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I am examining the effect of 'Phase' on reactions time (RT) data using a mixed model in lme4.

However, as is common with RT data, the residuals are non-normal.

This is the first model, which is a linear mixed model approach:

RT_lme<- lmer(RT ~ Phase.ct + (Phase.ct|Pt_ID) + (Phase.ct|Image),
data = Mooney_data, control=lmerControl(optimizer="bobyqa"))

summary(RT_lme)

Fixed effects:
            Estimate Std. Error       df t value Pr(>|t|)    
(Intercept)  1.44591    0.04533 80.20875  31.897   <2e-16 ***
Phase.ct     0.02967    0.01624 72.24639   1.827   0.0718 .

Figure 1 plot shows the non-normality problem.

Figure 1

As I realise that transforming RT data is not recommended, I followed the methods using in the paper by Lo & Andrews (2015). See here: https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2015.01171/full#h8

I therefore fit the following 2 generalised linear mixed models, which use different link functions:

1.

RT_lme1<- glmer(RT ~ Phase.ct + (Phase.ct|Pt_ID) + (Phase.ct|Image),
data = Mooney_data,family=Gamma(link=invfn()),control=glmerControl(optimizer="bobyqa"))

summary(RT_lme1)

Fixed effects:
            Estimate Std. Error t value Pr(>|z|)    
(Intercept) -778.393      8.627 -90.225  < 2e-16 ***
Phase.ct      22.547      8.098   2.784  0.00536 ** 

  1.  RT_lme2<- glmer(RT ~ Phase.ct + (1|Pt_ID),

    data = Mooney_data,family=inverse.gaussian(link=invfn()),control=glmerControl(optimizer="bobyqa"))

    summary(RT_lme2)

    Fixed effects: Estimate Std. Error t value Pr(>|z|)
    (Intercept) -736.62 12.71 -57.953 < 2e-16 *** Phase.ct 16.61 6.34 2.621 0.00877 **

However, both plots still show that the residuals are non-normal (example below). I have limited understanding of how altering the link function affects the model. Would this be expected to reduce non-normality? How do I select the best model (I thought to use AIC values but am concerned about non-normality in the plots)?

Figure 2

Here is a histogram of RT: Histogram of RT

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  • $\begingroup$ Could you show a histogram of the reaction time ? I would assume it follows a Poisson distribution, $\endgroup$
    – CaroZ
    Commented Mar 21 at 10:59
  • $\begingroup$ @CaroZ Why Poisson? It's not count data, is it? $\endgroup$
    – Christian Hennig
    Commented Mar 21 at 11:33
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    $\begingroup$ "As I realise that transforming RT data is not recommended" - why not? $\endgroup$
    – Christian Hennig
    Commented Mar 21 at 11:34
  • $\begingroup$ @CaroZ now added above $\endgroup$
    – SilvaC
    Commented Mar 21 at 11:40
  • $\begingroup$ op, one option is to 'assume' that by clt, the t statistic is still t-distributed. you can check this assumption by bootstrapping the data and seeing the distribution of your tstatistics (in particular the tail probabilities at significance level) $\endgroup$
    – seanv507
    Commented May 15 at 6:06

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