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

[John Fox]

Dear Bob,

If I understand correctly what you've done, the "newdata" that you're
using to get predicted values includes the three values of the response
variable, which are irrelevant to the predictions and cause each
prediction to be repeated three times.

I hope that this helps,
 John

On Tue, 27 Mar 2007 06:19:12 +1000
 Bob Green <bgreen at dyson.brisnet.org.au> wrote:
> 
> 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
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

--------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
http://socserv.mcmaster.ca/jfox/