# Mixed effects model - interpreting significant fixed effect coefficients with insignificant likelihood ratio test

I have a linear mixed effects (LME) model with a single nominal-valued fixed effect with 4 levels, and two nested random effects (measurements from cells at each level of the fixed effect, with multiple cells within each subject) w/ random slopes for the fixed effect. If I use a likelihood ratio test to compare the model with and without the fixed effect, I get a non-significant p-value, which would make me conclude that the fixed effect isn't significant. However, the confidence intervals for 2 of the four levels (so really 2/3, because the first is captured by the intercept) are quite negative, not close to including 0.

So, including the variable doesn't improve the model, but the expected values for two of the levels are clearly significant. Should I trust the likelihood ratio test, and ignore the confidence intervals of the coefficients? Report both, with an explanation of the disparity (and any suggestions on what that explanation might be - perhaps too much variability between subjects)? Or am I approaching this wrong?

• It would be a good idea to post your lmer/summary/anova code and output. Oct 19, 2016 at 0:14
• Possibly related (opposite situation): stats.stackexchange.com/questions/120768 Oct 19, 2016 at 0:16
• yeah, we definitely need a bit more information. We don't necessarily expect the Wald p-values (reported for the individual effects) to be exactly consistent with the LRT, but if they're quite different that seems surprising. (In general the LRT is more accurate than the Wald, but I'd like to be a little more confident that there's not something else strange happening.) Oct 19, 2016 at 0:53
• ... are you sure you fitted both models with method="ML" rather than method="REML" ... ?? Oct 19, 2016 at 0:56