# Why do my ANOVA tables keep returning $\chi^{2}$ values of 1?

I'm using ANOVA to test for differences between different values of the same factor for a mixed effects model which I produced. My model is: m2 <- lmer (ovsize ~ d.sheetratio + (1|nid), REML=FALSE). Following this, I subsetted the data so that each separate model described just data values for just one value of ratio.

me <- lmer (eovsize ~ eratio + (1|nide), REML=FALSE)
md <- lmer (dovsize ~ dratio + (1|nidd), REML=FALSE)
mc <- lmer (covsize ~ cratio + (1|nidc), REML=FALSE)
mb <- lmer (bovsize ~ bratio + (1|nidb), REML=FALSE)
ma <- lmer (aovsize ~ aratio + (1|nida), REML=FALSE)

At this point I get an error message which states that 'fixed-effect model matrix is rank deficient so dropping 1 column / coefficient'. Then when I do the ANOVA to compare each (e.g. me vs. ma) I get an output which looks like this:

Data:
Models:
mb: bovsize ~ bratio + (1 | nidb)
ma: aovsize ~ aratio + (1 | nida)
Df     AIC     BIC logLik deviance Chisq Chi Df Pr(>Chisq)
mb  3 -323.05 -316.06 164.53  -329.05
ma  3 -235.34 -229.37 120.67  -241.34     0      0          1

How can $\chi^{2}$ be 1 when each model is different? Is there an error in the method that I've used? Also, is the error message I received important?

You've misread your output: $\chi^2$ is 0, and p = 1. This is because you've entered the better-fitting model first, and it's not clear that these are nested models. If you enter the worse-fitting model first, you'll get $\chi^2_{(0)}>0,p\approx0$, but this isn't really a proper test, because any $\chi^2_{(0)}>0$ will have a $p\approx0$. To have df > 0, your models must be nested. Non-nested models also pose some challenges for comparing AIC, as Ben Bolker mentions in comments here: Likelihood ratio test - lmer R - Non-nested models.