cubicBsplines - Computation of a Cubic B-Spline Basis and Its Derivatives

Computation of a cubic B-spline basis for arbitrary knots. It also provides the 1st and 2nd derivatives, as well as the integral of the basis elements. It is used by the author to fit penalized B-spline models, see e.g. Jullion, A. and Lambert, P. (2006) <doi:10.1016/j.csda.2006.09.027>, Lambert, P. and Eilers, P.H.C. (2009) <doi:10.1016/j.csda.2008.11.022> and, more recently, Lambert, P. (2021) <doi:10.1016/j.csda.2021.107250>. It is inspired by the algorithm developed by de Boor, C. (1977) <doi:10.1137/0714026>.

Last updated 2 years ago

3.65 score 1 stars 3 packages 2 scripts 222 downloads

ordgam - Additive Model for Ordinal Data using Laplace P-Splines

Additive proportional odds model for ordinal data using Laplace P-splines. The combination of Laplace approximations and P-splines enable fast and flexible inference in a Bayesian framework. Specific approximations are proposed to account for the asymmetry in the marginal posterior distributions of non-penalized parameters. For more details, see Lambert and Gressani (2023) <doi:10.1177/1471082X231181173> ; Preprint: <arXiv:2210.01668>).

Last updated 1 years ago

3.02 score 21 scripts 557 downloads

degross - Density Estimation from GROuped Summary Statistics

Estimation of a density from grouped (tabulated) summary statistics evaluated in each of the big bins (or classes) partitioning the support of the variable. These statistics include class frequencies and central moments of order one up to four. The log-density is modelled using a linear combination of penalised B-splines. The multinomial log-likelihood involving the frequencies adds up to a roughness penalty based on the differences in the coefficients of neighbouring B-splines and the log of a root-n approximation of the sampling density of the observed vector of central moments in each class. The so-obtained penalized log-likelihood is maximized using the EM algorithm to get an estimate of the spline parameters and, consequently, of the variable density and related quantities such as quantiles, see Lambert, P. (2021) <arXiv:2107.03883> for details.

Last updated 2 years ago

3.00 score 2 stars 4 scripts 206 downloads

DALSM - Nonparametric Double Additive Location-Scale Model (DALSM)

Fit of a double additive location-scale model with a nonparametric error distribution from possibly right- or interval-censored data. The additive terms in the location and dispersion submodels, as well as the unknown error distribution in the location-scale model, are estimated using Laplace P-splines. For more details, see Lambert (2021) <doi:10.1016/j.csda.2021.107250>.

Last updated 17 days ago

2.98 score 19 scripts 564 downloads