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I am having trouble interpreting the Exp(B) value in a multinomial logistic regression in which my outcome variable is categorical (3 categories) and my predictor is a scale variable. The Exp(B) value for Category 3 (reference is Category 1) is 8.849E-51, with confidence intervals of 2.734E-51 - 2.865E-50. There is a similar value for Category 2. This is the first time I have performed multinomial logistic regression so I might be misunderstanding but this very small Exp(B) doesn't appear to make sense from looking at my data. I have read this post but can't make sense of this result based on this.

Data set

Output

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    That estimate is nearly zero. The fact that the confidence interval includes a negative quantity is just a side-effect of using a method not especially suited to extremes. – Nick Cox Nov 03 '15 at 16:47
  • How much data do you have? When you list your confidence intervals, does "-" mean *through*, or $(2.734\times 10^{-51},\ -2.865\times 10^{-50})$? How many observations do you have in each response category? – gung - Reinstate Monica Nov 03 '15 at 17:04
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    @gung's comment clearly applies to mine. If the dash means comma, not minus, then the quantity is not negative at all. – Nick Cox Nov 03 '15 at 18:08
  • @NickCox, I just realized that I put the lower limit 2nd, though... What I had meant was: "or $(-2.865\times 10^{-50},\ 2.734\times 10^{-51} )$?" – gung - Reinstate Monica Nov 03 '15 at 18:12
  • On second reading, the CI is almost certainly from about 3E-51 around 9E-51 to 3E-50. Each step is about the same on a logarithmic scale, or a factor of 3, which seems reasonable. – Nick Cox Nov 03 '15 at 18:17
  • I have 15 responses in total, 8 in Category 1, 2 in Category 2 and 5 in Category 3. Apologies for not being clear on the confidence intervals. The lower limit is 2.734E-51 and the upper limit is 2.865E-50. – Pandora Nov 04 '15 at 11:05
  • @NickCox, the mean value of the response variable is very different in each category, and the pseudo R squared value for the regression is .904 (Nagelkerke). I am confused by the Exp(B) value being close to zero for Category 1 when it otherwise appears to be important to the model. – Pandora Nov 04 '15 at 11:17
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    Unless you show more information about your data and model, I don't see how we can easily comment further. It could be anything from coding error through misunderstanding what the model does to fitting an inappropriate model to your data. – Nick Cox Nov 04 '15 at 11:20
  • @NickCox I have edited my original post to add my data set and the output I am getting for the model – Pandora Nov 04 '15 at 11:38
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    Thanks. I don't see a model statement here. It looks as if this comes from some menu-driven software, say SPSS. 15 observations, 3 categories, 1 continuous predictor is a really small sample for this kind of exercise. More generally, the problem is to predict category from what you are calling "response"? – Nick Cox Nov 04 '15 at 11:46
  • @NickCox yes I am using SPSS v19.0. And yes I wish to predict category from 'response'. I will add the model fitting information part of the output to my original post. – Pandora Nov 04 '15 at 11:53
  • I haven't used SPSS in this millennium. I typed the data into Stata and its `mlogit` would not even converge. Much more testing would be needed but a conjecture is that SPSS has converged at an inappropriate solution. It's clear that there is a relationship between your variables, but multiple logit appears to be not the way to explore it (without much more data, which naturally may not be possible). – Nick Cox Nov 04 '15 at 12:24
  • Thanks @NickCox, your feedback has been very helpful. I will explore other methods of analysis. – Pandora Nov 04 '15 at 12:28
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    You have perfect separation between category 1 and the other two categories based on `response`. That would explain the lack of convergence of `mlogit` experienced by @NickCox as well as many of the strange results here, such as perfect goodness of fit tests and the huge coefficient of `response`. – whuber Nov 04 '15 at 13:22
  • @whuber Well spotted! – Nick Cox Nov 04 '15 at 13:32

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