# Interpretation of estimates for a model with 2 categorial factors

I ran a model with 2 fixed factors that are categorial:

Ind: 10 levels
CRENEAU: 4 levels


For the parameter nu (I am running a gamlss of family BEZI), I get this summary:

Nu link function:  logit
Nu Coefficients:
Estimate
(Intercept)     2.180e+00
IndF2           9.259e-01
IndF3           9.259e-01
IndF4          -4.184e-01
IndF5           4.126e-15
IndT1          -6.434e-01
IndT2           9.259e-01
IndT3          -1.623e+00
IndT4           3.763e-01
IndT5          -1.412e+00
CRENEAUEVENING -3.071e-01
CRENEAUMORNING  2.379e-01
CRENEAUNOON     5.507e-01


CRENEAU and Ind are 2 different factors linked to my response. I understand that the intercept is the level of IndF1. But what is the estimate for the missing level of CRENEAU? Is there only one intercept for both factors that is equal ?

• Yes, the intercept is the value for all of your reference levels. Oct 18, 2023 at 10:26

If you were to write out the equation, the intercept is the log odds of your outcome variable (Y) when all predictors included in the model are set to zero.
So it is the log odds of Y when none of the nine included IND categories apply and none of the three included CRENEAU categories apply.
Hence, it is the log-odds for individuals in the base category for both categories! So for those in INDF1 and CRENEAUNIGHT (this is me guessing the base categories).