In plant breeding, we often talk of estimate of random effect i.e. BLUP and variance component on quantitative variables such as yield, plant height and etc. My thought is that estimate of BLUP or variance component for qualitative trait that are ranked or ordinal is wrong and unreliable. Take for example, if disease severity is scaled from 1 = no symptom to 5 = symptom is extremely severe. This is qualitative trait that is ranked! Is it appropriate to estimate the BLUP or variance component of random effect on such trait?
strictly speaking, methods assuming traits are continuous (and fitting a linear mixed model) are inappropriate if this assumption does not hold - you may wish to have a look at threshold model analyses instead.
yes, strictly speaking you can not use normal assumptions for this type of data, and you will need to go with Generalized Linear Mixed Models (GLMM) or another type of methodology (Bayesian?) in order to properly model the distribution of your data.
However, in practical terms, we do use LMM with normality assumptions for this type of variable in a regular basis. For example, sometimes we have a score from 1 to 5 for straightness of pine trees, where 0 is completely straight and 5 is very curved. This variable is discrete and ordinal, but if we check for some properties it can work quite well. First, you need to have equal spacing between your classes, this means that 1 to 2 is the same score change than 4 to 5, and this needs to be clearly defined in your measuring protocols. The other thing is that you ideally need to have several class values in your variable (ideally 10 or more), the reason is that this will give you a closer approximation to normality (central limit theorem) and therefore less issues. In any case, you will always have some 'doubts' about your heritability and BLUP estimates as you are 'approximating' your variable (e.g. true level of departure from straigthness) with something different (e.g. a score).
I completely agree with the previous comments. Besides that, you might apply some appropriate transformation function. Check the normality and independence of the residuals to give you a better clue of how your data behaves. In some cases this might be helpful even in mixed model analysis.I hope this can help.