bi-level multi-objective production planning problem with multi-choice parameters: a fuzzy goal programming algorithm, Algorithms, 12, 7, 143-162 (2019) |
| [20] | Cochran, WG., Sampling techniques (1977), New York: Wiley, New York · Zbl 0353.62011 |
| [21] | Warner, SL., Randomized response – a survey technique for eliminating evasive bias, J Am Stat Assoc, 60, 63-69 (1965) · Zbl 1298.62024 |
| [22] | Mangat, NS; Singh, R., An alternative randomized response procedure, Biometrika, 77, 439-442 (1990) · Zbl 0713.62011 |
| [23] | Mangat, NS; Singh, R., An improved randomized response strategy, J R Stat Soc B, 56, 1, 93-95 (1994) · Zbl 0788.62013 |
| [24] | Horvitz, DG; Shah, BV; Simmons, WR., The unrelated question randomized response model, Proc Soc Stat Sect Am Stat Assoc, 64, 520-539 (1967) |
| [25] | Kuk, AYC., Asking sensitive questions indirectly, Biometrika, 77, 436-438 (1990) · Zbl 0711.62011 |
| [26] | Chua, TC; Tsui, AK., Procuring honest responses indirectly, J Stat Plan Inference, 90, 107-116 (2000) · Zbl 1109.62305 |
| [27] | Padmawar, VR; Vijayan, K., Randomized response revisited, J Stat Plan Inference, 90, 293-304 (2000) · Zbl 0958.62010 |
| [28] | Chang, HJ; Huang, KC., Estimation of proportion of a qualitative character, Metrika, 53, 269-280 (2001) · Zbl 1008.62519 |
| [29] | Chaudhuri, A., Using randomized response from a complex survey to estimate a sensitive proportion in a dichotomous finite population, J Stat Plan Inference, 94, 37-42 (2001) · Zbl 0971.62002 |
| [30] | Singh, S., A new stochastic randomized response model, Metrika, 56, 131-142 (2002) · Zbl 1433.62037 |
| [31] | Ghufran, S.; Gupta, S.; Ahmed, A., A fuzzy compromise approach for solving multi-objective stratified sampling design, Neural Comp Appl, 1-12 (2020) |
| [32] | Hong, K.; Yum, J.; Lee, H., A stratified randomized response technique, Korean J Appl Stat, 7, 141-147 (1994) · Zbl 1262.62015 |
| [33] | Kim, JM; Warde, WD., A stratified Warner’s randomized response model, J Stat Plan Inference, 120, 12, 155-165 (2004) · Zbl 1232.62033 |
| [34] | Kim, JM; Elam, ME., A two-stage stratified Warner’s randomized response model using optimal allocation, Metrika, 61, 1-7 (2005) · Zbl 1120.62009 |
| [35] | Ghufran, S.; Khowaja, S.; Ahsan, MJ., Optimum allocation in two-stage stratified randomized response model, J Math Model Algor, 12, 4, 383-392 (2013) · Zbl 1277.62049 |
| [36] | Ghufran, S.; Khowaja, S.; Ahsan, MJ., Compromise allocation in multivariate stratified sample surveys under two stage randomized response model, Optimiz Lett, 8, 1, 343-357 (2014) · Zbl 1282.62023 |
| [37] | Ullah, S.; Ali, I.; Bari, A., Fuzzy geometric programming approach in multivariate stratified sample surveys under two stage randomized response model, J Math Model Algorith Oper Res, 14, 4, 407-424 (2015) · Zbl 1330.62269 |
| [38] | LINGO user’s guide. Chicago: Lindo Systems Inc; 2001. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
