[R-sig-ME] Serial correlation in random effects

[Daniel Bartling]

Hi Thierry,

Thank you I will take another look at it, but last time I did it seemed to
me that I could fit an AR1 for the temporal correlation for a single RE,
but could not fit the cross sectional correlation of different RE groups at
the same time. But I will try to dig out the code.

Regards Daniel

On 12 Mar 2018 4:25 PM, "Thierry Onkelinx" <thierry.onkelinx at inbo.be> wrote:

> Dear Daniel,
>
> Have a look at the INLA package (www.r-inla.org). It allows for several
> types of correlated random effects. See http://www.r-inla.org/
> models/latent-models
>
> Best regards,
>
>
> ir. Thierry Onkelinx
> Statisticus / Statistician
>
> Vlaamse Overheid / Government of Flanders
> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
> FOREST
> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
> thierry.onkelinx at inbo.be
> Havenlaan 88
> <https://maps.google.com/?q=Havenlaan+88&entry=gmail&source=g> bus 73,
> 1000 Brussel
> www.inbo.be
>
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> 2018-03-12 15:50 GMT+01:00 Daniel Bartling <danielbartling at gmail.com>:
>
>> Hi all,
>>
>>
>>
>> I would love to apply linear mixed models in Risk Management as they seem
>> to be tailor suited to many problems we face. We often assume that for
>> example credit default risk is driven by observable latent random factors
>> and we wish to understand the dynamics of these latent factors based on
>> repeated historical observations. Typically, these random factors consist
>> of different groups (e.g. credit defaults in different industry sectors
>> over different time periods). The industry sectors are correlated between
>> each other but that are also assumed to be serially correlated over time.
>> For example, the state of the industry sector “telecommunication” in year
>> t
>> is the result of both the auto correlation with “telecommunication” in
>> year
>> t-1 and the year t correlation with other industry sectors like
>> “information technology”.
>>
>>
>>
>> I would use the representation (-1 + sector|time) to estimate the model.
>>
>>
>> I generated dummy data based on different modeling assumptions and I am
>> able to estimate successfully the parameters that were used in generating
>> the data.
>>
>>
>>
>> However I have some questions:
>>
>>
>>
>> First of all, if I estimate the variance of the BLUPs, I get different
>> values for the variance covariance matrix than if I look directly at the
>> estimated variance covariance matrix as an estimation output. I understand
>> that there is a methodological difference between the BLUPs and the
>> estimated variance covariance matrix, because one is focusing on the
>> realized sample while the other is focused on the specific realised sample
>> (I found the directly estimated variance covariance to be a better fit,
>> while the BLUPs underestimated the variance covariance matrix). So how
>> valid is inference based directly on the BLUPs?
>>
>>
>>
>> More specifically, I wish to estimate AR1 parameters for the BLUPs in
>> order
>> to model the serial correlation described above. Is there a way to
>> determine this serial correlation of random effects directly in the
>> estimation with any available r package? I found many options to model
>> autocorrelation in the residuals but not serial correlation in the random
>> effects, especially when there also exists correlation between different
>> random effects groups.
>>
>>
>>
>> Thank you!
>>
>>
>> Regards
>>
>> Daniel Bartling
>>
>>         [[alternative HTML version deleted]]
>>
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>>
>
>

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