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

[Thierry Onkelinx]

Dear Daniel,

You could combine an AR1 per sector along time and an iid along year. The
former creates the AR1 correlation with the sector. The latter induces a
compound symmetry correlation among year. Thus making observations from
different sector but within the same year more similar to each ofther.

f(time, model = "ar1", replicate = sector) + f(year, model = "iid")

You could post the question to the INLA mailing list. Adding the
mathematical equation for the model you want will help.

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 bus 73, 1000 Brussel
www.inbo.be

///////////////////////////////////////////////////////////////////////////////////////////
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than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
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ensure that a reasonable answer can be extracted from a given body of data.
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<https://www.inbo.be>

2018-03-12 16:31 GMT+01:00 Daniel Bartling <danielbartling at gmail.com>:

> 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/mode
>> ls/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
>>
>> ////////////////////////////////////////////////////////////
>> ///////////////////////////////
>> To call in the statistician after the experiment is done may be no more
>> than asking him to perform a post-mortem examination: he may be able to say
>> what the experiment died of. ~ Sir Ronald Aylmer Fisher
>> The plural of anecdote is not data. ~ Roger Brinner
>> The combination of some data and an aching desire for an answer does not
>> ensure that a reasonable answer can be extracted from a given body of data.
>> ~ John Tukey
>> ////////////////////////////////////////////////////////////
>> ///////////////////////////////
>>
>> <https://www.inbo.be>
>>
>> 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]]
>>>
>>> _______________________________________________
>>> R-sig-mixed-models at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>
>>

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