[R-sig-ME] How to consider temporal autocorrelation in a GLMM

Thierry Onkelinx th|erry@onke||nx @end|ng |rom |nbo@be
Tue Jun 29 16:26:55 CEST 2021

Dear Andre,

My go-to for temporal and/or spatial autocorrelation is the INLA package. I
wrote a blogpost on temporal autocorrelation (

An iid random intercept as lme4, implies a compound symmetry correlation
among the levels: every pair of levels has the same correlation. With
temporal correlation why can strong correlation for levels close in time.
That is something you can do with correlated random effects in INLA. See
the blog post for details.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

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

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Op di 29 jun. 2021 om 13:03 schreef A Mauchamp via R-sig-mixed-models <
r-sig-mixed-models using r-project.org>:

> Hello,
> I am currently analyzing (in R) ecological monitoring data that have 5
> successive years, one point per year and multiple sites and replicates
> within sites. Having a combination of fixed (environmental variables) and
> random (sites) effects, I need to use mixed models.
> Using glmer of the package lme4, I would like to account for the strong
> correlation between one year data and the following that I observe for most
> variables.
> I found this idea here
> https://stackoverflow.com/questions/24452796/accounting-for-temporal-correlation-in-glmm
> which looks very simple and straightforward.
> It would result in a formula as
> y_t ~ env1 + env2 + env3 + y_t-1 + (1|site)
> However in some cases, all environmental effects disappear and the only
> relation that remains is with y_t-1.
> I also found this approach:
> y ~ env1+ env2 + time + (1|replicate) + (1|site) that treats time as fixed
> effect and groups the repeated measures of replicates. Though I am not sure
> it is correct.
> Would it be correct to use time as a random effect ?
> Data are either count data (Poisson error distribution) or quantitative
> and gaussian.
> Which would be the most appropriate way of dealing with such repeated
> measures /short time series ?
> Which reference could I use to support the method ?
> My data series is indeed to short to go for a real time-series analysis
> and I don't think I can go for more than one year lag.
> Thank you for any suggestion,
> Andre
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