GEOSTATS: analyses with rates and proportions
- My question concerns current thinking on correlations involving ratio
variables that are proportions and rates. If this problem would be
better posted on another list, i would be interested in suggestions.
Let me also say that my background in is in psychology rather than
We are interested in identifying block group level census correlates
(e.g., persons under age 29, males, no high school diploma, etc) of an
unlawful behavior measured by 911 calls for service (911 calls are
aggregated to the block group level).
Because the block group population varies considerably, we
standardized all variables by dividing by block group population prior
to computing correlations and a regression model. A reviewer kindly
pointed out that correlations involving ratio variables have been long
recognized to lead to spurious correlations between ratio variables
even when the numerators of the ratio variables are themselves
uncorrelated. He also provided two citations (a 1972? conference paper
by Schuessler and a 1974 Sociological Methodology chapter by Fuiguitt
and Lieberson). I also looked at Cohen and Cohen's book on regression.
From these references, i get that a) it is not correct to infer an
association between the numerator components of two ratio variables
from the association between the two ratio variables. b) One must be
clear on whether the research question concerns the rate of the event
or the underlying count of the event. And, c) that controlling for the
denominator (here, populations) is generally alway preferable to using
In response to points a) and b), i would say that we actually are
interested in relationships between the ratio measures rather than
between the ratio numerators because ratios are more informative for
planning purposes and because relationships between the ratio
numerators can best be done by person-level data because of
aggregation bias. When we re-ran analyses using the cout versions of
the variables and treating population as a control variable (point c),
we encountered serious collinearity problems (no surprise). All of
this leads me to think we should stick with ratio measures.
I think i should also be concerned about spatial autocorrelation.
However, i am not quite clear on how to work with it. I would welcome
any advice members might have on this concern.
I am interested in how members of this list would work with this
problem. Citations would also be welcome. Please respond either on or
off the list.
Thanks, Gene Maguin
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