SE of Reference category in Multinomial Logit Model

I used R to fit a Multinomial Logit model to my data. The data includes some categorical variables as effect coded variables. For example, one variable has four levels of which one is the reference level. When I fit the model I get coefficients and corresponding Standard Errors for all three non-reference levels. Then I can recover the coefficient of the reference level as -1*(Coeff1+Coeff2+Coeff3)

But how can I find the Standard Error of the coefficient of the reference level?
There is no intercept included in the model, but even if this was the case, I do not see how it could be used to derive the standard error of the coefficient of the reference category.


Less is more. Stay pure. Stay poor.
In logistic regression the intercept represents the log odds of the reference groups and is typically reported with SE. I was unsure if in multinomial, one of the intercepts represented this value?

What do you need the SE of the reference for since its OR is 1?
Ok thanks, but also the Standard Error of reference category is important for further analyses. By the way, I think my question is far to specific, hopefully I am able to make it somewhat simpler. The type of model probably is irrelevant, the main thing is that several categorial variables with more than two levels are included in regression via effect coding. For simplicity, let's say we consider two categorical variables with both three levels. Then running a regression (without intercept) will yield, for each categorical variable, only coefficient estimates and corresponding standard errors for two levels. The coefficient estimate of the reference level can be recoverd using the fact that for each categorical variable the coefficients sum up to zero. So coef_referencelevel=-1*(Coeff1+Coeff2)

However, is there also some formula which yiels the standard error of this coefficient of the reference level? I am able to find this SE by rerunning the regression with one of the other levels as reference level, but in order to do so I first have to create new effect coded variables.. Probably this is not the most efficient way to do this, therefore my question is: Is there an easier way to recover the SE of the coefficient of the reference level, e.g. via an analytical expression


Less is more. Stay pure. Stay poor.
Well I haven't usee effect coding, so I am going to back away from this post before I over confuse both of us beyond recovery.