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I am modeling binominal data with random effects and spatial autocorrelation using MASS::glmmPQL(). Plotting the residual semivariogram of a model fit without accounting for spatial autocorrelation leads me to the following semivariogram:

enter image description here

Hence, I set up a corSpatial object to account for the spatial autocorrelaton within my data.

correl = corSpatial(value = c(1911, 0.03), form = ~ry + rx, nugget = TRUE,
                    fixed = FALSE, type = "spherical")

After inspecting the fit of the model which accounts for spatial autorcorrelation using the correl object introduced above, I get the following output when calling summary() (note that "date" is a random effect):

Correlation Structure: Spherical spatial correlation
 Formula: ~ry + rx | date 
 Parameter estimate(s):
      range      nugget 
329.0934685   0.2516632

I visualized the residuals(?) again in a variogram using nlme::Variogram()

plot(nlme::Variogram(fit5, form = ~rx + ry, data = d, maxDist = 20000, 
               breaks = c(50, 200, 400, 600, 1000, 1500, 2000, seq(2700,29700,by = 1000)), 
               robust = FALSE), smooth = TRUE, span = 0.65, showModel = FALSE)

enter image description here

Leaving me confused.

  1. How do I interpret the summary() outcome?

  2. How to deal with the nlme::Variogram() output showing a totally different shape compared to the resid. svgm/summary() output?

  3. What did I do wrong?

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