f: Defining smooth terms in DDPstar formulae

In DDPstar: Density Regression via Dirichlet Process Mixtures of Normal Structured Additive Regression Models

Defining smooth terms in DDPstar formulae

Description

Auxiliary function used to define smooth terms using Bayesian P-splines within DDPstar model formulae. The function does not evaluate the smooth - it exists purely to help set up a model using P-spline based smoothers.

Usage

f(..., by = NULL, nseg = 5, bdeg = 3, pord = 2, atau = 1, btau = 0.005,
  prior.2D = c("anisotropic", "isotropic"))

Arguments

...	a list of up to two covariates to construct the smooth term.
by	a numeric or factor variable of the same dimension as each covariate. Following package mgcv, in the numeric case the elements multiply the smooth, evaluated at the corresponding covariate values (a ‘varying coefficient model’). Here, the smooth function does not exclude the intercept, so the by variable should not be added as an additional main effect. In the factor case, a replicate of the smooth is produced for each factor level. In this case, these smooths will exclude the intercept, so the factor needs to be added as a main effect as well (see details).
nseg	the number of segments for the (marginal) B-spline bases used to represent the smooth term. Numerical vector of length equal to the number of covariates. Atomic values are also valid, being recycled. The default value is 5.
bdeg	the order of the polynomial for the (marginal) B-spline bases for this term. Numerical vector of length equal to the number of covariates. Atomic values are also valid, being recycled. The default value is 3 (cubic B-splines).
pord	penalty order. Numerical vector of length equal to the number of covariates. Atomic values are also valid, being recycled. The default value is 2 (second-order penalty).
atau	a numeric value. Hyperparameter; shape parameter of the gamma prior distribution for the precisions (inverse variances) of the smooth term. The default is 1.
btau	a numeric value. Hyperparameter; rate parameter of the gamma prior distribution for the precisions (inverse variances) of the smooth term. The default is 0.005.
prior.2D	character string. Indicates whether the same precision parameter should be used for both variables in two-dimensional smooth functions (isotropy), or if each variable should have a different precision parameter (anisotropy). In the latter case, the Bayesian extension of the PS-ANOVA model by Lee et al. (2013) is used. The default is "anisotropic".

Details

The functions f() is designed to represent either one dimensional smooth functions for main effects of continuous explanatory variables or two dimensional smooth functions representing two way interactions of continuous variables using Bayesian P-splines. By default, the values of the arguments nseg, pord and bdeg are repeated to the length of the explanatory covariates. The two dimensional smooth terms are constructed using the tensor-product of marginal (one-dimensional) B-spline bases (Eilers and Marx, 2003). In this case, the Bayesian extension of the PS-ANOVA model by Lee et al. (2013) is considered when prior.2D = "anisotropic". It is also possible to include factor-by-curve interactions between a continuous covariate (e.g., x1) and a categorical covariate (e.g., x2) by means of argument by: y ~ x2 + f(x1, by = x2).

Value

The function is interpreted in the formula of a DDPstar model and creates the right framework for fitting the smoother. List containing (among others) the following elements:

vars	names of the covariates involved in the smooth term.
nseg	the number of segments for the (marginal) B-spline basis for each covariate (numerical vector of length equal to the number of covariates).
pord	the penalty order (numerical vector of length equal to the number of covariates).
bdeg	the order of the polynomial for the (marginal) B-Spline bases for this term (numerical vector of length equal to the number of covariates)
atau	shape parameter of the gamma prior distribution
btau	rate parameter of the gamma prior distribution

References

Eilers, P.H.C. and Marx, B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89-121.

Eilers, P.H.C. and Marx, B.D. (2003). Multidimensional calibration with temperature interaction using two- dimensional penalized signal regression. Chemometrics and Intelligence Laboratory Systems, 66, 159-174.

Lang, S. and Brezger, A. (2004). Bayesian P-splines. Journal of Computational and Graphical Statistics, 13(1), 183-212.

Lee, D.-J., Durban, M., and Eilers, P. (2013). Efficient two-dimensional smoothing with P- spline ANOVA mixed models and nested bases. Computational Statistics & Data Analysis, 61, 22-37.

See Also

rae, DDPstar

Examples

library(DDPstar)
data(dde)
dde$GAD <- dde$GAD/7 # GAD in weeks

formula.dde <- GAD ~ f(DDE, bdeg = 3, nseg = 20, pord = 2, atau = 1, btau = 0.005)

set.seed(10) # For reproducibility
fit_dde <- DDPstar(formula = formula.dde, 
  data = dde, mcmc = list(nburn = 20000, nsave = 15000, nskip = 1), 
  prior = list(a = 2, b = 0.5, aalpha = 2, balpha = 2, L = 20), 
  standardise = TRUE, compute.lpml = TRUE, compute.WAIC = TRUE, compute.DIC = TRUE)
summary(fit_dde)

DDPstar documentation built on April 3, 2025, 8:46 p.m.