I have collected some data in which measurements have been made at varying distances from an ‘origin’. Multiple ‘origins’ are measured within a ‘cluster’, so I am modeling the effect of distance using Linear Mixed Effect Models. In the `lme4`

package, the formula is essentially `y~Dist+(1+Dist|Cluster/Origin)`

.

Now, I have made different types of measurement at each point, and I would like to compare the models of different measurement types to get an idea for how they differ. For example, I compare the percentage change per distance between measurement types.

I have heard that the coefficient of variation is often used in chemistry to estimate repeatibility and that it can be used in comparison between models as it is scale invariant. I would like to compare the coefficients of variation of the estimated slope of each model. I would calculate it (quite simply) as:

$$ dfrac{s_b}{b} $$

Where $s_b$ is the estimated standard error in the slope, and $b$ is the estimated slope.

I have two main concerns that I would appreciate some help with:

- I have been unable to find examples of CV being used to compare slopes, as it is primarily used to compare means.
- This formula would ignore the random variations allowed by the model in the slope. Is this problematic and is there a good way of resolving it?