[R] ROC optimal threshold

Frank E Harrell Jr f.harrell at vanderbilt.edu
Fri Mar 31 23:01:51 CEST 2006

Tim Howard wrote:
> Dr. Harrell, 
> Thank you for your response. I had noted, and appreciate, your perspective on ROC in past listserv entries and am glad to have an opportunity to delve a little deeper.
> I (and, I think, Jose Daniel Anadon, the original poster of this question) have a predictive model for the presence of, say, animal_X. This is a spatial model that can be represented on maps and is based on known locations where  animal_X is present and (usually) known locations where animal_X is absent. Output of the analysis (using any number of analytic routines, including logit, randomForest, maximum entropy, mahalanobis distance...) is a full map where every spot on the map has a probability that that particular location has the appropriate habitat for animal_x.
> This output can be visualized by just using a color scale (perhaps blue for low probability to red for high probability), BUT, there are times when we want to apply a cutoff to this probability output and create a product where we can say either "yes, animal_X habitat is predicted here" or "no, animal_X habitat is not predicted here."
> Note this is the final analytic step. There are no later anaylsis steps and so (possibly) adjustments for multiple comparisons do not come into play.
> Indeed, it seems that using a standard process to find a threshold reduces the arbitrariness of the probabiliity color scale (at what probability do we set 'red'? at what probability do we set 'blue'?).
> Are there alternative approaches that reduce the drawbacks you allude to? 
> How would you turn a surface of probabilities into a binary surface of yes-no?
> Thank you for your time.
> Sincerely,
> Tim Howard
> Ecologist
> New York Natural Heritage Program


I think that 'animal_X habitat is predicted here' would hide a lot of 
useful information, especially "gray zones" or uncertain areas.   I 
think that a continuous mapping of probabilities to a gray scale or to 
the heat spectrum would work best.  Bill Cleveland also has another idea 
of using 5 saturation levels on each of 2 hues to get 10 levels with 
easier human discrimination.  You might also consider thermometer plots 
which give some of the most accurate human perception of a continuous 
variable.  For the first 2 ideas you may have to round probabilities to 
give just 10 intervals (or use deciles).

If you choose cutpoints from the data, there is uncertainty from the 
cutpoint that may have to be taken into account.  See for example 


>>>>Frank E Harrell Jr <f.harrell at vanderbilt.edu> 03/31/06 11:20 AM >>>
> Choosing cutoffs is frought with difficulties, arbitrariness, 
> inefficiency, and the necessity to use a complex adjustment for multiple 
> comparisons in later analysis steps unless the dataset used to generate 
> the cutoff was so large as could be considered infinite.

Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University

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