Some non-standard models

We conclude this section with just a brief mention of some of the other facilities available in S-PLUS for special regression and data analysis problems.

Local approximating regressions.

The loess() function fits a nonparametric regression by using a locally weighted regression. Such regressions are useful for highlighting a trend in messy data or for data reduction to give some insight into a large data set.

Robust regression

There are several functions available for fitting regression models in a way resistant to the influence of extreme outliers in the data. The most sophisticated of these is rreg(), but others include lmsfit() for least median squares regression and l1fit() for regression using the norm. However these do not as yet have the facility of using formulæ to specify the model function, for example, and conform to an older protocol, which makes them sometimes rather tedious to use. There is also a robust() facility to change a glm family object into a robust version for use with the glm() model fitting function.

Generalized additive models.

This technique aims to construct an regression function from smooth additive functions of the determining variables, usually one for each determining variable. The function gam() is in many ways similar to the other model fitting functions outlined above. In addition there are other model fitting functions that do a similar job. These include avas() and ace(). On the other hand ppreg() is available for projection pursuit regression, but this technique is still very much in need of a complete theoretical treatment and further practical experience. These latter functions are again conforming to an older protocol for model fitting functions and lack the convenience of the newer functions.

Tree based models

Rather than seek an explicit global linear model for prediction or interpretation, tree based models seek to bifurcate the data, recursively, at critical points of the determining variables in order to partition the data ultimately into groups that are as homogeneous as possible within, and as heterogeneous as possible between. The results often lead to insights that other data analysis methods tend not to yield.

Models are again specified in the ordinary linear model form. The model fitting function is tree(), but many other generic functions such as plot() and text() are well adapted to displaying the results of a tree-based model fit in a graphical way.