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 adjusted accordingly.

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

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