I am trying to understand better the meaning of a negative
value of pseudo-R2 for tobit. There is a treatment of the
question in the Stata FAQ's at http://www.stata.com/support/faqs/stat/pseudor2.html
The pseudo-R2 is defined as 1 - L1/L0 (where L1 is the LL
with variables and L0 is the LL for constant only) and the
FAQ notes that because f(x) can exceed 1 for non-discrete
density functions, either L1 or L0 can be positive:
For continuous distributions, the log-likelihood is the log
of a density. Since density functions can be greater than 1
(cf. the normal density at 0), the log-likelihood can be
positive or negative.
I am confused by the invocation of the normal density
function in the paragraph because phi(0) is 0.39894228 (in
Stata, "display normden(0)"). (Is that right?) But I think
the point is that f(x) can exceed 1 for some non-discrete
pdf's; hence log(f(x)) is not necessarily negative and the
pseudo-R2 can be negative (or greater than one). Can
someone clarify or verify?
I also have a practical question: a colleague is getting
large negative pseudo-R2 from a tobit, around -0.30. Does
this indicate a problem or can we take seriously the FAQ,
that "For many models, including tobit, the pseudo-R2 has no
real meaning."
Best regards,
Michael Ash, Assistant Professor
of Economics and Public Policy
Department of Economics and CPPA
University of Massachusetts
Amherst, MA 01003
Tel 413-545-6329 Fax 413-545-2921
Email [email protected]
http://people.umass.edu/maash
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