Simulation comparison of the empirical properties of the best predictor under the assumption of linear mixed model with correlated and uncorrelated random effects

Małgorzata K.  Krzciuk

doi:https://doi.org/10.59139/ws.2025.01.1

Małgorzata K. Krzciuk Uniwersytet Ekonomiczny w Katowicach, Wydział Zarządzania, Polska / University of Economics, Faculty of Management, Poland ORCID: https://orcid.org/0000-0002-5906-5744 Wiadomości Statystyczne. The Polish Statistician, vol. 70, 2025, 1, s. 1-18 Opublikowano online: 31 stycznia 2025 DOI https://doi.org/10.59139/ws.2025.01.1

17 Wyświetlenia 9 Pobrania

ARTYKUŁ

(Angielski) PDF

STRESZCZENIE

In the paper, we are considering the problem of the prediction for small areas under the assumption of a linear mixed model with correlated random effects. The aim of the simulation study was to analyse the properties of the proposed empirical best predictors (EBP) under the assumption of the model with two correlated random effects specific for domains. Additionally, we addressed the problem of the reduced accuracy resulting from the estimation of model parameters and the influence of model misspecification in the case of the lack of correlation. Scripts for the Monte Carlo simulation analyses are prepared in R language and based on real data on entities registered in the REGON base in 2017 from the Local Data Bank of Statistics Poland.
The study demonstrates that the EBP for a model with correlation has good properties even if no correlation between random effects is assumed. In such a case, the mean loss of accuracy resulting from the model misspecification is no more than 2%. The results indicate that for larger sample sizes and more realisations of random effects, the model parameters, for example ????, are estimated more accurately, which can have a significant impact on the properties of the proposed predictor, including its accuracy.

SŁOWA KLUCZOWE

small area estimation, prediction, empirical best predictor, EBP, linear mixed model, Monte Carlo, simulation study

JEL

C53, C51, C63, C83

BIBLIOGRAFIA

Battese, G. E., Harter, R. M., & Fuller, W. A. (1988). An error-components model for prediction of county crop areas using survey and satellite data. Journal of the American Statistical Association, 83(401), 28–36. https://doi.org/10.1080/01621459.1988.10478561.

Biecek, P. (2012). Analiza danych z programem R. Modele liniowe z efektami stałymi, losowymi i mieszanymi. Wydawnictwo Naukowe PWN.

Brewer, K. E. W. (1975). A simple procedure for sampling ?pswor. Australian Journal of Statistics, 17(3), 166–172. https://doi.org/10.1111/j.1467-842X.1975.tb00954.x.

Dempster, A. P., Rubin, D. B., & Tsutakawa, R. K. (1981). Estimation in Covariance Components Models. Journal of the American Statistical Association, 76(374), 341–353. https://doi.org/10.2307/2287835.

Dumont, C., Chenel, M., & Mentré, F. (2014). Influence of covariance between random effects in design for nonlinear mixed-effect models with an illustration in pediatric pharmacokinetics. Journal of Biopharmaceutical Statistics, 24(3), 471–492. https://doi.org/10.1080/10543406.2014.888443 .

Gadbury, G. L., Xiang, Q., Yang, L., Barnes, S., Page, G. P., & Allison, D. B. (2008). Evaluating Statistical Methods Using Plasmode Data Sets in the Age of Massive Public Databases: An Illustration Using False Discovery Rates. PLoS Genetics, 4(6), 1–8. https://doi.org/10.1371 /journal.pgen.1000098 .

Krzciuk, M. K. (2020). On empirical best linear unbiased predictor under a Linear Mixed Model with correlated random effects. Econometrics. Ekonometria. Advances in Applied Data Analysis, 24(2), 17–29. https://doi.org/10.15611/eada.2020.2.02.

Krzciuk, M. K., & Żądło, T. (2014a). On some tests of variance components for linear mixed models. Studia Ekonomiczne. Zeszyty Naukowe Uniwesytetu Ekonomicznego w Katowicach, 189, 77–85. https://www.ue.katowice.pl/fileadmin/_migrated/content_uploads/8_M.K.Krzciuk_T.Zadlo_On_some_tests_of_variance..._01.pdf.

Krzciuk, M. K., & Żądło, T. (2014b). On some tests of fixed effects for linear mixed models. Studia Ekonomiczne. Zeszyty Naukowe Uniwesytetu Ekonomicznego w Katowicach, 189, 49–57. https://www.ue.katowice.pl/fileadmin/_migrated/content_uploads/5_M.K.Krzciuk_T.Zadlo_On _some_tests_of_fixed..._01.pdf .

Marhuenda, Y., Molina, I., Morales, D., & Rao, J. N. K. (2017). Poverty mapping in small areas under a twofold nested error regression model. Journal of the Royal Statistical Society. Series A (Statistics in Society), 180(4), 1111–1136. https://doi.org/10.1111/rssa.12306.

Menec, V., Lix, L., Steinbach, C., Ekuma, O., Sirski, M., Dahl, M., & Soodeen, R. A. (2004). Patterns of Health Care Use and Cost at the End of Life. Manitoba Centre for Health Policy. http://mchp-appserv.cpe.umanitoba.ca/reference/end_of_life.pdf.

Molina, I., & Rao, J. N. K. (2010). Small area estimation of poverty indicators. Canadian Journal of Statistics, 38(3), 369–385. https://doi.org/10.1002/cjs.10051.

Molina, I., & Rao, J. N. K (2015). Small Area Estimation. John Wiley and Sons. https://doi.org/10.1002/9781118735855.

Moura, F. A. S., & Holt, D. (1999). Small area estimation using multilevel models. Survey Methodology, 25(1), 73–80. https://www150.statcan.gc.ca/n1/en/pub/12-001-x/1999001/article/4714-eng.pdf?st=1HNkUIbE.

Nelsen, R. B. (1999). An Introduction to Copulas. Springer. http://dx.doi.org/10.1007/978-1-4757-3076-0.

Ogungbenro, K., Graham, G., Gueorguieva, I., & Aarons, L. (2008). Incorporating correlation in interindividual variability for the optimal design of multiresponse pharmacokinetic experiments. Journal of Biopharmaceutical Statistics, 18(2), 342–358. https://doi.org/10.1080/10543400701697208.

Pratesi, M., & Salvati, N. (2008). Small Area Estimation: The EBLUP Estimator Based on Spatially Correlated Random Area Effects. Statistical Methods & Applications, 17(1), 113–141. https://doi.org/10.1007/s10260-007-0061-9.

Pratesi, M., & Salvati, N. (2009). Small Area Estimation in the Presence of Correlated Random Area Effects. Journal of Official Statistics, 25(1), 37–53.

R Core Team. (2022). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. https://www.r-project.org/.

Schreck, N., Slynko, A., Saadati, M., & Benner, A. (2024). Statistical plasmode simulations-Potentials, challenges and recommendations. Statistics in Medicine, 43(9), 1804–1825. https://doi.org/10.1002/sim.10012.

Skoglund, J., & Karlsson, S. (2001). Specification and estimation of random effects models with serial correlation of general form (SSE/EFI Working paper series in Economics and Finance, No. 433). https://swopec.hhs.se/hastef/papers/hastef0433.pdf.

Tiao, G. C., & Ali, M. M. (1971). Analysis of correlated random effects: linear model with two random components. Biometrika, 58(1), 37–51. https://doi.org/10.2307/2334315.

Torabi, M., & Rao, J. N. K. (2008). Small area estimation under a two-level model. Survey Methodology, 34(1), 11–17. https://www150.statcan.gc.ca/n1/en/pub/12-001-x/2008001/article/10612-eng.pdf?st=ga0W1sNZ.

Tzavidis, N., Zhang, L.-C., Luna, A., Schmid, T., & Rojas-Perilla, N. (2018). From start to finish: a framework for the production of small area official statistics. Journal of the Royal Statistical Society. Series A (Statistics in Society), 181(4), 927–979. https://doi.org/10.1111/rssa.12364.

Wolfinger, R. (1993). Covariance structure selection in general mixed models. Communications in Statistics – Simulation and Computation, 22(4), 1079–1106. https://doi.org/10.1080/03610919308813143.

Wyss, R., Schneeweiss, S., van der Laan, M., Lendle, S. D., Ju, C., & Franklin, J. M. (2021). Using Super Learner Prediction Modeling to Improve High-dimensional Propensity Score Estimation. Epidemiology, 29(1), 96–106. https://doi.org/10.1097/EDE.0000000000000762.

Wróć do: