Role of Random Walk 1or 2 models in climate predictors

[Vincent Arumadri]

Hello INLA Group,

Hope this can be answered here because I could not find a specific answer on the topic anywhere else.

I am working on a model with mosquito-borne disease counts as an outcome and precipitation and temperature as predictors. Similar previous published studies on this have use random walk 1/2 models in INLA to account for temporal dimension (seasonality and interannual variation) in disease counts. 

However, I thought this would be explained by the predictors. I can understand the inclusion of random walk models where there are no climate predictors. What is the role of adding the random walk models to account for seasonality and and interannual variation in disease counts? Are the climate predictors not accounting for that? 

Thanks in advance!

[Finn Lindgren]

Hi,

In, short, the existence of informative predictor variables does not imply that those predictors 1) have a linear relationship with the response variable expectation (on the link function scale, typically a log-link for count variables) and/or 2) are sufficient predictors in their own right, even with some non-linear modelled relationship (which might itself be via a rw1/2 model!)

A rw1/2 model might then be added to compensate for those missing aspects of the model. An ar1 or ar2 model is also an option.

A combination of the above factors is likely why those other works have incorporated such model components.

Finn

On 28 Sep 2025, at 20:38, Vincent Arumadri <varu...@gmail.com> wrote:

Hello INLA Group,

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[Vincent Arumadri]

Hi Finn, 

Thank you for your reply. It has improved my understanding already. 

Just as a follow-up and so I can fully explain this to others, perhaps I can give more context – the climate predictors themselves are have a non-linear relationship with the response varaible that is defined using natural cubic splines using another package. In the INLA, they then add random effects (rw1/2) to month and year variables to account for seasonality and interannual variation respectively together with the predictors in the model. Is the motivation for addition of the rw1/2 models as temporal random effects in this case still to compensate for the missing aspects of the model? Such that seasonality and interannual variation cannot be fully explained by the predictors and these rw1/2 compensate for the aspects a model without rw1/2 random effects would miss.

Thanks again in advance.

Vincent. 

[Finn Lindgren]

You’d need to ask the authors of the study in the question to get the actual answer (I can’t know why they did what they did, but can only guess, in particular without having read what they wrote…), but regarding seasonality, I’d say that unless the predictor variables have a seasonal pattern in them, one would need _some_ kind of model component to handle it. A cyclic rw2 model is a simple but often effective way to model seasonal patterns.

But if you need to know why some specific authors did what they did, and it’s not clear from their paper, then contacting them and asking should give an authoritative answer about their motivations!

Finn

On 28 Sep 2025, at 21:28, Vincent Arumadri <varu...@gmail.com> wrote:

Hi Finn, 

To view this discussion, visit https://groups.google.com/d/msgid/r-inla-discussion-group/e7828ec6-a839-46db-a44e-e8bc03193721n%40googlegroups.com.

[Vincent Arumadri]

Hi Finn,

Thank you for the added explanation. I will reach out to the authors for further details. 

Vincent