On Dec 29, 2003, at 2:33 AM, Richard wrote:
How about the general issue of using -lrtest- rather than -test- when
doing
linear regression? Is it considered appropriate? Is -test- considered
more optimal? My experience has been that -lrtest- and -test- tend to
give
similar, but not identical, results, when used with regards to the
- -regress- command.
Any graduate econometrics text will discuss the differences in approach
between Wald statistics (e.g. F tests of subset hypotheses in a linear
regression context), Lagrange multiplier (LM) statistics and
(log-)likelihood ratio tests. Greene 5th ed. has a nice discussion in
section 17.5 of these three asy equivalent test procedures.
The limiting distribution of the Wald statistic is J*F -> Chi^2(J) for
J restrictions on the parameter space, so that Stata could display
Chi^2 stats rather than F stats. The Wald stat is based on the
unrestricted model (and requires estimation of only that model); the LM
stat is based on the restricted model (likewise, as it evaluates the
gradient of the LLF of that model); and the LLR statistic requires
estimation of both models, and comparison of their LLR values. For
algebraic reasons W >= LLR >= LM. Greene suggests that in small samples
one might want to use a conservative approach, which would agree with
the notion of using the LLR stat generated by -lrtest- in a linear
regression context. But it is a lot more work than using the Wald stat
generated by -test-.
Kit
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