[R] fitted probabilities in multinomial logistic regression are identical for each level

[Bob Green]

I was hoping for some advice regarding possible explanations for the 
fitted probability values I obtained for a multinomial logistic 
regression. The analysis aims to predict whether Capgras delusions 
(present/absent) are associated with group (ABH, SV, homicide; values 
= 1,2,3,), controlling for previous violence. What has me puzzled is 
that for each combination the fitted probabilities are identical. I 
haven't seen this in the worked examples I have come across and was 
interested to know if this is a problem or what might be the cause 
for this. I ran an analysis with another independent variable and 
obtained a similar pattern.

Any assistance with this is appreciated

Bob Green

 > predictors <- expand.grid(group=1:3, in.acute.danger = c("y","n"), 
violent.convictions = c("y","n"))
 > p.fit <- predict(mod.multacute, predictors, type='probs')
 > p.fit
            1         2         3
1  0.4615070 0.3077061 0.2307869
2  0.4615070 0.3077061 0.2307869
3  0.4615070 0.3077061 0.2307869
4  0.7741997 0.1290310 0.0967693
5  0.7741997 0.1290310 0.0967693
6  0.7741997 0.1290310 0.0967693
7  0.4230927 0.3846055 0.1923017
8  0.4230927 0.3846055 0.1923017
9  0.4230927 0.3846055 0.1923017
10 0.7058783 0.1647063 0.1294153
11 0.7058783 0.1647063 0.1294153
12 0.7058783 0.1647063 0.1294153


 > mod.multacute <- multinom(group ~ in.acute.danger * 
violent.convictions, data = kc,  na.action = na.omit)
# weights:  15 (8 variable)
initial  value 170.284905
iter  10 value 131.016050
final  value 130.993722
converged
 > summary(mod.multacute, cor=F, Wald=T)
Call:
multinom(formula = group ~ in.acute.danger * violent.convictions,
     data = kc, na.action = na.omit)

Coefficients:
   (Intercept) in.acute.dangery violent.convictionsy 
in.acute.dangery:violent.convictionsy
2   -1.455279        1.3599055           -0.3364982 
          0.02651913
3   -1.696416        0.9078901           -0.3830842 
          0.47860722

Std. Errors:
   (Intercept) in.acute.dangery violent.convictionsy 
in.acute.dangery:violent.convictionsy
2   0.2968082        0.5282077            0.6162498 
           0.9936493
3   0.3279838        0.6312569            0.6946869 
           1.1284891

Value/SE (Wald statistics):
   (Intercept) in.acute.dangery violent.convictionsy 
in.acute.dangery:violent.convictionsy
2   -4.903094         2.574566           -0.5460419 
          0.02668862
3   -5.172256         1.438226           -0.5514486 
          0.42411327

Residual Deviance: 261.9874
AIC: 277.9874
 > Anova (mod.multacute)
Anova Table (Type II tests)

Response: group
                                     LR Chisq Df Pr(>Chisq)
in.acute.danger                      10.9335  2   0.004225 **
violent.convictions                   0.5957  2   0.742430
in.acute.danger:violent.convictions   0.1895  2   0.909600
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1