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# Ratio variables in regression analysis

Hi all,

Should we be using ratio variable as predictors in regression analysis? If yes, how the estimate should be interpreted?

Thanks

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‎07-24-2017 01:34 PM
Posts: 2,115

## Ratio variables in regression analysis

Many predictors are natural ratios and are interpreted like any other continuous measure.  The place that gets tricky is if the ratio is bounded and the data are near the bound.  For instance, often a % is bounded at 0 and 100.  If the data are in the middle, the usual normal theory works fine (An example of that is the "ejection fraction" for the heart.  It can officially be between 0 and 100%, but 60% is "normal" and it is rarely observed outside 10-90%, so we just use the standard analysis approach).  If the data are near the edge, then you probably need to explore some variance stabilizing transformation (see any good regression reference).

Doc Muhlbaier

Duke

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Solution
‎07-24-2017 01:34 PM
Posts: 2,115

## Ratio variables in regression analysis

Many predictors are natural ratios and are interpreted like any other continuous measure.  The place that gets tricky is if the ratio is bounded and the data are near the bound.  For instance, often a % is bounded at 0 and 100.  If the data are in the middle, the usual normal theory works fine (An example of that is the "ejection fraction" for the heart.  It can officially be between 0 and 100%, but 60% is "normal" and it is rarely observed outside 10-90%, so we just use the standard analysis approach).  If the data are near the edge, then you probably need to explore some variance stabilizing transformation (see any good regression reference).

Doc Muhlbaier

Duke

Posts: 2,655

## Ratio variables in regression analysis

Doc's advice is excellent. My concern with ratio variables is that they are often bounded below by zero, but unbounded above.  One way to address this is to separate the numerator and denominator in the predictor by taking the logs of both and including those as predictors.  The correlation between the two predictors should (note SHOULD) cover the situation.  It is even more important for ratio variables as dependent variables.

Steve Denham

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