How are smooth terms specified in GAM formula?

How are smooth terms specified in GAM formula?

Smooth terms are specified in a gam formula using s, te, ti and t2 terms. Various smooth classes are available, for different modelling tasks, and users can add smooth classes (see user.defined.smooth ). What defines a smooth class is the basis used to represent the smooth function and quadratic penalty (or multiple penalties)…

How to include an interaction term in GAM?

The “a” in “gam” stands for “additive” which means no interactions, so if you fit interactions you are really not fitting a gam model any more. That said, there are ways to get some interaction like terms within the additive terms in a gam, you are already using one of those by using the by argument to s.

What does low rank and isotropic mean in smoothing?

By isotropic is meant that rotation of the covariate co-ordinate system will not change the result of smoothing. By low rank is meant that they have far fewer coefficients than there are data to smooth.

How are cubic regression splines defined in GAM?

Cubic regression splines. bs=”cr”. These have a cubic spline basis defined by a modest sized set of knots spread evenly through the covariate values. They are penalized by the conventional intergrated square second derivative cubic spline penalty.

Are there any smooths in the mgcv package?

The smooths built into the mgcv package are all based one way or another on low rank versions of splines. For the full rank versions see Wahba (1990). Note that smooths can be used rather flexibly in gam models.

How are smooth classes invoked in tensor products?

Smooth classes are invoked directly by s terms, or as building blocks for tensor product smoothing via te, ti or t2 terms (only smooth classes with single penalties can be used in tensor products). The smooths built into the mgcv package are all based one way or another on low rank versions of splines. For the full rank versions see Wahba (1990).

How to avoid nonsensical predictor functions with GAM?

With GAMs, you can avoid wiggly, nonsensical predictor functions by simply adjusting the level of smoothness. In other words, we can impose the prior belief that predictive relationships are inherently smooth in nature, even though the dataset at hand may suggest a more noisy relationship.

Why do I want to use Gam for my model?

As mentioned in the intro, there are at least three good reasons why you want to use GAM: interpretability, flexibility/automation, and regularization. Hence, when your model contains nonlinear effects, GAM provides a regularized and interpretable solution – while other methods generally lack at least one of these three features.

When was Generalized Additive Model ( GAM ) invented?

Generalized additive models were originally invented by Trevor Hastie and Robert Tibshirani in 1986 (see [1], [2]). The GAM framework is based on an appealing and simple mental model: Relationships between the individual predictors and the dependent variable follow smooth patterns that can be linear or nonlinear.

How are smooths produced in a tensor product?

Tensor product smooths are smooth functions of several variables where the basis is built up from tensor products of bases for smooths of fewer (usually one) variable (s) (marginal bases). The multiple penalties for these smooths are produced automatically from the penalties of the marginal smooths.

What’s the K for smoothing in mgcv GAM?

By default, te () smooths have k = 5^2 for 2d surfaces. I forget what it is for s () so check the documents.

Can a GAM be used as an adaptive smoother?

Adaptive smoothers can spend the allotted smoothness “allowance” in parts of the data where the response is changing rapidly. gam () has capabilities for using adaptive smoothers.

How to use generalized additive model in GAM?

So a typical GAM might use a scatterplot smoothing function, such as a locally weighted mean, for f1 ( x1 ), and then use a factor model for f2 ( x2 ).

How to predict with random effects in mgcv?

Error in Predict.matrix.tprs.smooth (object, dk$data) : NA/NaN/Inf in foreign function call (arg 1) In addition: Warning message: In Ops.factor (xx, object$shift [i]) : – not meaningful for factors I think this is being called because VesselID is a factor, but I’m using it a smooth for the random effects.