Multinomial logit regression with ordinal independent variables

Question

I've got some ordinal variables b and a and a categorized variable c. I would like to fit a multinomial logit regression from the library car. I tried to ignore the ordinal scale. I have the following data:

 a<-c( 3, 4,   4,   4,   3, 4,   3, 3, 4,   2, 2, 4,   3, 3, 3, 1,   3, 2, 2, 3, 3, 1,   3, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 1,   2, 2, 2, 2, 3, 2, 3, 4,   4,   3, 3, 2, 2, 3, 3, 3, 2, 1,   1,   1,   1,   1,   1,   2, 3, 4,   3, 3, 4,   3, 4,   3, 2, 3, 3, 3, 3, 3, 4,   3, 4,   3, 3, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 2, 3, 2, 3, 1,   2, 2, 1,   1,   4,   3, 3, 2, 2, 2, 2, 2, 2, 3, 4,   4,   4,   3, 3, 3, 3, 3, 4,   4,   3, 3, 2, 3, 3, 3, 3, 4,   3, 4,   2, 2, 3, 3, 3, 2, 2, 3, 2, 4,   2, 2, 2, 2, 2, 1,   2, 2, 1,   1,   3, 4,   3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 1)


 c<-c(5 ,3 ,4 ,3 ,4 ,4 ,2 ,2 ,3 ,4 ,2 ,5, 3, 5, 4 ,3 ,2 ,4 ,4 ,4, 4 ,4, 4, 2 ,3, 4 ,2 ,3 ,3 ,3 ,4 ,3 ,3 ,2 ,2 ,3 ,3 ,3 ,3 ,4 ,2 ,4 ,3, 3, 3, 4, 4, 3, 3 ,2 ,3 ,3 ,3 ,3, 4 ,4, 4, 3, 2, 2 ,4 ,4 ,3 ,3 ,2 ,2 ,1 ,2 ,2 ,2 ,1 ,2 ,5 ,2 ,3 ,3 ,2, 4 ,3 ,1 ,2 ,3 ,2 ,3 ,3 ,3 ,3 ,3 ,3 ,2 ,2 ,2 ,2 ,3 ,2 ,4 ,3, 3 ,2 ,3, 2, 4, 3, 3, 3 ,3 ,4 ,2 ,2 ,4 ,3 ,3 ,3 ,3 ,3 ,2 ,3, 3 ,3, 3, 4 ,4 ,4 ,1 ,3 ,3 ,3 ,4 ,4 ,4 ,3 ,2 ,4 ,4 ,2 ,4 ,4 ,4 ,4 ,2 ,3 ,3, 2, 2 ,3 ,2 ,3 ,4 ,5 ,2, 3 ,3 ,2 ,3 ,2 ,2 ,3 ,2 ,2 ,4 ,4 ,3 ,3 ,2, 4 ,4 ,2 ,4 ,3 ,4, 4, 3 ,2 ,3)
b<-c(3 ,2, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 4, 2, 3, 1, 3, 1, 2, 4, 2, 1, 3, 2, 2, 2, 1, 3, 3, 3, 2, 2, 2, 2, 1, 3, 1, 3, 2, 3, 1 ,3 ,3 ,2, 2, 3, 1, 3, 2, 2, 2, 2, 2, 2, 3, 4, 3, 3, 2, 1, 4, 3 ,3 ,2 ,2, 1, 2, 2, 2, 2, 1, 2, 5, 3, 3, 4, 3, 4, 1, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 2, 2, 3, 2 ,4 ,2 ,3 ,2 ,2 ,2 ,4 ,2 ,2 ,2 ,2 ,2 ,2, 1, 5 ,4 ,3 ,2, 2 ,2 ,2 ,2 ,4 ,2 ,2 ,4 ,3 ,3 ,1 ,2 ,2 ,2 ,2 ,2 ,2, 2, 2, 2, 2, 2 ,2 ,2 ,2 ,2 ,2 ,2, 2, 2, 2 ,2 ,2 ,2 ,2 ,5 ,4 ,3 ,2 ,1 ,1 ,1 ,4 ,3 ,2 ,2 ,3 ,3 ,3 ,2 ,2 ,2 ,2 ,2, 3, 2 ,2 ,2 ,2 ,2 ,1)

now I ignored the ordinal scale and treated them as factors to fit the multinomial logit regression

require(car)
a<-as.factor(a)    
b<-as.factor(b)
c<-as.factor(c)
multinom(formula = a ~ b + c)

Call:
multinom(formula = a ~ b + c)

Coefficients:
  (Intercept)        b2       b3       b4        b5         c2         c3         c4        c5
2   0.3410779  1.009797 41.80056 45.22081 -13.02923 -0.5229982  0.9216514  0.2170273 -18.03928
3  -1.4697131  2.698228 44.91938 47.04268 -16.24570 -0.7341395  0.7088424  1.2495310  20.70641
4 -46.0095393 33.603384 75.13911 79.00502  56.91264 -7.4198320 13.0220759 14.2526951  33.85774

Std. Errors:
  (Intercept)        b2        b3        b4           b5           c2        c3        c4           c5
2   1.2654428 0.6530052 0.4659520 0.5495402          NaN 1.337075e+00 1.4180126 1.4993079 8.028986e-16
3   1.6649206 0.9361438 0.5123106 0.5879588 2.446562e-15 1.640462e+00 1.7003411 1.7558418 8.601766e-01
4   0.3399454 0.4767032 0.3699569 0.4144527 3.321501e-11 6.973173e-08 0.6549144 0.6953767 8.601766e-01

Residual Deviance: 328.1614
AIC: 382.1614  

I think I found the mistake....the column b5 is empty for a1 and a2.

table(b,c,a)
, , a = 1

   c
b    1  2  3  4  5
  1  0  3  2  2  0
  2  1  7  1  0  0
  3  0  0  0  0  0
  4  0  0  0  0  0
  5  0  0  0  0  0

, , a = 2

   c
b    1  2  3  4  5
  1  1  5  2  2  0
  2  1 12 21  4  0
  3  0  1  6  1  0
  4  0  2  1  1  0
  5  0  0  0  0  0

But do you know how to solve this problem?

Answer 1

Ordinal independent variables are always tricky. As far as I know, there are essentially four sorts of ways of dealing with them, the first two are within the multinomial logistic scheme: Treat them as categorical and ignore the ordinality or treat them as continuous and pretend they are interval. One way of ameliorating some of the concerns of the latter pretense is to choose several different ordinal schemes and see if it makes a substantial difference. The latter two are row column effects association models (see Agresti, p. 154-184) or nonmodel based methods (see Agresti, p 184-224).