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GEOSTATS: analyses with rates and proportions

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  • Gene Maguin
    My question concerns current thinking on correlations involving ratio variables that are proportions and rates. If this problem would be better posted on
    Message 1 of 1 , Dec 31, 1997
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      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
      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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