On 18 Dec 1999, Archtopist wrote:
> Happy holidays! I am developing a map of the annual probability of
> burning (in a wildfire) for a mountainous area. I have a map with
> cells labeled according to
> a) one of five vegetation types and
> b) housing density and
> c) the year(s) when wildfire occurred in the cell.
> I want to find out if there are differences in the likelihood of fire
> depending on vegetation and housing density.
Sounds daunting. If your timeline is long enough, neither vegetation
type nor housing density will be constant, and it is possible that
housing density may be changing even for relatively short timelines,
almost certainly changing at different rates in different cells. (After
all, if you go far enough back, housing density = 0 for all cells...)
> I've constructed a 2X5 contingency table for vegetation type (burn/no
> burn, veg type 1, type 2... type 5) and ran a chi square using the
> number of acres in each cell as N.
> I am concerned that this is a large and arbitrary sample - in that I
> could have used meters or inches, thus changing the rather large chi
> square value.
> Do you agree that chi square tests are not an option, and could you
> recommend an alternative (some sort of test of equality of
> proportions)?
Right. As Rich Ulrich has already agreed, chi-square tests are not an
option: at least, not the usual two-way contingency-table chi^2.
Besides the methodological problem of what counts as 1 thing (event, or
whatever) in a contingency table, there is the logical problem that you
can deal with only two variables at a time, you've already mentioned
three that you want to use, and there may well be others worth
considering (see below).
We may agree that the simplifying assumption, that vegetation type and
housing density are both constant for the period(s) for which you have
data, is probably over-simple and perhaps even unrealistic, but it does
permit one to consider alternative styles of analysis, some of which may
be amenable to the introduction of time dependencies...
One imaginable approach is to define something like a rate of wildfire
incidence -- number of wildfires per year per acre, say, or number of
acres burnt per year per acre of cell -- and compute that for each of
your cells as a dependent variable. [There may well be a number of ways
to do this, which would lead to a series of d.v.s that might usefully be
examined.] Predict this variable, using some version or subset of the
general linear model, from the variables you've mentioned: vegetation
type, housing density, calendar year (or other chronological indicator),
possibly some variables you haven't mentioned (size of cell in acres?
average altitude? average age of forest growth? relative dampness or
dryness of forest conditions that year? number of electrical storms that
year?), and their several interactions.
-- DFB.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
