I've been trying to analyse a dataset of response times following Lo & Andrews' (2015) proposal here: https://doi.org/10.3389/fpsyg.2015.01171
They propose using a GLMM that assumes a Gamma or inverse Gaussian distribution (with an identity link function). For example:
glmer(rt.cut ~ (1|subject) + (1|targetnumber) + primetype * form * group + scale(order) + scale(rt.previous), exp, family=inverse.gaussian(link="identity"), control=glmerControl(optimizer="bobyqa", optCtrl=list(maxfun=20000))))
(I could only get this to converge by using bobyqa, increasing iterations, and simplifying the random effects structure)
I am concerned about the interpretation of coefficients when using treatment contrasts. Specifically, I get different t-values for interactions, depending on the reference level of one of the factors.
For example, these are the 3-way interactions when using one of the levels of "form" as the reference:
primeType2:formInf:groupL2 -39.094 15.266 -2.56 0.01044 * primeType3:formInf:groupL2 -37.020 15.495 -2.39 0.01689 *
And these are the same interactions when using the other level of "form" as the reference:
primeType2:formFinite:groupL2 39.0939 17.5759 2.224 0.0261 * primeType3:formFinite:groupL2 37.0203 18.0101 2.056 0.0398 *
The estimates are exactly the same (as expected), but the SEs are larger in the second case.
Why does this arise and why should I choose one or the other treatment coding?