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
IQ was evaluated with a different test in
M2. If it helps, you can think of is as "analytic IQ" in
M1 and "creative IQ" in
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?