## Stata 15 help for j_chibar

```
What is chibar2?

The likelihood-ratio (LR) test that is displayed is testing on the
boundary of the parameter space.  You are probably testing whether an
estimated variance component (something that is always greater than zero)
is different from zero by using an LR test.

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 here.  The distribution of the LR test statistic is
therefore not the usual chi-squared with 1 degree of freedom but is
instead a 50:50 mixture of a chi-squared with no degrees of freedom (that
is, a point mass at zero) and a chi-squared with 1 degree of freedom.

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-squared with 1
degree of freedom is greater than the calculated LR test statistic.

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