statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, 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 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 In 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 overfi ...

, and multicollinearity.

Description

Given a

data Data ( , ) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted for ...

set

\_^n

of ''n'' statistical units, where

\_^n

represent predictors and

y_i

is the outcome, the ''additive model'' takes the form :

= \beta_0+\sum_^p f_j(x_)

or :

Y= \beta_0+\sum_^p f_j(X_)+\varepsilon

Where

\mathrm \epsilon = 0

\mathrm(\epsilon) = \sigma^2

and

\mathrm f_j(X_) = 0

. The functions

f_j(x_)

are unknown

smooth function In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives (''differentiability class)'' it has over its domain. A function of class C^k is a function of smoothness at least ; t ...

s fit from the data. Fitting the ''AM'' (i.e. the functions

f_j(x_)

) 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.

Description

See also

References

Further reading