Is there a way to include both time correlation term and spatial correlation term in a single lme model?

Dear Nir,

I doubt that 7 irregular time points allows to estimate a sensible autocorrelation structure...

The INLA package allows models with multiple random effects. Each random effect can have a different correlation structure. Note that with INLA the random effects are correlated whereas nlme adds a correlation structure to the residuals.

You can find the INLA package at r-inla.org

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
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx at inbo.be
www.inbo.be

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-----Oorspronkelijk bericht-----
Van: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] Namens Nirmala Liyanage
Verzonden: maandag 15 september 2014 9:48
Aan: r-sig-mixed-models at r-project.org
Onderwerp: [R-sig-ME] Is there a way to include both time correlation term and spatial correlation term in single lme model?

Dear All,
I have an irregular time series dataset of soil moisture measured over two years period on a forest soil in Australia which I collected as a student. I suspect my dataset has a temporal and spatial correlation structure.  The data were collected in seven sampling events (first two within six months apart, second and third within year and after that approximately one month apart between sampling).  Data were also collected in two soil depths.  I have six predictor variables and I want to add both spatial and temporal correlation in a single model.  The summary of the model I tried, which only includes spatial correlation and time as a random effect, is as follows.


ARSMC7Gaus.lme <- lme(LogMC~V1 + V2 +V3 + V4 + V5  + V6 + as.factor(SDepth), random = ~1|Time,correlation = corGaus(1, form = ~xmga+ymga, nugget = TRUE), data=ARSMC6)



summary (ARSMC7Gaus.lme)

Linear mixed-effects model fit by REML
Data: ARSMC6
       AIC      BIC   logLik
  -488.679 -441.782 256.3395

Random effects:
Formula: ~1 | Time
        (Intercept)  Residual
StdDev:  0.01643712 0.1243742

Correlation Structure: Gaussian spatial correlation
Formula: ~xmga + ymga | Time
 Parameter estimate(s):
    range    nugget
1.5809160 0.3307183
Fixed effects: LogMC ~ V1 + V2 + V3 + V4 + V5 + V6 + as.factor(SDepth)
                        Value Std.Error  DF    t-value p-value
(Intercept)          3.728646 0.4874570 365   7.649179  0.0000
V1                   0.001482 0.0004610   3   3.214425  0.0488
V2                   0.005831 0.0020212 365   2.884979  0.0041
V3                  -0.061032 0.0060525   3 -10.083730  0.0021
V4                   0.002323 0.0001736   3  13.381117  0.0009
V5                   0.008451 0.0029611 365   2.853999  0.0046
V6                   0.003676 0.0005210 365   7.054582  0.0000
as.factor(SDepth)15 -0.029451 0.0080961 365  -3.637632  0.0003
Correlation:
                    (Intr)  V1     V2     V3     V4     V5     V6
V1                  -0.101
V2                   0.181  0.000
V3                   0.276 -0.017 -0.001
V4                   0.732 -0.128  0.001  0.402
V5                  -0.488 -0.013 -0.097  0.001  0.011
V6                  -0.657 -0.031 -0.328  0.001  0.027  0.688
as.factor(SDepth)15 -0.096  0.048 -0.097  0.047 -0.094  0.009  0.030

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max
-3.55288638 -0.60507563 -0.04411639  0.54770394  3.87767186

Number of Observations: 376
Number of Groups: 7

Above model is significantly different from the null model (without spatial structure and time as a random effect).


               Model df       AIC       BIC   logLik   Test L.Ratio p-value

ARSMC7.lme         1 10 -396.4002 -357.3194 208.2001

ARSMC7Gaus.lme     2 12 -488.6790 -441.7820 256.3395 1 vs 2 96.2788  <.0001

I used R 3.0.1 and package nlme

Note; to make this model to work I had to add 0.05cm to x coordinate of the second soil depth (shift from original x coordinates of all second depth values). Otherwise I got following error message (##Error in getCovariate.corSpatial(object, data = data) :
##cannot have zero distances in "corSpatial")

My questions are
1. Ideally, we would like to have time as a correlation term in the model and no random effect (i.e. gls). Is there a way that I could also include time as a correlation term in addition to the spatial correlation term?
2. Currently Time is coded as 1-7 but they are not recorded in regular time intervals. What is the best way to put that in to the model?

Thank you very much,
Kind regards,
Nir


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