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
CANADA T1K 3M4
