Using Fence Methods for Model Selection

This method is a new class of model selection strategies, for mixed model selection, which includes linear and generalized linear mixed models. The idea involves a procedure to isolate a subgroup of what are known as correct models (of which the optimal model is a member). This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from among those within the fence according to a criterion which can be made flexible. References: 1. Jiang J., Rao J.S., Gu Z., Nguyen T. (2008), Fence Methods for Mixed Model Selection. The Annals of Statistics, 36(4): 1669-1692. < https://projecteuclid.org/euclid.aos/1216237296>. 2. Jiang J., Nguyen T., Rao J.S. (2009), A Simplified Adaptive Fence Procedure. Statistics and Probability Letters, 79, 625-629. < https://www.researchgate.net/publication/23991417_A_simplified_adaptive_fence_procedure> 3. Jiang J., Nguyen T., Rao J.S. (2010), Fence Method for Nonparametric Small Area Estimation. Survey Methodology, 36(1), 3-11. < http://publications.gc.ca/collections/collection_2010/statcan/12-001-X/12-001-x2010001-eng.pdf>. 4. Jiming Jiang, Thuan Nguyen and J. Sunil Rao (2011), Invisible fence methods and the identification of differentially expressed gene sets. Statistics and Its Interface, Volume 4, 403-415. < http://www.intlpress.com/site/pub/files/_fulltext/journals/sii/2011/0004/0003/SII-2011-0004-0003-a014.pdf>. 5. Thuan Nguyen & Jiming Jiang (2012), Restricted fence method for covariate selection in longitudinal data analysis. Biostatistics, 13(2), 303-314. < https://academic.oup.com/biostatistics/article/13/2/303/263903/Restricted-fence-method-for-covariate-selection-in>. 6. Thuan Nguyen, Jie Peng, Jiming Jiang (2014), Fence Methods for Backcross Experiments. Statistical Computation and Simulation, 84(3), 644-662. < https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3891925/>. 7. Jiang, J. (2014), The fence methods, in Advances in Statistics, Hindawi Publishing Corp., Cairo. . 8. Jiming Jiang and Thuan Nguyen (2015), The Fence Methods, World Scientific, Singapore. < https://www.abebooks.com/9789814596060/Fence-Methods-Jiming-Jiang-981459606X/plp>.