OK, I'm really slow to responding to this thread, but I've been thinking
about it. Are there covariates available (besides time) that can be
used? If yes, doesn't it make sense to look at this using a spatial
autoregressive regression model? Since the lakes typically don't touch,
then the spatial weight matrix would need to be based on distance. I'm
not sure what the correct projection is if it goes really far north, and
as far south as the southern Niagara Peninsula. A distance preserving
projection would make the most sense, but UTM (the likely culprit) I
know will breakdown if some of the lakes are too close to the north pole.
Dan
On 02/10/2011 08:26 PM, Rolf Turner wrote:
On 11/02/2011, at 10:14 AM, david depew wrote:
Thanks Rolf,
I see your point, and I admit that I've waffled a bit on this
issue. I'm hesitant to drive down the kriging path (although
indicators might be suitable), because there are many known (and
unknown) covariates that affect the contaminant burden, and few of
these are quantified at the scale or resolution we would require to
make such an approach useful (at least based on my experience).
Regarding the data; the sites were not "chosen" as one would choose
locations to sample, rather they are a mix of quasi - synoptic and
randomized sampling designs from ~ 50 or so different investigators/
agencies. We've simply mashed them into one large database for our
purposes. The habitat of the organisms is fixed in space (lakes),
but given that there is no real selection protocol for sites, I
wondered if this fit into the "grey" area.
Well, it's pretty well all grey to me! :-)
I'm afraid I have no insights to offer. But let me say that whether
or not the sites were ``chosen'' in any organised fashion, their
locations
are in effect given to you. They did not arise from a random process.
Or rather, if they did, you are not interested in studying the process
which gave rise to the locations but rather properties of observations
made at those locations.
A mathematical description of the structure is, I think, that you have
a random field, defined on a discrete set of points, an irregular
lattice
--- the observation points in your data base. There is also a time
variable
involved, and associated covariates are observed. It might be
appropriate
to include time as a covariate. Or not. You might consider the
lattice
of points to be three dimensional, with a time dimension.
Saying all that doesn't really help to develop an appropriate
analysis strategy. However it make help to focus the mind and to
formulate clearly and precisely just what problems you are trying to
solve.
cheers,
Rolf Turner
On Thu, Feb 10, 2011 at 3:42 PM, Rolf Turner
<r.tur...@auckland.ac.nz> wrote:
On 11/02/2011, at 6:00 AM, david depew wrote:
Dear list,
A brief and (hopefully) simplistic question regarding point pattern
analysis.
We have compiled a large, continental database of chemical burdens
in a
model organism. Currently, the data span 40 years and covers the
entire
country of Canada (including the high arctic). We have categorized the
numeric data into categorical data (i.e. categorical marks) based
on risk
thresholds. We'd like to assess whether or not there are
interesting spatial
patterns ( i.e. clusters of levels of risk (high vs low)), much like a
case/control approach. My question is as follows;
Is there a "best" geographic projection for this approach?
Currently all
data are in Latitude/Longitude. My inclination is to use something
along the
lines of an equal area projection to maintain a reasonable
representation of
spatial dispersion.
This doesn't sound to me like ***point pattern*** data. It sounds
like
you have taken measurements of ``chemical burdens'' in a particular
organism, at a number of ***chosen*** sites over a number (40) of
years.
Thus the observation points are deterministic, not random, and so
point
pattern analysis doesn't come into it.
It may be the case that some sort of combination of kriging and
time series
or repeated measures analysis might be called for. But here I
speak of
that of which I know nothing.
cheers,
Rolf Turner
--
David Depew
Postdoctoral Fellow
School of Environmental Studies
Queen's University
Kingston, Ontario
K7L 3N6
david.de...@queensu.ca
P: (613) 533-6000 x77831
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