A measure of how much the random effects changes if the case is deleted. Runs with large values should be investigated. Large values can be caused by typographical errors, a poor model incorrect model, or a design point far from the remaining cases.
“Large” is the value of the red line. It is set to the \(\chi^2\) critical value for a \((1-\alpha)\cdot 100\%\) confidence level with 1 degree of freedom for each variance component estimate on the ANOVA. If there are blocks, groups and residuals on the ANOVA, then 3 degrees of freedom are used. If only groups and residuals, then 2 degrees of freedom are used.
Never ignore a run just because the diagnostics plots indicate it may be a problem. Verify that the data is wrong in some way before ignoring it.