selection of parametric terms in GAM - DSM

[Antonella Pane]

Hello everybody, 

I running a DSM to study the variables that influence the spatial distribution of territorial ungulates. My models are a mix of smooth terms and parametric (categorical) terms, for example, predation risk level (low/high).

To select smooth terms, I am using a shrinkage approach, as explained here: http://workshops.distancesampling.org/online-dsm-2020/slides/dsm3-multiple_smooths-section.pdf

My question is: what is the best way of selecting parametric terms in these DSM? Is it using p-values or maybe trying models with and without the term and assess model fit, deviance, AIC?

I apologize if this question is rather basic but I cannot find a lot of information regarding the combination of smooth and parametric terms in the literature.

Thank you very much in advance!

[Eric Rexstad]

Antonella

Fitting GAMs is not my area of expertise, so take these comments with a large pinch of salt.

Inclusion of discrete (categorical) covariates in a GAM examines whether the shape of the smooths differ among levels of the discrete covariate; in effect looking at interaction between a smooth and a discrete covariate.

Have a look at Gavin Simpson's description of a case study including both discrete covariates and smooths

https://fromthebottomoftheheap.net/2017/12/14/difference-splines-ii/

There are likely other members of the list who can offer more penetrating insights into model selection with discrete covariates.

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Eric Rexstad
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University of St Andrews
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[Antonella Pane]

Hello Eric and everybody,

 

Thank you very much for your reply and the link. It's quite clear.

I will look at the interaction between discrete and some smooth terms in my model. 

I wonder if it is also ok to just use a discrete term without assessing the interaction with a smooth term. I don't think many of these interactions have a biological meaning in my model. In that case, what would be the best way to select these terms?

Thank you very much again!

Antonella

[David Lawrence Miller]

Hi Antonella, hi listfolk,

In one sense, it's fine to use p-values to do this selection.

However, if your parametric terms vary in space then you may have
problems. As illustrated in this paper,

https://www4.stat.ncsu.edu/~bjreich/papers/FixedEffectsYouLove.pdf

when you include a spatial random effect (e.g., a smooth of space) to
your model, you can change the effect size of parametric terms in the
model. In this case your p-values will not be "correct". This may be
especially problematic if you intend to interpret those effect sizes.
Selection via AIC or other statistics won't get around this issue. This
is somewhat of an open problem in spatial statistics, most recently
addressed in this (somewhat technical in places) paper:
https://arxiv.org/abs/2009.09420

If you don't intend to interpret the effect size (and only intend to
estimate abundance) or if your fixed effects don't vary in space then
this is less of an issue and using, say, p-values will likely be okay.

Hope this helps.

--dave

On 23/12/2020 22:29, Antonella Pane wrote:

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[Antonella Pane]

Hi David, 

Thank you very much for your complete answer! It has definitely helped to understand a little bit better how to proceed.

Best, 

Antonella