[R-sig-ME] Repeated Observations Linear Mixed Model with Outside-Group Spatial Correlation

Thierry Onkelinx thierry.onkelinx at inbo.be
Wed Mar 22 10:07:11 CET 2017 

Dear Michael,

The correlation structures in nlme assume correlation among the
residuals **within** the most detail level of the random effects.
Residuals of observations originating from different levels of the
random effects are assumed to be uncorrelated. So nlme can do what you
would like to do.

As Ben already mentioned, INLA is useful as it allows for spatially
correlated random effects. You can find information on the INLA
website (www.r-inla.org) and in a few books. e.g.
- Blangiardo & Cameletti (2015) Spatial and Spatio-temporal Bayesian
Model with R - INLA
- Zuur et al (in press) Beginner's Guide to Spatial, Temporal and
Spatial-Temporal Ecological Data Analysis with R-INLA: Using GLM and
GLMM

Best regards,
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature
and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

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


2017-03-21 22:19 GMT+01:00 Michael Hyland <mhyland op u.northwestern.edu>:
> Thanks for the quick response.
>
> This is a subset. Full dataset is 12,266 observations across 530 groups (or
> Bikeshare stations).
>
> for
> model_spatial.gau <- update(model_spatial, correlation = corGaus(form = ~
> latitude +longitude ), method = "ML")
> and
> model_spatial.gau <- update(model_spatial, correlation = corGaus(form = ~
> latitude +longitude| id ), method = "ML")
> the error is "cannot have zero distances in "corSpatial" which I assume is
> due to the repeated observations having the same exact lat and lon;
> therefore zero distance
>
> Moreover, when I do anything with '| id' I think the model only accounts
> for 'within-group' correlations, not across stations
>
>
> On Tue, Mar 21, 2017 at 4:12 PM, Ben Bolker <bbolker op gmail.com> wrote:
>
>> Your approach seems about right.
>>
>> - What precisely does "unsuccessful" mean?  warnings, errors,
>> ridiculous answers?
>> - Is this your whole data set or a subset?
>> - centering and scaling predictors is always worth a shot to fix
>> numeric problems
>> - INLA is more powerful than lme for fitting spatial correlations,
>> although it's a *steep* learning curve ...
>>
>>
>> On Tue, Mar 21, 2017 at 5:08 PM, Michael Hyland
>> <mhyland op u.northwestern.edu> wrote:
>> > Hi,
>> >
>> > I'm new to the listserv.
>> >
>> > A shortened version of my dataset is below. I am developing a model to
>> > forecast monthly ridership at Bikeshare stations. I want to predict
>> 'Cnts'
>> > as a function of 'Population' - 'Temperature'. The dataset is unbalanced
>> > (unequal number of observations for each station) and most of covariates
>> do
>> > not vary over time, but a few do.
>> >
>> > I have successfully used lmer() and lme() in R to capture the dependency
>> > between the error terms for repeated observations from a given station
>> > ('id').
>> >
>> > model_spatial = lme(log(counts) ~ log(Population)
>> >                  +Drive +Med_Income + Buff2 +Rain + Temperature
>> >                  , data = Data, random = ~1|id, method = "ML" )
>> >
>> > model_All = lmer(log(counts) ~ log(Population)
>> >                  +Drive +Med_Income + Buff2 +Rain + Temperature
>> >                  + (1|id)
>> >                   , data = Data )
>> >
>> > However, a Moran's I test of the residuals suggests that the residuals
>> are
>> > spatially correlated.
>> > station.dists <- as.matrix(dist(cbind(Data$longitude, Data$latitude)))
>> > station.dists.inv <- 1/station.dists
>> > station.dists.inv[is.infinite(station.dists.inv)] <- 0   #Distance
>> value is
>> > inf for repeated observations from the same station
>> > Data$resid_all = resid(model_spatial)
>> > Moran.I(Data$resid_all, station.dists.inv)
>> >
>> >
>> > Hence, I need to develop a model in R that accounts for spatial
>> correlation
>> > across stations, while simultaneously capturing correlations between
>> > observations from a single station.  I've tried the following updates to
>> > the lme() model, but have been unsuccessful.
>> > model_spatial.gau <- update(model_spatial, correlation = corGaus(form = ~
>> > latitude +longitude ), method = "ML")
>> > model_spatial.gau <- update(model_spatial, correlation = corGaus(form = ~
>> > latitude +longitude| id ), method = "ML")
>> >
>> > Is there a way to formulate the correlation matrix in lme() or lmer()
>> such
>> > that the correlation between repeated obvservations of a given station
>> *and*
>> > the spatial autocorrelation between stations is accounted for?
>> >
>> >
>> > year month id Cnts latitude longitude Population Drive Med_Income Buff2
>> Rain
>> > Temperature
>> > 2015 8 2 2597 41.87264 -87.62398 4256 0.3418054 76857 127 0.07 71.8
>> > 2015 9 2 2772 41.87264 -87.62398 4256 0.3418054 76857 128 0.15 69
>> > 2015 10 2 684 41.87264 -87.62398 4256 0.3418054 76857 128 0.07 54.7
>> > 2015 11 2 394 41.87264 -87.62398 4256 0.3418054 76857 128 0.15 44.6
>> > 2015 12 2 148 41.87264 -87.62398 4256 0.3418054 76857 129 0.16 39
>> > 2016 1 2 44 41.87264 -87.62398 4256 0.3418054 76857 129 0.03 24.7
>> > 2015 5 3 2303 41.86723 -87.61536 16735 0.4312349 75227 90 0.15 60.4
>> > 2015 6 3 3323 41.86723 -87.61536 16735 0.4312349 75227 98 0.24 67.4
>> > 2015 7 3 5920 41.86723 -87.61536 16735 0.4312349 75227 98 0.09 72.3
>> > 2015 8 3 4405 41.86723 -87.61536 16735 0.4312349 75227 98 0.07 71.8
>> > 2015 9 3 3638 41.86723 -87.61536 16735 0.4312349 75227 99 0.15 69
>> > 2015 10 3 2061 41.86723 -87.61536 16735 0.4312349 75227 99 0.07 54.7
>> > 2015 11 3 1074 41.86723 -87.61536 16735 0.4312349 75227 99 0.15 44.6
>> > 2015 12 3 374 41.86723 -87.61536 16735 0.4312349 75227 100 0.16 39
>> > 2016 1 3 188 41.86723 -87.61536 16735 0.4312349 75227 100 0.03 24.7
>> > 2016 2 3 474 41.86723 -87.61536 16735 0.4312349 75227 100 0.04 30.4
>> > 2015 6 4 2968 41.85627 -87.61335 16735 0.4312349 75227 68 0.24 67.4
>> > 2015 7 4 4266 41.85627 -87.61335 16735 0.4312349 75227 68 0.09 72.3
>> > 2015 8 4 3442 41.85627 -87.61335 16735 0.4312349 75227 68 0.07 71.8
>> > 2015 9 4 2552 41.85627 -87.61335 16735 0.4312349 75227 69 0.15 69
>> > 2015 10 4 1301 41.85627 -87.61335 16735 0.4312349 75227 69 0.07 54.7
>> >
>> >
>> > Thanks,
>> > Mike Hyland
>> >
>> >         [[alternative HTML version deleted]]
>> >
>> > _______________________________________________
>> > R-sig-mixed-models op r-project.org mailing list
>> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>
>         [[alternative HTML version deleted]]
>
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