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I am looking to understand the assumptions of using a generalized additive model.

1) Are the assumptions the same as the assumptions for each equivalent link function in a generalized linear model - e.g. as linear regression, logistic regression etc. along with the assumption that the additive smooth structure is correct and the errors are independent?

2) If these are the same assumptions, do they only play a role when you are making hypothesis tests (e.g. making inference about linear and smooth components)?

ADD: From Simon Wood (author of mgcv package in R), sounds like one indeed treats the need to check assumptions of GAM as the assumptions underlying the generalized linear model with the same link.

  • Since a GAM is just a penalized GLM, residual plots should be checked, exactly as for a GLM. I The distribution of scaled residuals should be examined, marginally, and plotted against covariates and fitted values. residuals(model) extracts residuals.
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2 Answers 2

The similarity between the two is the link function and being additive but otherwise the generalized additive model is more general because the functions of the covariates need not be linear. In fact they are nonparametric functions whereas in the generalized linear model they are linear in the parameters.

I think that if you are fitting by least squares then in both cases you would be testing normality and constant variance just as you would for OLS linear regression.

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I was specifically wondering about residual analysis - requiring normality, constancy of variance and the rest of the linear regression assumptions. Likewise assuming iid observations. Then if you use a logit link, I believe one checks assumptions of logistic regression. I agree that the covariates need not be linear. –  B_Miner Jul 14 '12 at 1:05

This might be a bit late but for a GLM, the residuals aren't completely normally distributed (Faraway, 2006). Using the halfnorm (faraway package) function is a good way to detect outliers that are off the trend with noticeable jumps.

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