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I would like to get confidence intervals for the percentages of difference outcomes expected from an intercept only multinomial regression. The package emmeans provides confidence intervals but they provide values that go out of the possible percentage bounds (below 0% and above 100%). Is there a package or manual approach that can get at these confidence intervals?:

example_data <-
  tibble::tibble(outcome = c(rep("a", 100), rep("b", 5), rep("c", 75)))

multinomial_fit <-
nnet::multinom(outcome ~ 1,
               data = example_data)

emmeans::emmeans(multinomial_fit,
                 "outcome",
                 type = "response")

The same issue applies in models with ordinal outcomes (cumulative regression models).

Jamie
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1 Answers1

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A couple of options. Make sure you read the documentation as there are a few different methods available that might lead to different results.

DescTools::MultinomCI(table(c(rep("a", 100), rep("b", 5), rep("c", 75))))

         est    lwr.ci    upr.ci
a 0.55555556 0.4833333 0.6319100
b 0.02777778 0.0000000 0.1041322
c 0.41666667 0.3444444 0.4930211

MultinomialCI::multinomialCI(table(c(rep("a", 100), rep("b", 5), rep("c", 75))), alpha=0.05)

          [,1]      [,2]
[1,] 0.4833333 0.6319879
[2,] 0.0000000 0.1042101
[3,] 0.3444444 0.4930990
George Savva
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  • Thank you this is great George. Do you know of a similar thing for cumulative/ordinal regression models? – Jamie Mar 06 '23 at 10:44
  • I don't know. To be honest I'm struggling with how an intercept only ordinal regression is different to an intercept only multinomial. If there's no predictor in an ordinal model then we just have the thresholds to set, which feels the same as estimateing a multinomial model? I could be wrong about this, and there's some discussion here, the 'profile' confindence interval following `polr` might help you https://stats.oarc.ucla.edu/r/dae/ordinal-logistic-regression/ – George Savva Mar 06 '23 at 10:55
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    Thanks, I will check this out. I think that the confidence intervals plasuibly can be slightly different because of how the cumulative model is constructed - but thanks I'll check out this link! – Jamie Mar 06 '23 at 14:03
  • If you find out then do update as an answer here. – George Savva Mar 06 '23 at 14:15