## Calculating probabilities from logit parameters estimated with effect coding

Hello,
I calculated this multinomial logit model using an effect coding (-1 0 1). The variable edu3 is the education level (3 categories), sex has of course 2 categories and eduM3 is the education of the mother in 3 categories.

Parameter edu3 Estimate Pr*>*ChiSq

Intercept 0 -1.6882 <.0001
Intercept 1 -0.2962 <.0001
sex 0 0 0.0797 <.0001
sex 0 1 0.1304 <.0001
eduM3 0 0 1.8393 <.0001
eduM3 0 1 0.6276 <.0001
eduM3 1 0 -0.5476 <.0001
eduM3 1 1 0.3453 <.0001

From this, I would like to compute the resulting probabilities for every possible case, for example, the probability for a man (sex=0) whose mother has a education level 0 (edum3=0) to get an education level 0 (edu3=0).

The cross table for sex=0 gives this:

Table*1*of*eduM3*by*edu3
Controlling*for*sex=0
eduM3 edu3
0 1 2
0 32.36 41.17 26.46
1 5.56 51.08 43.36
2 4.38 24.93 70.7

In this example, the wanted probability should then be 0.3236. However, when I implement parameters in the formula, I get this:
EXP(-1.6882+0.0797+1.8393)/(1+EXP(-1.6882+0.0797+1.8393)+EXP(-0.2962+0.1304+-0.5476)) = 0.4581

Why? I guess that something is wrong with my formula. It probably has something to do with the fact that I used an effect coding rather than a dummy coding.