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Each [[basis function]] <math>B_i(x)</math> takes one of the following three forms:
1) a constant 1. There is just one such term, [[The Intercept|the intercept]].
In the ozone formula above, the intercept term is 5.2.
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{{further|Cross-validation (statistics)|Model selection|Akaike information criterion}}
The backward pass compares the performance of different models using Generalized Cross-Validation (GCV), a minor variant on the [[Akaike information criterion]] that approximates the [[leave-one-out cross-validation]] score in the special case where errors are Gaussian, or where the squared error [[loss function]] is used. GCV was introduced by Craven and [[Grace Wahba|Wahba]] and extended by Friedman for MARS; lower values of GCV indicate better models. The formula for the GCV is
: GCV = RSS / (''N'' · (1 − (effective number of parameters) / ''N'')<sup>2</sup>)
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* [[Recursive partitioning]] (commonly called CART). MARS can be seen as a generalization of recursive partitioning that allows for continuous models, which can provide a better fit for numerical data.
* [[Generalized additive model]]s. Unlike MARS, GAMs fit smooth [[Local regression|loess]] or polynomial [[Spline (mathematics)|splines]] rather than hinge functions, and they do not automatically model variable interactions. The smoother fit and lack of regression terms reduces variance when compared to MARS, but ignoring variable interactions can worsen the bias.
* [[TSMARS]]. Time Series Mars is the term used when MARS models are applied in a [[time series]] context. Typically in this set up the predictors are the lagged time series values resulting in autoregressive spline models. These models and extensions to include moving average spline models are described in "Univariate Time Series Modelling and Forecasting using TSMARS: A study of threshold time series autoregressive, seasonal and moving average models using TSMARS".
* [[Bayesian MARS]] (BMARS) uses the same model form, but builds the model using a Bayesian approach. It may arrive at different optimal MARS models because the model building approach is different. The result of BMARS is typically an ensemble of posterior samples of MARS models, which allows for probabilistic prediction.<ref>{{cite journal |last1=Denison |first1=D. G. T. |last2=Mallick |first2=B. K. |last3=Smith |first3=A. F. M. |title=Bayesian MARS |journal=Statistics and Computing |date=1 December 1998 |volume=8 |issue=4 |pages=337–346 |doi=10.1023/A:1008824606259 |s2cid=12570055 |url=https://link.springer.com/content/pdf/10.1023/A:1008824606259.pdf |language=en |issn=1573-1375}}</ref>
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