1-d quiz results

normal random dots
In this case, the points (other than the points (2,4) and (4,2)) were generated from a random normal distribution with mean 3. If you see a pattern, that's just your brain acting up!

A sensible strategy would be to use the sample mean as an estimate, without weighting nearby points any heavier than points far away.

























dots cluster
The clustering of the points about (2,4) might make you suspicious that there is, indeed, spatial autocorrelation. We don't have enough points to actually hope to model it, but it appears that it exists. It might be smart to just assume the simplest model, a linear model, and estimate the value at 3 at about 3 (linear regression would get you about the same answer).

Taking a mean in the face of spatial autocorrelation here would not be smart: you'd get a value of around 4, when it appears that the region around 2 was heavily oversampled. IDW (Inverse Distance Weighting) is just as bad an idea as taking a mean. The problem is the same: you'll overweight the region around 2.

A sensible variogram model used in kriging will downweight the cluster, and would produce a value of around 3.

























two dots
If you were inclined to choose 3 as your estimate, then you might justify it for three reasons: The first reason assumes no spatial autocorrelation, while the third assumes perfect spatial autocorrelation. The second is a mix of the two. If all you have is the two dots, and no prior information, then the second and third methods are completely unjustified (since they assume spatial autocorrelation).

























linear dots
Based on that distribution of points, you're probably safe in assuming that there is a linear relationship here! (That is, after all, how they were generate!) In that case, 3 is the proper estimate. This is a deterministic relationship: no stochastic (random) behavior here.

























trendy dots
Again, you're probably safe in assuming that there is a deterministic relationship here. This is a job for trend surface analysis, perhaps, rather than kriging (although variogram analysis would produce a model with small nugget which indicating strong spatial autocorrelation, and would give a pretty decent fit).

The points were generated as quadratics (locally) passing through the two points (2,4) and (4,2).


























Website maintained by Andy Long. Comments appreciated.
aelon@sph.umich.edu