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Options when linear mixed model residuals are non-normally distributed

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Hey everyone,

In a project I've been working on I've run into non-normally distributed residuals in a linear mixed model, with some fixed effects and just random intercepts (no random slopes). Non-normality of the residuals, of course, violates the assumption that the error term is normally distributed. I have uploaded a qqplot and histogram of the level 1 residuals.

The model has dependent variable time (0, 1, 3, 4, 5, 9, 14, ..., 432) and several binary and categorical variables, as well as one continuous variable.

Code:
predict lev1, rstandard
qnorm lev1
histogram lev1, rstandard
Array
Array





Ultimately I want to visualize the random intercept, and I am afraid that a log-transformation may eliminate that option. Moreover, the fact that interpretation of linear mixed models is relatively simple is something I like.

What approaches that allow visualizing the random intercepts would you recommend for me? Are perhaps GLMMS a good choice? And with what family and link function?

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