SPDE model to predict air pollutant

[Felipe Barletta]

Dear friends of INLA,

I'm currently working on a spatial model using INLA and I’m having some trouble interpreting the posterior mean values from my model's predictions. Specifically, I’m not sure why the predicted values (posterior means) behave the way they do, as they seem inconsistent with the observed data and the spatial pattern I expected.

I fitted a SPDE model to predict an air pollutant (NO2) in Portugal. I have monthly measures from some stations between 2010 and 2018.

The model is:

############
formula <- y ~ 1 + f(spatial.field, model = spde)

result <- inla(
    formula,
    data = inla.stack.data(stack.full),
    family = "gaussian",
    control.predictor = list(A = inla.stack.A(stack.full), compute = TRUE),
    control.compute = list(dic = TRUE, cpo = TRUE),
    verbose = FALSE
)

And the summary of my response variable is:

Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
   2.50   10.47   17.95   20.68   23.18   68.80

But the summary of predicted values of posterior mean is:

summary(df_pred$mean)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  20.68   20.68   20.68   20.68   20.68   20.68

> var(df_pred$mean)
[1] 2.873496e-09
> sd(df_pred$mean)
[1] 5.3605e-05

I attached the data and a reproducible code.

If anyone could help clarify what might be influencing these results or suggest steps to better understand the model output, I’d really appreciate it.

Thank you

[Elias T. Krainski]

I didn't followed some bits of your code and tried to "fix" it (to my own understanding) and found no issues as I have

summary(result$summary.fitted.values$mean[1:n])

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.

  10.94   16.23   20.69   20.68   24.29   32.24

and got the attached picture.

Regards,

Elias

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[Elias T. Krainski]

the "fixed" code ;)

[Felipe Barletta]

Muito Obrigado Elias.

It's perfect.

I still have difficulty understanding how to define the mesh.

By the way, I compared these results with those obtained using the geoR package.

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