According to Lo and Andrews, 2015 (https://doi.org/10.3389/fpsyg.2015.01171) raw Reaction Time (RT) should be analyzed with a GLMM, instead of transformed values with LMM or even ANOVA. They and others point out a gamma or inverse gaussian with an identity link function should be used.
My data is from RTs before and after sleep (~2200h and ~0730h). Participants (22) were asked to press a button every time a cross was displayed on the screen. This was measured multiple times on each participant, on each timepoint and in two conditions (placebo and intervention (participants received a stimulus that affects their sleep pattern).
head(data): (trimmed >100ms and <2000ms)
subjectNumber expDay age bmi weight height treatment waiting reaction timep
2 N1 24 22.53 73 180 Control 6026 588 Before sleep
2 N1 24 22.53 73 180 Control 4470 326 Before sleep
2 N1 24 22.53 73 180 Control 2334 336 Before sleep
2 N1 24 22.53 73 180 Control 6005 289 Before sleep
2 N1 24 22.53 73 180 Control 4636 318 Before sleep
2 N1 24 22.53 73 180 Control 3515 315 Before sleep
I'm interested in knowing if my intervention improved the reaction time. It's possible that people have better performance in the morning irregardless of any intervention (less tired), so the model should take this into account.
An interaction term (intervention*timepoint) is needed and will say if intervention had any effect after sleep, seeing that before sleep there should be no difference.
So far my model looks like this:
glmer(reaction ~ treatment * timep + (1|subjectNumber), data=., family = inverse.gaussian(link = "identity"))
summary():
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: inverse.gaussian ( identity )
Formula: reaction ~ treatment * trial + (1 | subjectNumber)
Data: .
AIC BIC logLik deviance df.resid
33283.9 33320.1 -16636.0 33271.9 3064
Scaled residuals:
Min 1Q Median 3Q Max
-3.1321 -0.4575 -0.1539 0.2122 17.8238
Random effects:
Groups Name Variance Std.Dev.
subjectNumber (Intercept) 4.071e+02 20.17610
Residual 1.404e-04 0.01185
Number of obs: 3070, groups: subjectNumber, 20
Fixed effects:
Estimate Std. Error t value Pr(>|z|)
(Intercept) 341.394 12.128 28.150 < 2e-16 ***
treatmentIntervention 4.614 2.709 1.703 0.08860 .
timepAfter sleep 7.745 2.763 2.803 0.00507 **
treatmentStimulation:trialAfter sleep -3.636 3.895 -0.933 0.35058
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) trtmnS trlAfs
trtmntStmlt -0.089
trilAftrslp -0.083 0.467
trtmntSt:As 0.048 -0.685 -0.701
The AIC is ridiculously high when compared to other RT models I've seen (range of 100--300), so with my short experience with these models I'm unsure about how good is the fit.
Is it correct to say, according to the above, that the treatment has no effect on RT, but sleep in general improves RT irregardless of treatment? I'm afraid this sleep effect may confound things in a way as to make this design invalid in the first place.