Keith, read my suggestion good; I didn't suggest replacing all zeroes in the distance matrix! You either rearrange points and recompute distances, or modify off-diagonal zero-distance entries in the covariance matrix.
Sounds like you modified the zero entries on the diagonal as well. -- Edzer Keith Dunnigan wrote: > Edzer, > > Thanks for your help! I tried the first suggestion.., I replaced all > the zero's in the distance matrix with a different value.., but I still > have the same problem. I get negative eigenvalues. I tried various > constants, replacing the zero with positive numbers up to 5, with no > luck. > > Anyone have any other ideas? > > Keith > > -----Original Message----- > From: Edzer J. Pebesma [mailto:[EMAIL PROTECTED] > Sent: Tuesday, September 11, 2007 2:30 PM > To: Keith Dunnigan > Cc: r-sig-geo@stat.math.ethz.ch > Subject: Re: [R-sig-Geo] Positive Definite Covariance Matrix for Grid > Sampled Data > > Keith, > > indeed kriging usually fails when one or more point pairs have zero > distance. One solution in terms of distances would be to shift these > points a bit, such that no zero distances occur anymore. In terms of the > > covariances, the solution would be to lower the corresponding > off-diagonal entries with a small amount. > > If you have measurements with a known measurement error variance, it may > > make sense to use this variance as the amount to subtract from all > off-diagonal elements of the covariance matrix. > > Hope this helps, > -- > Edzer > > Keith Dunnigan wrote: > >> Hello all, >> >> >> >> First I would like to apologize if this question is inappropriate >> > for > >> this list. I am new here, I found this list doing a web search and it >> seemed like the members here would have knowledge in this area. If >> there are more appropriate lists of forums for this question, I would >> appreciate that information. >> >> >> >> I do the majority of my work as a biostatistician in the >> pharmaceutical industry, so I am new to this area. I am working on a >> couple of small projects in this area though. I have consulted a >> > couple > >> of basic texts ("Introduction to Geostatistics" by Kitanidis, and "An >> Introduction to Applied Geostatistics" by Isaaks & Srivastava). >> >> >> >> The gist of what I have gathered from my reading is that standard >> practice is not to use the actual covariance matrix calculated from >> > the > >> data. This is because this matrix may in general not be positive >> definite. Instead standard practice seems to be to pick from one of >> several standard covariance models, which are guaranteed to be >> > positive > >> definite. After fitting the most appropriate model then, one >> > generates > >> the covariance matrix from this model and the distance matrix. The >> resulting matrix should be positive definite. >> >> >> >> The only problem is, I am not finding that to be true. For >> > instance, > >> when I apply the exponential model to my distance matrix and calculate >> the eigenvalues, I find that some of them are negative. Very, very >> small, but negative (For example -1.2 x 10exp-13). I applied a couple >> of models and found this to be true. Could someone help me with this? >> >> >> >> This is a small data set. I have a distance matrix that is 20 by >> > 20. > >> The exponential model I have used has range parameter R = 14 and sigma >> squared parameter 86.618. Letting the distance be x, the exponential >> model then is c(x) = sigmasq * exp( ((-3)*x)/R . >> >> >> >> My distance matrix is such that most of the covariances have very >> small values (effectively zero), except for the first couple of >> distances. That may be the trouble, what do geo folks usually do in >> situations such as this? I have copied the distance matrix below in >> > the > >> case any of you wants to take a look at this. >> >> >> >> 0 162 232 246 474 0 162 232 246 474 0 162 232 246 >> 474 0 162 232 246 474 >> >> 162 0 70 84 312 162 0 70 84 312 162 0 70 84 312 >> > 162 > >> 0 70 84 312 >> >> 232 70 0 14 242 232 70 0 14 242 232 70 0 14 242 >> > 232 > >> 70 0 14 242 >> >> 246 84 14 0 228 246 84 14 0 228 246 84 14 0 228 >> > 246 > >> 84 14 0 228 >> >> 474 312 242 228 0 474 312 242 228 0 474 312 242 228 0 >> > 474 > >> 312 242 228 0 >> >> 0 162 232 246 474 0 162 232 246 474 0 162 232 246 474 >> > 0 > >> 162 232 246 474 >> >> 162 0 70 84 312 162 0 70 84 312 162 0 70 84 312 >> > 162 > >> 0 70 84 312 >> >> 232 70 0 14 242 232 70 0 14 242 232 70 0 14 242 >> > 232 > >> 70 0 14 242 >> >> 246 84 14 0 228 246 84 14 0 228 246 84 14 0 228 >> > 246 > >> 84 14 0 228 >> >> 474 312 242 228 0 474 312 242 228 0 474 312 242 228 0 >> > 474 > >> 312 242 228 0 >> >> 0 162 232 246 474 0 162 232 246 474 0 162 232 246 474 >> > 0 > >> 162 232 246 474 >> >> 162 0 70 84 312 162 0 70 84 312 162 0 70 84 312 >> > 162 > >> 0 70 84 312 >> >> 232 70 0 14 242 232 70 0 14 242 232 70 0 14 242 >> > 232 > >> 70 0 14 242 >> >> 246 84 14 0 228 246 84 14 0 228 246 84 14 0 228 >> > 246 > >> 84 14 0 228 >> >> 474 312 242 228 0 474 312 242 228 0 474 312 242 228 0 >> > 474 > >> 312 242 228 0 >> >> 0 162 232 246 474 0 162 232 246 474 0 162 232 246 474 >> > 0 > >> 162 232 246 474 >> >> 162 0 70 84 312 162 0 70 84 312 162 0 70 84 312 >> > 162 > >> 0 70 84 312 >> >> 232 70 0 14 242 232 70 0 14 242 232 70 0 14 242 >> > 232 > >> 70 0 14 242 >> >> 246 84 14 0 228 246 84 14 0 228 246 84 14 0 228 >> > 246 > >> 84 14 0 228 >> >> 474 312 242 228 0 474 312 242 228 0 474 312 242 228 0 >> > 474 > >> 312 242 228 0 >> >> >> >> Thanks in advance for any help you can provide! Warmest Regards, >> >> >> >> Keith Dunnigan >> >> Statking Consulting >> >> Cincinnati Ohio >> >> >> >> >> [[alternative HTML version deleted]] >> >> _______________________________________________ >> R-sig-Geo mailing list >> R-sig-Geo@stat.math.ethz.ch >> https://stat.ethz.ch/mailman/listinfo/r-sig-geo >> >> > > > _______________________________________________ R-sig-Geo mailing list R-sig-Geo@stat.math.ethz.ch https://stat.ethz.ch/mailman/listinfo/r-sig-geo
