# How to compare fixed effects of linear mixed models

I have two linear mixed models that I ran with the lmer function from the lme4 package. The models are identical except that I calculated the input fixed factor in slightly different ways. I now want to test whether the fixed effects estimates output by the models significantly differ.

What is the appropriate test for doing this?

In one model, the fixed effect estimate is -9.1. In the other, the fixed effect estimate is -2.0. So, qualitatively, they seem significantly different, although I do not know how to make this judgement statistically.

A longer description of my problem follows here...

I have these two models:

M1 <- lmer(result ~ IQ + (1|Participant), data = DF)

M2 <- lmer(result ~ IQ + (1|Participant), data = DF)

As you can see, they are identical -- I'm trying to test whether participants' (my random factor) result vary by their "intelligence", or IQ, which is a binary categorical variable such that participants are either classed as high or low. However, IQ was evaluated with a different test in M1 and M2. If it helps, you can think of is as "analytic IQ" in M1 and "creative IQ" in M2.

The output of M1 displays a fixed effect estimate of -9.1 (i.e., roughly, a low IQ individual scored 9.1 points worse than a high IQ individual).

The output of M2 displays a fixed effect estimate of -2.0.

Qualitatively, it appears that the IQ test used in the case of M1 ends up categorising participants in a way that is significantly different than the IQ test used in M2. But my question is: how might I compare the fixed effect estimates to make this judgement, statistically?

• Can you elaborate on what you mean by 'slightly different ways'? Sep 26, 2019 at 20:56
• Please see my edits to the original post. Hope it helps? Sep 27, 2019 at 10:41
• Suggestion: please call your variables different names. The analytic IQ is a different variable than the creative IQ.
– Dave
Sep 27, 2019 at 10:57