I am fitting a multinomial logistic regression using the multinom() function
from V&R's nnet library.
When I use predict(my.model, type = "probs") I do get fitted values for the
probabilities, which appear correct.
I would like to work out the actual theta and beta values (intercepts and
slopes) for each category in the response variable. However I am unable to
work out what exactly the coefficients provided by multinom() are and how
they can be converted to coefficients to calculate the probabilities.
To understand how multinom() works, I used the example on prevalence of
pneumoconiosis (normal, category2 and severe) predicted by period of
exposure of coalminers provided by McCullagh & Nelder (1983) Generalized
Linear Models, Table 5.2.
> my.model <- multinom (category ~ log(period), weights = n)
> my.model
Call:
multinom(formula = category ~ log(period), weights = n)
Coefficients:
(Intercept) log(period)
normal 8.935987 -2.1653653
severe -3.039118 0.9021238
Residual Deviance: 408.8689
AIC: 416.8689
McCullagh & Nelder give beta of 2.594 and theta 10.572 for the severe
category. How do I get from the multinom() coefficients to the ones given in
McCullagh & Nelder?
data:
period category n
1 5.8 normal 98
2 15.0 normal 51
3 21.5 normal 34
4 27.5 normal 35
5 33.5 normal 32
6 39.5 normal 23
7 46.0 normal 12
8 51.5 normal 4
9 5.8 category2 0
10 15.0 category2 2
11 21.5 category2 6
12 27.5 category2 5
13 33.5 category2 10
14 39.5 category2 7
15 46.0 category2 6
16 51.5 category2 2
17 5.8 severe 0
18 15.0 severe 1
19 21.5 severe 3
20 27.5 severe 8
21 33.5 severe 9
22 39.5 severe 8
23 46.0 severe 10
24 51.5 severe 5
I am using S-Plus 6.0 Rel 2 on Win2000.
Any help much appreciated!
Jorn Scharlemann
--
Dr Jorn P.W. Scharlemann
Conservation Biology Group
Department of Zoology
University of Cambridge
Downing Street
Cambridge CB2 3EJ
Email: jpws2@cam.ac.uk
Tel: +44 (0)1223-336 675
Fax:+44 (0)1223-336 676
http://www.zoo.cam.ac.uk/zoostaff/cbg/index.html
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