[R] weights in multinom

[Jol, Arne]

Best R Help,

I like to estimate a Multinomial Logit Model with 10 Classes. The
problem is that the number of observations differs a lot over the 10
classes:

Class | num. Observations
A | 373
B | 631
C | 171
D | 700
E | 87
F | 249
G | 138
H | 133
I | 162
J | 407
Total: 3051

Where my data looks like:

x1	x2	x3	x4	Class
1	1,02	2	1	A
2	7,2	1	5	B
3	4,2	1	4	H
1	4,1	1	8	F
2	2,4	3	7	D
1	1,2	0	4	J
2	0,9	1	2	G
4	4	3	0	C
.	.	.	.	.

My model looks like:
estmodel <- multinom(choice ~ x1 + x2 + x3 + x4, data = trainset) 

When I estimate the model and use the resulting model for prediction of
'new' observations the model has a bias towards the Classes with a large
number of observations (A,B,D,J), the other classes are never predicted
by the model.

I thougth that the option "weights" of the multinom function could be
usefull but I am not sure how to use this in the above case.

Is there someone with experience regarding such a weigthing approach in
multinom? If someone could help me with suggestions it would be great!

Nice day,
Arne