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Re: st: Wald test in Random Coefficient Model

From   Stas Kolenikov <>
Subject   Re: st: Wald test in Random Coefficient Model
Date   Fri, 25 Feb 2011 10:26:10 -0500

On Fri, Feb 25, 2011 at 10:05 AM, Joerg Luedicke
<> wrote:
>> The behavior of this test is not quite what we would expect.
>> The problem is that the null hypothesis is on the boundary of
>> the parameter space, i.e. the null hypothesis is that the
>> country level variance equals 0, and a variance can only be
>>>= 0. There is a discussion of that in (Gutierrez et al. 2001).
> That's right. I guess the rule of thumb in this case would be to
> divide the p-value by 2?

Nope. That's the rule of thumb that works when you have only one
restriction. Here you have two, on the random intercept and on the
random slope, so the correct asymptotic distribution is a mixture of
chi^2(0), chi^2(1) and chi^2(2). The latter one is the most
conservative, but even that distribution gives you a p-value of zero,
as shown in the line:

> LR test vs. logistic regression:     chi2(3) =  2132.55   Prob > chi2 = 0.0000

If you insist on Wald test (on the difference between tests in the
asymptotic trio, see, then you would
need figure out what the parameterization of the variance components
is (type -matrix list e(b)-) and then use -test- or -testnl- to create
the test of interest. If the variance components are parameterized
using logs, then you cannot achieve a value of zero, and would have to
use the LR test.

Stas Kolenikov, also found at
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