# GLMM inverse gaussian and treatment contrasts (response times)

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?