according to the following link https://stats.stackexchange.com/a/11068/196391
and what I saw in some papers, we can supress the intercept and consider ALL the dummy variables (which have coded the levels of categorical variable) in the model.
I tried to do so in JMP and it found singularity!
I am wondering which of the following three approaches are correct when we have more than one categorical variable?
1- considering a dummy variable for each level of each categorical variables and include all the dummies in the model except the reference dummies of each of the categorical variables (and keep the intercept in the model)
2- considering ALL the dummy variables of each of the categorical variables and suppress the intercept in the model
3- considering categorical variables in the model as they are (no dummy coding)