j_chibar.hlp

是一个经济学管理应用软件 很难找的 但是经济学学生又必须用到

{smcl}
{* 22mar2005}{...}
{title:What is this chibar2 thing?}

{pstd}
The likelihood ratio test that is displayed is testing on the boundary
of the parameter space.  Most likely, you are testing whether an estimated
variance component (something that is always greater than zero) is
different from zero using an LR test.

{pstd}
Suppose for now that the two models being compared differ only with respect
to the variance component in question, in which case the test statistic will
be displayed as "chibar(01)".  In such cases, the limiting distribution of the
maximum-likelihood estimate of the parameter in question is a normal
distribution that is halved, or chopped-off at the boundary -- zero in this
case.  As a result the distribution of the LR test statistic is not the usual
chi-square with 1 degree of freedom, but instead a 50:50 mixture of a
chi-square with no degrees of freedom (i.e. a point mass at zero) and a
chi-square with 1 degree of freedom.

{pstd}
The p-value of the LR test takes this into account, and will be set to 1
if it is determined that your estimate is close enough to zero to be, in
effect, zero for purposes of significance.  Otherwise, the p-value displayed
is set to one-half of the probability that a chi-square with 1 degree of
freedom is greater than the calculated LR test statistic.

{pstd}
Sometimes you are testing whether a variance component is zero {it:in addition} to testing whether {it:k} other parameters (not affected by boundary
conditions) are zero.  Such situations often arise when comparing models fit
by {cmd:xtmixed}.  For such tests, the distribution of the likelihood-ratio
test statistic is a 50:50 mixture of chi-square distributions with {it:k}
and {it:k}+1 degrees of freedom, shown on the output as "chibar(4_5)", for
example.   As was the case with chibar(01), significance levels are adjusted
accordingly.

{pstd}
Finally, if you are testing more than one boundary-affected parameter, the
theory is much more complex and, in most cases, intractable.  When this
occurs, Stata will either display significance levels that are
{help j_xtmixedlr:conservative} and marked as such, or not display an 
LR test at all.


{title:References}

{phang}
Gutierrez, R. G., S. L. Carter, and D. M. Drukker. 2001.
On boundary-value likelihood-ratio tests.  {it:Stata Technical Bulletin}
60:15-18. Reprinted in {it:Stata Technical Bulletin Reprints}, vol. 8, 
pp. 233-236.{p_end}

{phang}McLachlan, G. J. and K. E. Basford. 1988.  {it:Mixture Models}.
New York: Marcel Dekker.{p_end}

{phang}Self, S. G. and K.-Y. Liang. 1987. Asymptotic properties of 
maximum likelihood estimators and likelihood ratio tests under nonstandard
conditions.  {it:Journal of the American Statistical Association} 
82: 605-610.{p_end}

{phang}Stram, D. O. and J. W. Lee. 1994. Variance components testing
in the longitudinal mixed effects model. {it:Biometrics} 50: 1171-1177.{p_end}


{title:Also see}

{psee}
Manual:  {bf:[XT] xtmixed}
{p_end}