In
statistics, an additive model (AM) is a
nonparametric regression method. It was suggested by
Jerome H. Friedman and Werner Stuetzle (1981) and is an essential part of the
ACE algorithm. The ''AM'' uses a one-dimensional
smoother to build a restricted class of nonparametric regression models. Because of this, it is less affected by the
curse of dimensionality than e.g. a ''p''-dimensional smoother. Furthermore, the ''AM'' is more flexible than a
standard linear model, while being more interpretable than a general regression surface at the cost of approximation errors. Problems with ''AM'', like many other machine learning methods, include
model selection,
overfitting
mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably". An overfitt ...
, and
multicollinearity.
Description
Given a
data
In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpret ...
set
of ''n''
statistical unit
In statistics, a unit is one member of a set of entities being studied. It is the main source for the mathematical abstraction of a "random variable". Common examples of a unit would be a single person, animal, plant, manufactured item, or country ...
s, where
represent predictors and
is the outcome, the ''additive model'' takes the form
:
or
:
Where
,
and
. The functions
are unknown
smooth function
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if ...
s fit from the data. Fitting the ''AM'' (i.e. the functions
) can be done using the
backfitting algorithm proposed by Andreas Buja,
Trevor Hastie and
Robert Tibshirani (1989).
[Buja, A., Hastie, T., and Tibshirani, R. (1989). "Linear Smoothers and Additive Models", ''The Annals of Statistics'' 17(2):453–555. ]
See also
*
Generalized additive model
*
Backfitting algorithm
*
Projection pursuit regression
In statistics, projection pursuit regression (PPR) is a statistical model developed by Jerome H. Friedman and Werner Stuetzle which is an extension of additive models. This model adapts the additive models in that it first projects the data matri ...
*
Generalized additive model for location, scale, and shape (GAMLSS)
*
Median polish
*
Projection Pursuit Projection pursuit (PP) is a type of statistical technique which involves finding the most "interesting" possible projections in multidimensional data. Often, projections which deviate more from a normal distribution are considered to be more inte ...
References
Further reading
*Breiman, L. and
Friedman, J.H. (1985). "Estimating Optimal Transformations for Multiple Regression and Correlation", ''
Journal of the American Statistical Association
The ''Journal of the American Statistical Association (JASA)'' is the primary journal published by the American Statistical Association, the main professional body for statisticians in the United States. It is published four times a year in Ma ...
'' 80:580–598. {{doi, 10.1080/01621459.1985.10478157
Nonparametric regression
Regression models