I ran a Wald Test on EViews and got these results but Id lik

I ran a Wald Test on EViews and got these results but I\'d like to better understand what each part means (especially the F Stat and Chi Square.) Thanks!

Solution

Inference for fixed effects in linear mixed models introduces some difficulties. In general, the methods used to construct F-tests in analysis of variance and regression cannot be used for the diversity of applications of the general linear mixed model available in ASReml. One approach would be to use likelihood ratio methods (see Welham and Thompson, 1997) although their approach is not easily implemented.

Wald-type test procedures are generally favoured for conducting tests concerning t. The traditional Wald statistic to test the hypothesis H₀ Lt = l for given L

and asymptotically, this statistic has a chi-square distribution on r degrees of freedom. These are marginal tests, so that there is an adjustment for all other terms in the fixed part of the model. It is also anti-conservative if p-values are constructed because it assumes the variance parameters are known.

The small sample behaviour of such statistics has been considered by Kenward and Roger (1997) in some detail. They presented a scaled Wald statistic, together with an F-approximation to its sampling distribution which they showed performed well in a range (though limited in terms of the range of variance models.

The Wald test is usually discussed as a chi-squared test, because it is usually applied to problems where only the asymptotic sampling distribution is known. But if we do know the sampling distribution for finite samples, we certainly want to use that.