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Re: st: Re: Problems with -hetgrot-


From   Richard Williams <Richard.A.Williams.5@nd.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Re: Problems with -hetgrot-
Date   Sun, 14 Mar 2004 19:38:59 -0500

At 06:14 PM 3/14/2004 -0600, Scott Merryman wrote:
Richard,

I believe there is an error in Greene's text. As you reported, Greene gives the
LR statistics as 120.915. However, if you compute this by hand, given the
individual sigma^2, the result is:

. disp 100*ln(15708.84) - 20*(ln(9410.91) + ln(755.85) + ln(34288.49) +
ln(633.42) + ln(33455.51))
104.41512

which is what you and I got.
I did the same thing! But if he has an error, I don't think that is where it is. In Greene, 4th edition, p. 597, he says that iterated fgls (the Model 3 I presented) can be used to compute the LR statistic. But, he also says that "If only least squares results are available...[they may be used], possibly with some loss of power in small samples." That is what your above calculation does; it uses the least squares estimates rather than the ML estimates.

What Greene apparently does is use the estimate of sigma from the OLS estimates (15708.84) with the ML estimates for the group sigmas. The calculation (using the #s reported on p. 598_ is

. disp 100*ln(15708.84) - 20*(ln(8657.72) + ln(175.80) + ln(40210.96) + ln(1240.03) + ln(29825.21))
120.92892

What I don't understand is why he is using the 15708.84 from the least squares estimates, rather than using a ML estimate of sigma. This would seem to be inconsistent with what he says on the middle of p. 597.

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