Interpreting Spatio-Temporal Variograms

Question

I've got spatio-temporal disease data at the county/annual level for 2000-2014. I'm analyzing it to try to pull out temporal variations in disease incidence and was told that I should generate a spatio-temporal variogram. The variogram appears to show a relationship but I'm having a hard time finding out how to interpret the graph (which is attached).

Is this graph showing that disease rates 10-15 years apart are more strongly correlated at <100 km, 200 km, and 500km? and that the temporal correlation drops off sharply at around 8 years apart?

If I remember correctly, the lower the gamma, the greater the autocorrelation? I've looked for a guide on interpretation for a while now but all I can find are guides on how to generate models from this data.

Answer 1

A variogram is a measure of dissimilarity in space/time. The lower is the variogram value, the higher is the correlation between the two pairs of data points.

Thinking about spatio-temporal correlation simultaneously is often tricky. For exploratory analysis purpose, statisticians sometimes tend to separately think about the spatial variogram at zero-time lag and the temporal variogram at zero-spatial lag, which are the two line plots you see when you look at the figure from the front and side planes. Variograms often give you a rough estimate about how your space-time correlation looks like. However, accurate estimates are usually evaluated by fitting a covariance model to your data.

From the figure above, I can draw the following observations:

1. There seems to exist a strong temporal correlation up to almost 8 years apart (which is what the statisticians call: temporal range), after which correlation starts to die out.
2. There seems to exist a fairly spatial correlation up to 200 kms apart.
3. Your data seems to exhibit (a nugget effect), meaning that the data is noisy, because the intercept of the spatial and temporal variograms should be zero if the data is perfectly non-noisy. But in your case, the temporal variogram and spatial variograms have non-zero values for the intercepts.
4. From the wigly look of the space-time surface, I might conclude that your data seems to exhibit some spatial-temporal interaction, which might support the argument of fitting a non-separable covariance model to the data, rather than separable models.