[R-sig-Geo] multiple regression analysis

Dylan Beaudette debeaudette at ucdavis.edu
Tue Nov 9 19:15:23 CET 2010


Or, you could include additional variables into the model structure that 
describe vertical patterns. If you choose to do this, then it would also be 
wise to account for correlation between observations with depth and in space. 
Assuming that you can describe your response variable with some covariates 
that you have measured in space, I would start looking at models such as:

# this might help

# account for patterns in depth + covatiates:
# y is the response
# x is one of your covariates
# rcs(depth) is a set of restricted cubic spline basis functions
# that can accommodate just about any smooth shape with depth
ols(y ~ x * rcs(depth))

# you can account for correlation between observations in depth with 
# generalized least squares
# correlation structure is modeled with a continuous AR(1) process
Gls(y ~ x * rcs(depth), cor=corCAR1(form= ~ depth | bore_hole_id))

# this can be further extended to account for spatial correlation...


On Tuesday, November 09, 2010, Peter Kirchner wrote:
> Hi MatevÅŸ,
> If I understand you correctly and your goal is to conduct a
> spatial analysis of the variables of parent material, and particle size
> e.g. clay, based on depth you will first need to make some decisions on how
> to classify your data based on depth. Then you could create a 2d raster
> file representation of their relationship by kriging or co-kriging your
> classified point data using each variable of interest. Stacking these
> rasters will then allow an analysis on a 3d basis, allowing the data to be
> further analyzed using regression, principal components, or other methods.
> Hope this helps,
> Peter
> ************************************
> Peter
> Kirchner, Graduate Research Scientist 
> University of California, Merced
> pkirchner at ucmerced.edu (209) 834-7628 
> -----Original Message-----
> From:
> r-sig-geo-bounces at stat.math.ethz.ch
> [mailto:r-sig-geo-bounces at stat.math.ethz.ch]
> On Behalf Of MatevÅŸ Pavlic
> Sent: Sunday, November 07, 2010 11:25 PM
> To:
> r-sig-geo at stat.math.ethz.ch
> Subject: [R-sig-Geo] multiple regression
> analysis
> Hi all, 
> This is more a help on ideas that on actuall R code.
> Those of you which are geologist or work with boreholes woudl understand
> that i would like to achieve. 
> I'll tr to explain as good as I can...so
> here it goes..
> I have around 1000 geomechanical (geological) borehole logs
> in a database.
> The logs contain staial info, lithology and some laboratory
> data. My initial goal is 
> compare the boreholes that are closer together
> (ie.e closer that 50 meters) to see if they are similiar lithologicaly. I
> thought maybe this can be done with some kind of multiple 
> regression
> analysis where one would test if layers (ie. Clayey layer in Bhole 1 in
> depth 5m and in Bhole2 this layer is in depth 7 meters) are in same depth
> and if geology on 
> that depth is the same in Bhole1 as in Bhole 2. For
> example if boreholes would have similiar lithology on similar depth that
> the regresion R^2 would be 1 and if not that it would be less than 1.
> This
> is of course my idealized way of approaching the problem. The idea is to
> get a general a feel for the heterogenity of the changing geology (in depth
> profile) over and area and to create a map 
> of heterogenity of geology of
> the observed area. Does any of this make sense are i am way off?
> Any ideas
> and/or experiences with such a problem is greatly appreciated, 
> Regards, m
> 	[[alternative HTML version deleted]]

Dylan Beaudette
Soil Resource Laboratory
University of California at Davis

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