- Dec 31, 1997My 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

geography.

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

ratio variables.

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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