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

Dexter Locke dexter.locke at gmail.com
Wed Mar 22 15:46:51 CET 2017 

Dear list,

You may consider also the citations below and HSAR package:
https://cran.r-project.org/web/packages/HSAR/vignettes/hsar.html

Dear Michael,

Do you have comparable code for extracting the residuals of the model and
testing for spatial autocorrelation that works with your second model
"model_All" created with lme4::lmer ?  What package contains the "Moran.I"
function?

- Dexter

Dong, G., & Harris, R. (2014). Spatial Autoregressive Models for
Geographically Hierarchical Data Structures. *Geographical Analysis*,
n/a-n/a. http://doi.org/10.1111/gean.12049

Dong, G., Harris, R., Jones, K., & Yu, J. (2015). Multilevel Modelling with
Spatial Interaction Effects with Application to an Emerging Land Market in
Beijing, China. *PloS One*, *10*(6), e0130761.
http://doi.org/10.1371/journal.pone.0130761

Dong, G., Ma, J., Harris, R., & Pryce, G. (2016). Spatial Random Slope
Multilevel Modeling Using Multivariate Conditional Autoregressive Models: A
Case Study of Subjective Travel Satisfaction in Beijing. *Annals of the
American Association of Geographers*, *106*(1), 19–35.
http://doi.org/10.1080/00045608.2015.1094388

On Wed, Mar 22, 2017 at 5:07 AM, Thierry Onkelinx <thierry.onkelinx at inbo.be>
wrote:

> 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 at 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 at 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 at 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]]
> >> >
> >> > _______________________________________________
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> >> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >>
> >
> >         [[alternative HTML version deleted]]
> >
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