Abstract
An nonparametric additive model for the location and dispersion of a continuous response with an arbitrary smooth conditional distribution is proposed. B-splines are used to specify the three components of the model. It can deal with interval censored data and multiple covariates. After a simulation study, the relation between age, the number of years of full-time education and the net income (provided as intervals) available per person in Belgian households is studied from survey data.
Similar content being viewed by others
References
Brezger, A., Lang, S.: Generalized structured additive regression based on Bayesian P-splines. Comput. Stat. Data Anal. 50, 967–991 (2006)
Çetinyürek, A., Lambert, P.: Smooth estimation of survival functions and hazard ratios from interval-censored data using Bayesian penalized B-splines. Stat. Med. 30, 75–90 (2011). doi:10.1002/sim.4081
Collett, D.: Modelling Survival Data in Medical Research. Chapman & Hall, London (1994)
Eilers, P.H.C.: Ill-posed problems with counts, the composite link model and penalized likelihood. Stat. Model. 7, 239–254 (2007)
Eilers, P.H.C., Marx, B.D.: Flexible smoothing with B-splines and penalties (with discussion). Stat. Sci. 11, 89–121 (1996)
ESS: European Social Survey Round 3: data file edition 3.2. Norwegian Social Science Data Services, Norway (2006). http://www.europeansocialsurvey.org/
Fahrmeir, L., Tutz, G.: Multivariate Statistical Modelling Based on Generalized Linear Models, 2nd edn. Springer, Berlin (2001)
Haario, H., Saksman, E., Tamminen, J.: An adaptive Metropolis algorithm. Bernoulli 7, 223–242 (2001)
Hagenaars, A., De Vos, K., Zaidi, A.: Poverty Statistics in the Late 1980’s: Research Based on Micro-data. Office for Official Publications of the European Communities, Luxembourg (1994)
Hastie, T.J., Tibshirani, R.J.: Generalized Additive Models. Chapman & Hall, London (1990)
Hsieh, F.: Empirical process approach in a two-sample location–scale model with censored data. Ann. Stat. 24(6), 2705–2719 (1996)
Jørgensen, B.: The Theory of Dispersion Models. Chapman & Hall, London (1997)
Jullion, A., Lambert, P.: Robust specification of the roughness penalty prior distribution in spatially adaptive Bayesian P-splines models. Comput. Stat. Data Anal. 51, 2542–2558 (2007)
Komárek, A., Lesaffre, E., Hilton, J.: Accelerated failure time model for arbitrarily censored data with smoothed error distribution. J. Comput. Graph. Stat. 14, 726–745 (2005)
Lambert, P.: Smooth semi- and nonparametric Bayesian estimation of bivariate densities from bivariate histogram data. Comput. Stat. Data Anal. 55, 429–445 (2011)
Lambert, P., Eilers, P.H.: Bayesian density estimation from grouped continuous data. Comput. Stat. Data Anal. 53, 1388–1399 (2009)
Lambert, P., Eilers, P.H.C.: Bayesian multidimensional density smoothing. In: Proceedings of the 21st International Workshop on Statistical Modelling, pp. 313–320. Galway (2006)
Lambert, P., Lindsey, J.: Analysing financial returns using regression based on non-symmetric stable distributions. Appl. Stat. 48, 409–424 (1999)
Lambert, P., Collett, D., Kimber, A., Johnson, R.: Parametric accelerated failure time models with random effects and an application to kidney transplant survival. Stat. Med. 23(20), 3177–3192 (2004)
Lang, S., Brezger, A.: Bayesian P-splines. J. Comput. Graph. Stat. 13, 183–212 (2004)
McCullagh, P., Nelder, J.A.: Generalized Linear Models, 2nd edn. Chapman & Hall/CRC, London (1989)
Nelder, J., Wedderburn, R.: Generalized linear models. J. R. Stat. Soc. B 135, 370–384 (1972)
Rigby, R., Stasinopoulos, D.: Generalized additive models for location scale and shape. Appl. Stat. 54(3), 1–38 (2001)
Roeder, K., Wasserman, L.: Practical Bayesian density estimation using mixtures of normals. J. Am. Stat. Assoc. 92, 894–902 (1997)
Thompson, R., Baker, R.J.: Composite link functions in generalized linear models. Appl. Stat. 30, 125–131 (1981)
Van Keilegom, I., Akritas, M.: Transfer of tail information in censored regression models. Ann. Stat. 27(5), 1745–1784 (1999)
Vaupel, J., Manton, K., Stallard, E.: The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16(3), 439–454 (1979)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lambert, P. Nonparametric additive location-scale models for interval censored data. Stat Comput 23, 75–90 (2013). https://doi.org/10.1007/s11222-011-9292-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11222-011-9292-6