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

Thierry Onkelinx thierry.onkelinx at inbo.be
Mon Mar 12 16:25:38 CET 2018

Dear Daniel,

Have a look at the INLA package (www.r-inla.org). It allows for several
types of correlated random effects. See

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be
Havenlaan 88 bus 73, 1000 Brussel

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


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
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