Smoothing spline models are widely used in practice as a tool to achieve flexibility. There has been intensive research on its theoretical properties and applications. For references on non-parametric regression using smoothing splines, see Eubank (1988), Wahba (1990), Hastie and Tibshirani (1990), Green and Silverman (1994), Simonoff (1996), and Gu (2002).

As the popularity of building models using splines increases,
there is an increasing need for comprehensive and user friendly
software. Existing software include `GCVPACK`
(Bates et al., 1987) for fitting thin plate
splines, `RKPACK` (Gu, 1989) for fitting general
smoothing spline regression models as described in
Wahba (1990), and `GRKPACK` (Wang, 1997) for
fitting generalized smoothing spline regression models to data from
exponential families. All three packages were written
in Fortran which is inconvenient to use. Some user friendly S (S-plus and
R) functions have been developed recently. For example, the S function
`smooth.spline` fits cubic splines; `FIELDS`, a suite of
S-plus functions which can be downloaded from
*http://www.cgd.ucar.edu/stats/software.shtml*, fits cubic and thin
plate splines; `smooth.Lspline`, a S-plus function which can be
downloaded from
*ftp://ego.psych.mcgill.ca/pub/ramsay/Lspline*, fits L-splines;
and `gss`, a suite of R functions which can be
downloaded from *cran.r-project.org/src/contrib/PACKAGES.html*,
fits general smoothing spline regression models to data from
exponential families (Gu, 2002).

In this document we describe a suite of S functions, `ASSIST`,
with examples to show their usage. The purposes of the `ASSIST`
package are to
(a) provide a S complement of the `gss` package for fitting
general smoothing spline non-parametric regression models to data from
exponential families; (b) develop functions for fitting Gaussian data
with certain variance and/or covariance structures;
(c) develop functions for fitting more complicated
models such as semi-parametric linear mixed-effects models,
non-parametric nonlinear regression models,
semi-parametric nonlinear regression models,
and semi-parametric nonlinear mixed-effects models; and
(d) provide inference tools for some simple models. We adopt notations
in Wahba (1990).

Figure shows how the functions in ASSIST generalize existing S-Plus functions.

Basic knowledge of reproducing kernel Hilbert spaces and general smoothing spline models as described in the first two chapters of Wahba (1990) is necessary to fully understand this article. However, this is not required for using our functions to fit simple smoothing spline models.

We review the general smoothing spline regression model and
describe the corresponding S function `ssr` in Section 2.
We review the semi-parametric linear mixed-effects model and
describe the corresponding S function `slm` in Section 3.
We review the non-parametric nonlinear regression model and
describe the corresponding S function `nnr` in Section 4.
We review the semi-parametric nonlinear regression model and
describe the corresponding S function `snr` in Section 5.
We review the semi-parametric nonlinear mixed-effects model and
describe the corresponding S function `snm` in Section 6.
We illustrate how to use these functions with several real data
sets in Section 7. Computational concerns and tips are discussed
in Section 8. Finally, in Section 9, we conclude with discussions
on further work.