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st: Re: hypothesis tests


From   Christopher F Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: hypothesis tests
Date   Mon, 29 Dec 2003 06:51:57 -0500

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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