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From   "Dr. John R. Vokey" <>
Subject   st: ROCFIT
Date   Wed, 3 Dec 2003 00:05:02 -0700

In STATA (and all other ROC fit routines I have found beyond STATA):
``rocfit fits maximum-likelihood ROC models assuming a binormal distribution of the latent variable.''

Apparently, it does so (given ``binormal'') by transforming the hit and false-alarm rates as a function of rating category to Gaussian z-scores, and then fits a straight-line to the resulting (ln-)transformed proportions, attempting to minimise the error along both axes via iterative maximum likelihood. I have no problem with the binormality assumption, nor the natural logarithm (ln) transform. My question is: why iterative maximum likelihood? Why not just compute the principal component in the ln space, yielding a least-squares solution minimising error along both axes (and no need for iteration)? As the principal component is (most likely) what people attempt to draw by eye to the data points in that space, it would seem to be what we want, and much simpler to compute. What do we gain in offset to these advantages by iterative maximum likelihood? BTW, I am not interested for this question in log-likelihood theory of decision-making with which I am quite familiar---that is a separate issue; here we are talking about the ``best-fitting'' straight-line to the ln-transformed data. I shiver at raising The Ghost Piscatorial, but would like an answer that, unlike similar issues in the the Great One's books, is not left as an ``excercise for the reader.'' ;-)
Dr. John R. Vokey
Department of Psychology and Neuroscience
University of Lethbridge
Lethbridge, Alberta

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