Hi, Rich. The only answer I recall having seen on the listserve was one
suggesting multilevel (aka "hierarchical") modelling. If one wanted to
address the problem without ML modelling, I'd be inclined to proceed as
follows:
(1) I assume, in the absence of commentary to the contrary, that the
"strong spatial correlations" among the values in the 6x6 grids have much
the same structure from grid to grid and from respondent to respondent.
(Even if this is an oversimplification, it's a starting point.)
(2) Use the 6 rows and the 6 columns of the grid as categorical
variables in an ANOVA-like approach; the contents of each cell being, as
you write, the dependent variable. You don't mention what varible(s),
nor how many of them, you're using as predictor(s); but specify the
analysis as an ANCOVA, in a GLM routine if you're using MINITAB, with the
predictor(s) as covariates and the rows & columns as ANOVA factors.
You'll get a 5-df measure of "row" effect, a 5-df "column" effect, and a
25-df "interaction" effect; if these are large enough to be interesting,
you can try your hand at fitting various models to the pattern of results
using whatever you think is going on in the "spatial correlations".
If the structure of the spatial correlations is not replicated across
grids, or at least across SOME grids, this approach may not be fruitful;
but it can't hurt to try it, in any case.
I'm not sure what to make of the 14 grids. They might represent
another (14-level) ANOVA factor, but I can't tell from your description.
Hope this is helpful. As you probably recognized, it's essentially the
same kind of approach I suggested to Mike Granaas for his repeated
measures problem.
-- Don.
On Wed, 28 Feb 2001, Rich Strauss wrote:
> I don't have an answer, but I'm very glad this question was asked because
> I'm having a similar problem. I have 14 grids, values from which are to be
> used as the dependent variable in a regression. Each 6x6 grid consists of
> 36 observation points. Their are some fairly strong spatial correlations
> among the values at each grid, so I certainly can't treat them as if they
> were independent, yet reducing each grid to a single mean value (the other
> extreme) seems like a foolish waste of power. I'm trying to figure out how
> to use all of the observations, but also use the estimated spatial
> autocorrelations to weight them in the regression. (The design was
> originally created to answer a very different question, which is how I got
> into this mess.)
----------------------------------------------------------------------
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
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