Design-Based Generalized Linear Mixed Model For Binomial Outcome Two-Stage Survey Using Laplace Approximation With Application To 2021 Nigeria Malaria Indicator Survey Data
DOI:
https://doi.org/10.60787/tnamp.v21.511Keywords:
Design-based model, Sampling weights, Laplace approximation, Malaria indicator, Two-stage designAbstract
Applied statistical analyses have increasingly incorporated complex survey designs, though generalized linear mixed models (GLMMs) remain scarce. This study developed a GLMM for two-stage samples using integrated nested Laplace approximation (INLA) on the 2021 Nigeria Malaria Indicator Survey (NMIS) data. A binomial outcome GLMM was fitted, treating design sampling weights as a Gaussian latent model, and posterior estimates were obtained using INLA. Simulation and real data applications compared classical, weighted, MCMC, and INLA approaches, evaluated through accuracy and model diagnostics. Results indicated that incorporating design weights improved model fits, with the INLA GLMM showing superior performance. INLA also required the least computational time, highlighting its advantage for large survey datasets. The study recommends the design-based GLMM approach using INLA for analyzing large-scale survey data
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Guan, Y. and Haran, M. A (2018). A Computationally Efficient Projection- Based Approach for Spatial Generalized Linear Mixed Models. Journal of Computational and Graphical Statistics, DOI:10.1080/10618600.2018.1425625
Liu, L., and Xiang, L. (2019). Missing covariate data in generalized linear mixed models with distribution‑free random effects. Computational Statistics & Data Analysis, 134, 1‑16. doi:10.1016/j.csda.2018.10.011
Declercq, L., Jamshidi, L., Fernandez-Castilla, B., Beretvas, S.N., Moeyaert, M., Ferron, J.M. and Van den Noortgate, W. (2019). Analysis of single-case experimental count data using the linear mixed effects model: A simulation study. Behavior Research Methods (2019) 51:2477–2497. https://doi.org/10.3758/s13428-018-1091-y
Bandara, K., Abdel-Salam, A.G. and Birch, J.B. (2020). Model robust profile monitoring for the generalized linear mixed model for Phase I analysis. Appl Stochastic Models Bus Ind. 2020;36:1037–1059. DOI: 10.1002/asmb.2587.
Wang, Y., Zhang, X.Y., Lu, H., Croft, J.B. and Greenlund, K.J. (2022). Constructing Statistical Intervals for Small Area Estimates Based on Generalized Linear Mixed Model in Health Surveys. Open Journal of Statistics , 12, 70-81. https://doi.org/10.4236/ojs.2022.121005
Chauvet, J., Trottier, C. and Bry, X. (2019). Component-based regularisation of multivariate generalised linear mixed models. Journal of Computational and Graphical Statistics, In press, 10.1080/10618600.2019.1598870. hal-02064508
Achana, F., Gallacher, D., Oppong , R., Kim, S., Petrou, S., Mason, J. and Crowther, M. (2021). Multivariate Generalized Linear Mixed-Effects Models for the Analysis of Clinical Trial–Based Cost-Effectiveness Data. Medical Decision Making 2021, Vol. 41(6) 667–684
da Silva, G.P., Laureano, H.A., Petterle, R.R., Junior, P.J.R. and Bonat, W.H. (2022). Multivariate generalized linear mixed models for underdispersed count data. arXiv:2205.10486v1 [stat.ME] 21 May 2022
da Silva, G.P., Laureano, H.A., Petterle, R.R., Junior, P.J.R. and Bonat, W.H. (2023). Multivariate Generalized Linear Mixed Models for Count Data. arXiv:2301.00921v1 [stat.ME] 3 Jan 2023
Adeniyi, I. A. and Yahya, W. B. (2020). Bayesian Generalized Linear Mixed Effects Models Using Normal-Independent Distributions: Formulation and Applications. Munich Personal RePEc Arhcive Paper No. 99165
Liu, C. (1996). Bayesian robust multivariate linear regression with incomplete data. Journal of the American Statistical Association, 91(435), pp 1219-1227.
Yimer, B. B. and Shkedy, Z. (2021) Bayesian inference for generalized linear mixed models: A comparison of different statistical software procedures, RMS: Research in Mathematics & Statistics, 8:1, 1896102, DOI: 10.1080/27658449.2021.1896102
Plummer, M. (2003). JAGS; A Program for Analysis of Bayesian Graphical Models using Gibbs Sampling. Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), Vienna, 20-22 March 2003, 1-10.
Martinez-Minaya, J., Lindgren, F., Lopez-Quilez, A., Simpson, D. and Conesa, D. (2021). The Integrated nested Laplace approximation for fitting models with multivariate response. arXiv:1907.04059v2 [stat.CO] 24 Feb 2021
He, S. and Lee, W. (2022). Generalized linear mixed-effects models for studies using different sets of stimuli across conditions. Front. Psychol. 13:955722. doi: 10.3389/fpsyg.2022.955722
Xu, W. and Zhou, H. (2012). Mixed effect regression analysis for a cluster-based two- stage outcome-auxiliary-dependent sampling design with a continuous outcome. Biostatistics (2012), 13, 4, pp. 650–664 doi:10.1093/biostatistics/kxs013
Burgard, J. P. and Dörr, P. (2018). Survey-weighted generalized linear mixed models. Research Papers in Economics, No. 1/18, Universität Trier, Fachbereich IV – Volkswirtschaftslehre, Trier
Avery, L., Rotondi, N., McKnight, C., Firestone, M., Smylie, J. and Rotondi, M. (2019). Unweighted regression models perform better than weighted regression techniques for respondent-driven sampling data: results from a simulation study. BMC Medical Research Methodology (2019) 19:202
Florez, A. J., Molenberghs,G., Verbeke, G.Kenward, M.G. Mamouris, P. and Vaes, B. (2021). Fast two-stage estimator for clustered count data with overdispersion. I-BioStat, Universiteit Hasselt, B-3590 Diepenbeek, Belgium.
Dlangamandla, O. (2021). A Modelling Approach to the Analysis of Complex Survey Data. A thesis submitted to Department of Statistics Rhodes University.
Rueda, M.d.M., Cobo, B. and Arcos, A. (2021). Regression Models in Complex Survey Sampling for Sensitive Quantitative Variables. Mathematics 2021, 9, 609. https://doi.org/10.3390/math9060609
Lumley, T (2004). Analysis of complex survey samples. Journal of Statistical Software 2004, vol. 009, issue i08
Lumley, T. (2024). survey: analysis of complex survey samples. R package version 4.4.
Rue, H. and Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications, Chapman & Hall/CRC Press, London.
Held, L., & Sabanés Bové, D. (2014). Applied Statistical Inference. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-37887-4
Fitzmaurice, G., M., D., Verbeke, G. and Molenberghs, G. (2008). Longitudinal Data Analysis, Chapman & Hall.
Stiratelli, R., Laird, N. and Ware, J. H. (1984). Random-effects models for serial observations with binary response, Biometrics 40(4): pp. 961–971. Available from: http://www.jstor.org/stable/2531147.
Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association 88(421): 9–25. Available from: http: //www.jstor.org/stable/2290687.
Sauter, R. (2015). Generalised linear mixed models: likelihood and Bayesian computations with applications in epidemiology. 2015, University of Zurich, Faculty of Science. https://doi.org/10.5167/uzh-152199
Simpson, D., Illian, J. B., Lindgren, F., Sorbye, S. H., & Rue, H. (2017). Going off grid: Computationally efficient inference for log-Gaussian Cox processes. Biometrika, 103 (1), 4.
Ordonez, J.A., Prates, M.O., Bazan, J.L. and Lachos, V.H. (2024). Penalized complexity priors for the skewness parameter of power links. Can J Statistics, 52:98-117. https://doi.org/10.1002/cjs.11769
Handayani, D., Notodiputro, K. A., Sadik, K. and Kurnia, A. (2017). A comparative study of approximation methods for maximum likelihood estimation in generalized linear mixed models (GLMM). AIP Conf. Proc. 1827, 020033 (2017).
https://doi.org/10.1063/1.4979449
Rustand, D., van Niekerk, J., Krainski, E. T., Rue, H., & Proust-Lima, C. (2024). Fast and flexible inference for joint models of multivariate longitudinal and survival data using integrated nested Laplace approximations. Biostatistics, 2024, 25, 2, pp. 429–448. https://doi.org/10.1093/biostatistics/kxad019
Blangiardo M. and Cameletti M. (2015). Spatial and Spatio-temporal Bayesian Models with R –INLA. John Wiley & Sons, Chichester
Opitz T (2017). Latent Gaussian modeling and INLA: A review with focus on space-time applications. Journal of the French Statistical Society 158(3):62-85
Rue, H., Martino, S. and Chopin, N. (2009). Approximate Bayesian Inference for Latent Gaussian Models Using Integrated Nested Laplace Approximations (with discussion). Journal of the Royal Statistical Society, Series B, 71, 319-392.
Lumley, T. and Huang, X. (2023). Linear mixed models for complex survey data: implementing and evaluating pairwise likelihood. arXiv:2307.04944v1 [stat.ME] 11 Jul 2023
Nigeria Malaria Indicator Survey 2021 Final Report. Abuja, Nigeria, and Rockville, Maryland, USA: NMEP, NPC, and ICF.
van Niekerk, J., Bakka, H., Rue, H., and Schenk, O. (2021). New Frontiers in Bayesian Modeling Using the INLA Package in R. Journal of Statistical Software, 100(2). https://doi.org/10.18637/jss.v100.i02
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