Ordinary Kriging: “Warning message: In fit.variogram(data.var, vgm(“Mat”)) : No convergence after 200 iterations: try different initial values?”

Question

I am trying to fit a variogram for kriging using the sp and gstat packages in r, but when I fit the variogram using a mattern fit, I get this warning message:

Warning message:
In fit.variogram(data.var, vgm("Mat")) :
  No convergence after 200 iterations: try different initial values?

The fit variogram is below:

Is this something that needs to be corrected? If so, what can I do to correct this? When I generate the map of the finished ordinary kriging operation, it doesn't look too bad, but I am new to this and don't know if the warning message when fitting the variogram is a problem or not.

The data to reproduce this error can be found and downloaded here and is named "stack_variogram_question.csv." The file size is small (7 KB).

Here is the code to reproduce the warning message:

library(pacman)
p_load(sf,
       spatstat,
       gstat,
       sp,
       rgdal,
       raster,
       spdep)

setwd('path\\to\\file')

data <- read.csv("stack_variogram_question.csv")

# Convert to sp dataframe
lon <- data$Longitude
lat <- data$Latitude
coords <- cbind(lon, lat)

data_sp <- SpatialPointsDataFrame(coords, 
                                  data[, c("Name", 
                                           "total_auto_observations")], 
                                  proj4string = CRS('+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs'))

data_sp <- remove.duplicates(data_sp)


#Generate grids for interpolation.
grd <- SpatialPixels(SpatialPoints(makegrid(data_sp, n=50000)), proj4string = proj4string(data_sp))
coordnames(grd) <- c("X", "Y")


# Produce and fit the variogram
f.data <- as.formula(total_auto_observations ~ X + Y)
data_sp$X <- coordinates(data_sp[ ,1])
data_sp$Y <- coordinates(data_sp[ ,2])

# Compute the variogram
data.var <- variogram(f.data, data = data_sp, cutoff = 0.3)
plot(data.var, main = 'Auto Variogram')

# Fit variogram
data.fit <- fit.variogram(data.var, vgm('Mat')) #Mattern fit

The warning occurs right after the last line is run.

To plot the fitted variogram:

plot(data.var, 
     pch = 20, 
     cex = 1.5, 
     col = 'black', 
     ylab = 'Semivariance', 
     xlab = 'Distance (m)', 
     model = data.fit)

Answer 1

The code is struggling to find well-defined parameter estimates for the model. This is often a sign that the model is maybe over-defined (too many parameters) for the data it is fitting. Variograms can take a bit of tweaking to find well-fitted models, and sometimes fits look weird because they take into account the number of pairs used to create each variogram point as a weight, and that's hard to eyeball intuitively.

Also, you are working over a large range (the full range of your data) which means you'll lose any small-scale correlation. If you investigate that:

> data.var <- variogram(f.data, data = data_sp, cutoff = 0.01)
> data.fit <- fit.variogram(data.var, vgm('Mat')) #Matter
> plot(data.var, model=data.fit)

You get a fit with no errors:

Looking at a map of your data it might not be surprising:

because there's a lot of zeros and ones, so lots of close points with zero variance. Also that shows your data is mostly small and integers, so a Gaussian kriging model might not be valid if this is count data. You'll be getting negative numbers on the kriging prediction interval.

Note: After faffing around with gstat I threw the data (reprojected into a Mercator projection, so the distance scale is in metres) into autoKrige (from automap package) and got this:

which is what alerted me to the short-scale correlation in the first place.