Meyer, Mary C.; Hackstadt, Amber J.; Hoeting, Jennifer A. Bayesian estimation and inference for generalised partial linear models using shape-restricted splines. (English) Zbl 1230.62054 J. Nonparametric Stat. 23, No. 4, 867-884 (2011). Summary: A Bayesian approach to generalised partial linear regression models is proposed, where regression functions are modelled nonparametrically using regression splines, with assumptions about shape and smoothness. The knots may be modelled as fixed or free, incorporating a reversible-jump Markov chain Monte Carlo algorithm for the latter. The modelling framework along with vague prior distributions provides more flexibility compared with other Bayesian constrained smoothers; further, the method is simpler, more intuitive, easier to implement, and computationally faster. Inference concerning parametrically modelled covariates can be accomplished using approximate marginal distributions, with standard Bayes model selection methods for more general inference. Simulations show that the inference methods have desirable Bayesian and frequentist properties. In particular, these methods often perform similarly to standard parametric methods when the parametric assumptions are met and are superior when the assumptions are violated. The R code to implement the methods described here is available at www.stat.colostate.edu/ meyer/code.htm. Cited in 16 Documents MSC: 62G08 Nonparametric regression and quantile regression 62J12 Generalized linear models (logistic models) 62F15 Bayesian inference 65C40 Numerical analysis or methods applied to Markov chains 65C60 Computational problems in statistics (MSC2010) 62-04 Software, source code, etc. for problems pertaining to statistics Keywords:shape restrictions; monotone; smoothing; semi-parametric; reversible-jump Markov chain Monte Carlo Software:bnpmr; R PDFBibTeX XMLCite \textit{M. C. Meyer} et al., J. Nonparametric Stat. 23, No. 4, 867--884 (2011; Zbl 1230.62054) Full Text: DOI References: [1] DOI: 10.2307/2408384 · doi:10.2307/2408384 [2] DOI: 10.2307/2686057 · Zbl 04557029 · doi:10.2307/2686057 [3] DOI: 10.2307/1390616 · doi:10.2307/1390616 [4] DOI: 10.1111/j.1541-0420.2008.01060.x · Zbl 1159.62023 · doi:10.1111/j.1541-0420.2008.01060.x [5] DOI: 10.1198/073500107000000223 · doi:10.1198/073500107000000223 [6] DOI: 10.1007/978-1-4612-1276-8 · Zbl 0949.65005 · doi:10.1007/978-1-4612-1276-8 [7] Delecroix M., Computational Statistics 10 pp 155– (1995) [8] DOI: 10.1111/1467-9868.00128 · Zbl 0907.62031 · doi:10.1111/1467-9868.00128 [9] DOI: 10.1002/sim.1460 · doi:10.1002/sim.1460 [10] DOI: 10.1093/biomet/88.4.1055 · Zbl 0986.62026 · doi:10.1093/biomet/88.4.1055 [11] Givens G. H., Computational Statistics (2005) · Zbl 1079.62001 [12] DOI: 10.1093/biomet/82.4.711 · Zbl 0861.62023 · doi:10.1093/biomet/82.4.711 [13] DOI: 10.1214/aos/1009210683 · Zbl 1012.62030 · doi:10.1214/aos/1009210683 [14] DOI: 10.1002/sim.1306 · doi:10.1002/sim.1306 [15] DOI: 10.1198/016214503000143 · Zbl 1041.62059 · doi:10.1198/016214503000143 [16] DOI: 10.1111/j.1467-9868.2005.00521.x · Zbl 1101.62016 · doi:10.1111/j.1467-9868.2005.00521.x [17] DOI: 10.1016/j.csda.2006.04.021 · Zbl 1162.62444 · doi:10.1016/j.csda.2006.04.021 [18] DOI: 10.2307/2291091 · Zbl 0846.62028 · doi:10.2307/2291091 [19] DOI: 10.1198/1061860043010 · doi:10.1198/1061860043010 [20] DOI: 10.1016/0378-3758(94)00106-6 · Zbl 0833.62040 · doi:10.1016/0378-3758(94)00106-6 [21] DOI: 10.1016/S0167-9473(02)00066-X · Zbl 1072.62538 · doi:10.1016/S0167-9473(02)00066-X [22] DOI: 10.1214/aos/1176348117 · Zbl 0737.62038 · doi:10.1214/aos/1176348117 [23] DOI: 10.1111/1467-9469.00147 · Zbl 0932.62051 · doi:10.1111/1467-9469.00147 [24] DOI: 10.1214/ss/1009213727 · Zbl 1059.62535 · doi:10.1214/ss/1009213727 [25] DOI: 10.1214/08-AOAS167 · Zbl 1149.62033 · doi:10.1214/08-AOAS167 [26] DOI: 10.1198/016214502388618654 · Zbl 1048.62071 · doi:10.1198/016214502388618654 [27] DOI: 10.1111/j.0006-341X.2004.00184.x · Zbl 1125.62023 · doi:10.1111/j.0006-341X.2004.00184.x [28] Newton M. A., Journal of the Royal Statistical Society. Series B 56 pp 3– (1994) [29] Nierenberg D., American Journal of Epidemiology 130 pp 511– (1989) [30] DOI: 10.1111/j.0006-341X.2001.00518.x · Zbl 1209.62039 · doi:10.1111/j.0006-341X.2001.00518.x [31] R: A Language and Environment for Statistical Computing (2009) [32] DOI: 10.1093/biomet/80.3.489 · Zbl 0787.62115 · doi:10.1093/biomet/80.3.489 [33] DOI: 10.1214/ss/1177012761 · doi:10.1214/ss/1177012761 [34] Ramsey F. L., The Statistical Sleuth: A Course in Methods of Data Analysis, 2. ed. (2002) · Zbl 1329.62005 [35] DOI: 10.1111/1467-9868.00095 · doi:10.1111/1467-9868.00095 [36] DOI: 10.1111/j.1467-9868.2008.00677.x · Zbl 1231.62058 · doi:10.1111/j.1467-9868.2008.00677.x [37] DOI: 10.1007/BF02736124 · Zbl 1088.62055 · doi:10.1007/BF02736124 [38] DOI: 10.1198/106186007X180949 · doi:10.1198/106186007X180949 [39] DOI: 10.1198/106186008X321077 · doi:10.1198/106186008X321077 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.