LMM (lme4) model specification with random slopes

Question

I have a dependent variable Y recording a score on participants which performed a task measured at three time points. I would like to model the data using a LMM with random intercepts and slopes, with the lme4 package in R:

model<-lmer( Y ~ 1 + TIME + gender + TIME*gender+ (1+TIME|ID) ,  data = df)

but I obtain the following error when running the code:

Error: number of observations (=408) <= number of random effects (=408) for term (TIME | ID); the random-effects parameters and the residual variance (or scale parameter) are probably unidentifiable

As far as I understand, this occurs because there is only one observation per subject for each TIME category (How do you know the number of random effects in a mixed effects model?).

To me it seems reasonable that TIME is expected to vary within subjects and so I would include as a random effect. But I wonder if including only ID as random intercepts without random slopes is just the right model and how can I be sure about that?

Thanks

Answer 1

I have been having the same issue and as far as I can tell, it could be related to the type of variable that TIME is. Can you provide some sample data and try TIME as numeric instead of factor?

Here is a resource that further discusses the usage of random intercepts and slopes: https://psyteachr.github.io/stat-models-v1/linear-mixed-effects-models-with-one-random-factor.html

Alternatively, you might not have pseudoreplications in your data and thus a random intercepts only model may be the more appropriate model anyways.

Hopefully someone else with even more stats knowledge can comment here because I am still not certain what the real problem is. I also wanted to pass on this paper that encourages that if you can use a mixed ANOVA, it can more effectively model the random effects than the lme4 approach: Arnqvist, G. (2020). Mixed Models Offer No Freedom from Degrees of Freedom. Trends in Ecology & Evolution, 35(4), 329–335.