Hierarchal SLM model in INLA?

[Samuel Reiterbund-Olley]

Dear INLA helpdesk

I’m trying to fit a Hierarchal SLM in INLA for repeated measurements. Each area of interest has multiple house sales. I’ve also attempted this method using the HSAR package developed by Dong, but ran into issues with run time, as it uses MCMC estimation. I’m therefore keen to know whether this is possible in INLA or whether this might be developed in future INLA updates. I have successfully applied this hierarchical approach using CAR models in INLA.

I have attempted to use the SLM method/argument within INLA but have encountered errors presumably as my data has repeated measurements for each subject (area) and is unbalanced (each subject has a variable number of repeated observations (i.e. sales).

If required, please see the HSAR vignette and paper from Dong 2015 for further information, and the approach is also reviewed by your colleague Bivard 2017.

Example

I’m not able to share my data but have provided an example using the Boston dataset, and simply duplicated the dataset twice therefore, creating a repeated measurement type dataset. Please see attached notepad file for code, if required.

Many thanks

Samuel Reiterbund-Olley

References

https://cran.r-project.org/web/packages/HSAR/vignettes/HSAR.html

Dong, G. and Harris, R., 2015. Spatial autoregressive models for geographically hierarchical data structures. Geographical Analysis, 47(2), pp.173-191.

Bivand, R., Sha, Z., Osland, L. and Thorsen, I.S., 2017. A comparison of estimation methods for multilevel models of spatially structured data. Spatial Statistics, 21, pp.440-459

[Virgilio Gómez-Rubio]

Hi,

Thanks for your question. Your code is not reproducible because object boston.tr is not created before it is used. In any case, if you have observations nested within areas you can simply use an index from 1 to n when creating the sim latent effect and then assign to each observation the index corresponding to its area. I believe this is what you want to do.

In your code boston.tr$idx should NOT go from 1 to the number of rows but, instead, define the indices according to the area. There are different ways in which this can be done depending how your data is organized.

Best,

Virgilio

[lyh...@gmail.com]

Hi,

I do not think SLM can fit this hierarchal SLM model. The hierarchal SLM has a particular covariance structure, which does not equal the one in SLM model.
However, the hierarichal SLM model can be fitted by INLA coupled with MCMC.

[Zazaland]

Om

[Samuel Reiterbund-Olley]

Virgilio,

thanks for your reply,

apologies, yes, you are correct about the error in the code,

I've added an updated version of code. Hopefully this new version works if required. The boston dataset belongs to the spData package.

The original dataset consists of 1 record (each row) for each area and therefore the duplication dataset consists of 2 records for each region. 

so based on your suggestion the new index (new_idx) should consist as below??

thanks 

Samuel

[Virgilio Gómez-Rubio]

Hi,

>
> so based on your suggestion the new index (new_idx) should consist as below??

Yes, this should work provided that the model that you want to fit has nested observations within areas, so that the observations in the same area share the value of the random effect. I cannot recall seeing this model in the literature but it looks reasonable to me.

Best,

Virgilio

[Samuel Reiterbund-Olley]

Thanks for your reply,

yes, I wasn't sure if it was possible. I have some real world data to test on, and compare performance against CAR models. If I an get it to work, I'll feed back the result.

As explained in my introduction, I have tried Dong's full MCMC approach, but came up against run time issues. 

Are you referring to the INLABMA method? I found a paper by Teng 2023 where he used INLABMA for repeated measurements (i.e. more than one measurement per region), but it seemed to require a balanced dataset (i.e. equal number of observations per region). He also helpfully provided code in the paper, but not the starting dataset. 

ref

Teng, J., Ding, S., Zhang, H. and Hu, X., 2023. MCMCINLA estimation of varying coefficient spatial lag model—A study of China’s economic development in the context of population aging. Plos one, 18(5), p.e0279504. 

thanks

Samuel

[Samuel Reiterbund-Olley]

Thanks,

I'll try it out next week and feed back.

Many thanks for your help

Samuel

[Samuel Reiterbund-Olley]

Hi Virgilio,

I tried the SLM function with the new coding for region, but still threw off a similar error for 2 data points per region. As a comparison, I successfully ran the code with only one value per region and this is included at the end of the attached code.

I have uploaded the code again, if you have any time to run it yourself. If you try hopefully it runs successfully. 

thanks 

Samuel
(FYI - I wont be available for the next month)