I once read around here that with binary factors in mixed effects models ('lmer' specifically), one shouldn't specify both random and fixed effects. The person went on to note that some people wouldn't combine fixed and random even for three- and four-level factors. Unfortunately, I can't recall if the person referred to random intercepts and/or random slopes in particular--what's certain is this relates to the very concept of random effects.
Does it ring true? Please take this question as from a beginner. It might as well be that obviously having both random and fixed effects doesn't make sense for a binary factor because there's nothing to control there... So, I have tried setting random intercepts and a fixed effect for a binary factor, and indeed, the model doesn't converge--yet that's little testing.
Sincerely thank you for any tips
In fact you can do a bit more than that - you can have for a categorical variable (eg boy/girl dummy) defined at level 1 and you can have
a fixed effect - the average differential in attainment by gender; girls do better than boys on average
random effects over school - some schools differentially good for boys, some differentially good for girls - ie complex level 12variance;
AND diffenetial heteogeity within schools by different types of pupils - boys nore variable in their attainment than girls - complex level 1 random effects
This volume 1 shows examples mainly in Chapter 7
https://www.researchgate.net/publication/260771330_Developing_multilevel_models_for_analysing_contextuality_heterogeneity_and_change_using_MLwiN_Volume_1_updated_June_2015_Volume_2_is_also_on_RGate
This in MLwiN which is particularly good at modeling complex functions
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Book Developing multilevel models for analysing contextuality, he...
That makes sense. I guess I may have misunderstood the original comment I'm referring to. Thank you very much indeed
Many linear mixed models have both random and fixed effects, and this is quite common, for example, treatmetns might be fixed and your blocks random. Or even more elaborated with split-plot designs where you have two error terms.
Now, having the SAME factor as random and fixed is an issue. You can not do that as they represent the same factor, and you will have troubles with confounding, and therefore you will model will not fit. Often, LMM packages recognize this, and drop one of the terms.
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