In a mixed effects model the fixed effects allow for different y intercepts for given fixed effects. It does not allow the slopes to change where as random effect allows the slopes and intercept to change. Why do the fixed effects have this limitation?
For example, I might have height vs recorded at 10,11,12,13,14,15 years of age for some boys and girls. It seems reasonable to me that in boys the height vs age slope would be steeper than in girls. But modelling boys vs girls as fixed effects won't allow for different slopes where as random effects will. But boy and girl are fixed effects so a random effect model seems inappropriate. What would be the appropriate way to model something like this in a mixed effects model?