Vibration of rotating structures

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 include model selection, overfitting, and multicollinearity.

Description

Given a data set $\{y_i,x_{i1},\dots ,x_{ip}{\}}_{i=1}^n$ of n statistical units, where $\{x_{i1},\dots ,x_{ip}{\}}_{i=1}^n$ represent predictors and $y_i$ is the outcome, the additive model takes the form

$E[y_i|x_{i1},\dots ,x_{ip}]={\beta }_0+\sum _{j=1}^p{f}_j(x_{ij})$

or

$Y={\beta }_0+\sum _{j=1}^p{f}_j(X_j)+\epsilon$

Where $E[ϵ]=0$, $Var(ϵ)={\sigma }^2$ and $E[f_j(X_j)]=0$. The functions $f_j(x_{ij})$ are unknown smooth functions fit from the data. Fitting the AM (i.e. the functions $f_j(x_{ij})$) can be done using the backfitting algorithm proposed by Andreas Buja, Trevor Hastie and Robert Tibshirani (1989).

See also

• Generalized additive model
• Backfitting algorithm
• Alternating conditional expectation model
• Projection pursuit regression
• Generalized additive model for location, scale, and shape (GAMLSS)
• Median polish

References

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Further reading

• Breiman, L. and Friedman, J.H. (1985). "Estimating Optimal Transformations for Multiple Regression and Correlation", Journal of the American Statistical Association 80:580–598. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.