I have read for long time passively here but now I have 2 questions. I am confused about how to present group differences when I fit a model like e.g. this:
y ~ factorA * factorB + factorC*factorD + continuous_variable_s
When using lme4 or just the built in lm function in R, I needed to apply contr.sum to each factor because otherwise the comparison would be made to one reference group that might not be the comparison I need. But I always found this confusing and difficult to interpret, especially when group sizes were unequal.
Now, I have read in several texts that promote Bayesian data analyses that contrasting groups is much more straightforward here. But to me it is not clear how. I know how to extract the posterior sample and from that I saw that by default (just as with lme4 etc) contr.treatment is applied and there is a reference group. How do you usually do this kind of task to be able to compare the different groups?
Another question I have:
In linear regression, it makes sense to present the posterior distribution of \mu or the difference in \mu etc… But lets say we use the above model with the skew_normal distribution in the BRMS package. Then \mu by itself is not so meaningful (unless \alpha = 0, which means no skew). For such a model, would it make sense in a research article to use the full model to predict values for two disctinct groups and isntead of presenting single parameters such as \mu to predict mean or median of the difference in the predictions?