CODEWITHSUNDEEP
machine-learningstatisticsgam
vcar97
vcar97

Reputation: 1

Non-linear models GAM, MARS assumptions

Do models such as MARS and GAM assume heteroscedasticity and IID errors? There seems to be a disagreement in the literature about certain assumptions. Looks like MARS is more robust than GAM but it is not clearly stated in the original papers.

If normality is an issue, should one use transformed data (Box-Cox or Yeo-Johnson) for the regression?

Upvotes: -1

Views: 1110

Answers (1)

Gavin Simpson
Gavin Simpson

Reputation: 174908

GAMs don't assume conditional normality; the "G" stands for generalised and indicates these models build off of the generalized linear model framework, which traditionally can model data as draws a distribution from the Exponential family of distributions.

If you fit a GAM with a Gaussian conditional distribution, then that model would assume conditional normality, but the general class of GAMs does not as one can choose an appropriate distribution for the response.

The Gaussian GAM also assumes the observations are conditionally homoscedastic. Other response distributions imply mean-variance relationships; e.g. with a Poisson response distribution, the variance equals the mean and hence larger counts are assumed to have higher variance.

GAMs do assume that the observations are i.i.d.; GEEs, GLMMs, and GAMMs are extensions that relax the assumption of independece.

MARS originally fitted via OLS so it would pick up some of the assumptions of the general linear model, but typically one uses some form of cross-validation to assess the model fit. As long as the cross-validation scheme reflects the properties of the data, then the classical assumptions of the linear model don't really apply as you're not relying on th theory to do inference.

Upvotes: 2

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