# Generalized mixed-effect regression model (GLMM) with negative reaction times as a result of baseline RT subtraction

I am hoping to get some advice for examining differences in reaction times (repeated sampling) as a measure of cognitive load between groups.

Dataset: The response variable I am using is reaction times in ms relative to the mean(baseline RT) collected at multiple time points during a task. A small number (~.7%) includes negative reaction times given that RT = RT during task - mean baseline RT. Range of dataset is -125 to 3000 ms. Additionally, there are some missing response data points (177 out of 1764).

Plan: I am interested in using a generalized mixed-effect regression model (lme4::glmer) to examine differences between groups across time (fixed effects), with subjects as the random effects: RT ~ group:time + (1|subject). My plan is to use Inverse Gaussian GLMM with identity link function (as suggested in Lo and Andrews 2015).

However, I am running into two issues:

1. First issue that my dataset includes negative response times and I am wondering if anyone has suggestions for how to deal with this? My thoughts are to shift the data by adding a constant (e.g., Y + min(Y)) however I am not sure if this is appropriate. Does anyone have any advice or articles on how to handle this?
2. Even when dealing with all positive values (Y + min(Y)), I get the below error. I see that other people are also having this error with lme4::glmer but I haven't been able to find a clear reason for why this is happening other than it may be because of the NaN values. Does anyone know of the reasoning for this and/or any other packages to use for this type of analysis?

Error in (function (fr, X, reTrms, family, nAGQ = 1L, verbose = 0L, maxit = 100L, :
(maxstephalfit) PIRLS step-halvings failed to reduce deviance in pwrssUpdate

Any insights into issues 1 and/or 2 would be much appreciated!

Rather than add an arbitrary constant, I would consider not subtracting the mean in the first place.

As for the error, this could be due to many things. A few things to check are:

• does it work if you set nAGQ = 0 ?

• does it work if you set nAGQ = 10 ?

• does it work if you use the mixed_model function in package GLMMAdaptive ?

• does it work with a regular Gamma GLM (ie without random effects)

• does it work with a log link instead instead of the inverse Gaussian ? This obviously requires that all the responses must be positive.

• does it work with the linear model using a log-transormed response ? ie lmer(log(Y) ~ ...

• Thank you @Robert for your help with my question. I took your advice and decided not to subtract the mean. The model fit worked but I was still getting a warning so I tried using nAGQ = 0 and the warning went away. I was wondering though if you could explain what is happing when this is set to 0? I read that this can make the model fit less precise but am not sure if this is true and/or whether this is commonly done or appropriate? Thanks in advance! Jun 21 '21 at 18:07
• You're welcome. Yes, that will make the estimates less precise, so it's not the preferred solution. Did it converge with nAGQ = 10 ? What exactly was the warning [You said there was an error in your question, not a warning]. Did you try mixed_model and the other suggestions I gave ? Jun 21 '21 at 18:34
• Does this answer your question ? If so please consider marking it as the accepted answer. If not, please let us know why. Also, if you haven't already, please consider upvoting it. Jun 26 '21 at 12:21
• Sorry for the delayed response. I get an error when I run the model with nAGQ = 10... "Error in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, : (maxstephalfit) PIRLS step-halvings failed to reduce deviance in pwrssUpdate". But this does not occur for nAGQ = 0 or when I do not specify anything. Jun 29 '21 at 21:48
• That's a strange error from mixed_model Jun 30 '21 at 8:01