Mathematics and Statistics Vol. 14(1), pp. 91 - 97
DOI: 10.13189/ms.2026.140108
Reprint (PDF) (305Kb)

Design-Consistent Variance Estimation in Multistage Complex Surveys: A Simulation and MICS-Based Comparative Study

Ali Satty ^1,*, Zakariya M. S. Mohammed ^1,2
1 Department of Mathematics, College of Science, Northern Border University, Saudi Arabia
² Center for Scientific Research and Entrepreneurship, Northern Border University, Saudi Arabia

ABSTRACT

Ignoring survey design features such as clustering, stratification, and unequal weighting can lead to underestimated standard errors (SEs) and misleading inference in regression models. This study compares three designconsistent variance estimators, Taylor linearization (TL), Fay's balanced repeated replication (BRR), and the Rao–Wu–Yue bootstrap, using Monte Carlo simulations based on the two-stage stratified structure of UNICEF's Multiple Indicator Cluster Surveys (MICS). Nine scenarios combine intraclass correlation (ICC = 0.01–0.10) with weight variability (=0.2–1.0) to assess 95% coverage, SE calibration, and confidence interval (CI) width. Coverage was generally near nominal when clustering was weak to moderate (ICC ≤ 0.05), with mild under-coverage (about 90%) at ICC = 0.10 across methods. SEs were well calibrated (SE-ratios ≈ 0.93–1.03). CI width was driven primarily by weight heterogeneity, increasing markedly with larger , whereas ICC had a smaller impact. In an application to 2018–2019 MICS data on childhood diarrhea, point estimates (odds ratios) were identical across methods; BRR and RWY bootstrap yielded slightly wider, more conservative CIs. Overall, TL is most efficient under moderate design effects, while replication methods offer greater robustness when clustering and weight dispersion are high, providing practical guidance for MICS-type analyses.

KEYWORDS
Complex Survey Design, Variance Estimation, Taylor Linearization, Balanced Repeated Replication, Rao–Wu–Yue Bootstrap

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ali Satty , Zakariya M. S. Mohammed , "Design-Consistent Variance Estimation in Multistage Complex Surveys: A Simulation and MICS-Based Comparative Study," Mathematics and Statistics, Vol. 14, No. 1, pp. 91 - 97, 2026. DOI: 10.13189/ms.2026.140108.

(b). APA Format:
Ali Satty , Zakariya M. S. Mohammed (2026). Design-Consistent Variance Estimation in Multistage Complex Surveys: A Simulation and MICS-Based Comparative Study. Mathematics and Statistics, 14(1), 91 - 97. DOI: 10.13189/ms.2026.140108.