What is happening here?

[Aaron Gardony]

I have data from an experiment where participants make threat judgments of faces. The faces are computer modeled and parametrically vary along the threat dimension with 7 levels. Participants use one of two response devices to respond (b/w Ss variable). Threat/No threat response buttons appear on the left and right side of the screen and the side is counterbalanced across participants. I am looking at mouse trajectories, specifically area-under-the-curve (AUC). The fixed effects are:
response: i.e. the participant’s response, 2 levels, threat or no-threat
condition: i.e. the response device participants used, 2 levels, gun or controller
threat_level: i.e. the level of facial threat of the face stimulus, 7 levels
responseSide: the side of the screen the participant responded on for the trial, 2 levels, left or right

I initially specified the model like so. I did not include random effects for items as I got convergence errors.

lmm_AUC = afex::mixed(AUC ~ response * condition * threat_level * responseSide + (1|subject_nr), data = WCFT_data_outRM, method = "S",cl=cl)

When I look at the emmip plot for the threat_level main effect I see this.
emmip(lmm_AUC,~threat_level,type="response")

I realized that I should have included random slopes for these fixed effects. Including them all (maximal model) led to the model failing to converge and a long computation time and removing the correlation among the random slopes did not help. Reducing the random slope structure, I was able to add random slopes for the response effect without convergence errors.

lmm_AUC = afex::mixed(AUC ~ response * condition * threat_level * responseSide + (response|subject_nr), data = WCFT_data_outRM, method = "S",cl=cl)

But when I do this the emmip plot looks different.

Why would inclusion of random slopes for the response factor have an effect on the estimated marginal means for the threat_level factor?

[henrik]

That can happen due to hierarchical shrinkage, which nudges the individual-level effects to follow a normal distribution. If the individual-level effects show a normal distribution around their mean, which is one of the assumptions of the mixed-model framework, this should not have too dramatic effects. Your plot suggests that this assumption is violated here. In any case, it suggests also that the specific pattern across levels of threat is not very strong.

It is difficult to say more without additional details (at least the corresponding standard errors). But removing random-slopes should only be done mildly. Try removing the correlations among slopes first. Please have a look at this discussion in my chapter: http://singmann.org/download/publications/singmann_kellen-introduction-mixed-models.pdf

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