For response time data in a psychology experiment, is it appropriate to fit a glmer from the Gamma family (with identity link)?

Question

I ran a psychology experiment where participants categorized a target word into one of two categories (living thing or non-living thing?) by pressing one of two buttons, where the outcome of interest is the time it takes them to respond correctly. The target was preceded by a prime word that was either an English word or not (coded as lexical_status, 1 or 0), and either overlapped in spelling with it or not (coded as relatedness, also 1 or 0) - so it was a 2x2 design.

I am interested in estimating the main effects of lexical status and relatedness as well as their interaction on the response time. Each of the 64 participants categorized 320 distinct target words. Each participant (SUBJ_ID) saw each of the TARGET words only once during the experiment (so in just one of the four conditions) and each target word occurred many times in each of the 4 conditions (~15 times on average) across the whole experiment. Is this an appropriate model to fit for the data:

glmm_model_identity = glmer(RT ~ relatedness*lexical_status + 
       (1|TARGET) + (1|SUBJ_ID), 
       family = Gamma(link = "identity"), data = data_unrep_acc)

If not, what would be a more appropriate model?

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PS I tried fitting the below model but it did not converge, and the next model I tried fitting is the one in the post.

glmm_model_identity = glmer(response_time ~ 
   relatedness*lexical_status + 
   (0 + relatedness*lexical_status|TARGET) + 
   (0 + relatedness*lexical_status|SUBJ_ID), 
   family = Gamma(link = "identity"), data = data)

Answer 1

Your approach seems reasonable except that I suggest using the log link rather than the identity link to ensure that estimated mean reaction times are positive (except for the range of its inverse, the link function doesn't matter in this setting because your predictors are categorical). Also, you are assuming that the shape parameter of the gamma distribution is common across conditions. Have you checked the reasonableness of this assumption?

I am wondering why you are choosing a gamma GLMM rather than a LMM using log reaction time as the response. The assumptions of the latter are far easier to check, and the effects of the conditions are still interpretable (just on the scale of median, not mean, reaction time).

Answer 2

On Reaction Time Data

I echo the sentiments of Rachel's answer. Typically, reaction time data encompasses an inverse Gaussian distribution. Because of this, you generally have two options: 1) fit the data to a link function which supports this (this can be done in glmer but not very well with the Gamma family) 2) transform the RT data into normally distributed data. I think option two is a much better idea. The way to do this with reaction time data is by using the following formula for conversion:

$$ invRT = \frac{-1000}{RT} $$

This converts the data into a normal distribution and can often increase the precision of the mixed model you use it with (see Brysbaert & Stevens, 2019).

Convergence

Another issue you need to consider is whether or not your random effects structure fits your data well. I'm not surprised your first model converged and the second one didn't. This is a well known issue in mixed model research. I would say stick to your first model. Random intercept models that converge when others do typically have greater statistical power anyway (Matuscheck et al., 2017).

Autocorrelation of Trials

I don't believe I saw anywhere about whether or not your trials were randomized or not. I would check that your trial-level data isn't severely auto-correlated, as this is an often ignored but important aspect of mixed modeling (Baayen et al., 2017). The itsadug package has useful functions for checking this in mixed models (some examples are shown in Baayen et al.'s paper).

Citations

• Baayen, H., Vasishth, S., Kliegl, R., & Bates, D. (2017). The cave of shadows: Addressing the human factor with generalized additive mixed models. Journal of Memory and Language, 94, 206–234. https://doi.org/10.1016/j.jml.2016.11.006
• Brysbaert, M., & Stevens, M. (2018). Power analysis and effect size in mixed effects models: A tutorial. Journal of Cognition, 1(1), 9. https://doi.org/10.5334/joc.10
• Matuschek, H., Kliegl, R., Vasishth, S., Baayen, H., & Bates, D. (2017). Balancing Type I error and power in linear mixed models. Journal of Memory and Language, 94, 305–315. https://doi.org/10.1016/j.jml.2017.01.001