# Multinomial logistic regression low classification rate

I am running a multinomial logistic regression with SPSS and I have encountered a problem (?) with my data. I have a dependent variable (DV) with three categories, five independent variables (IV) as factors and four IVs as covariates. There are close to 4800 respondents in the data.

The distribution of my DV is: First category (40,6 %), second category (28,1 %), third category (31,3 %).

As I run the regression (last category as the reference), the classification table shows that only 1,3 % percent are classified in the second category. See below:

I have tried to find some solution to this dilemma, and the only thing I have come up is that the model is just not a good one considering the classification. The results of the logistic model otherwise seem "reliable", though.

Does anybody have any idea of what might be wrong or what could be done alternatively to this problem? Any help would be much appreciated!

Best regards

• What @sweezyjeezy means by linear thresholds, is linear decision boundaries. I think you misunderstood him. Thinking about it in 2-D, it may be that the observations that are labelled as second category are in the centre of the observations that are labelled first category so there is no straight line that can divide the two. Try running a decision tree and have a look at what the confusion matrix looks like. You can read this Jul 2, 2014 at 10:31
• Try a google search for threads on this site containing "logistic" and "classification rate". You'll find lots of info on the drawbacks of this method and on suggested other methods. Dec 29, 2016 at 22:42

Sorry, don't have enough rep to comment...

Note that multinomial regression is a linear classifier, and implicitly assumes linear thresholds between the classes, if this is not the case, then the most common classes can dominate. Have you tried using other techniques, e.g. SVM?

• Thanks for a quick reply! Linear thresholds between classes are assumed in my data (agree, neutral, disagree), so that shouldn´t be a problem. I´m not familar with SVT, but I´ll keep that in mind, thanks for the tip!
– O.S.
Jul 2, 2014 at 10:22
• Just to make sure we're on the same page : I mean linear thresholds in the feature space not the output, i.e. if you plot the data in the 5 dimensional space where the input vectors you are training on live (if I got you right), you want the different classes to be well seperated by linear thresholds Jul 2, 2014 at 11:21

The classifification table that SPSS provides is not a useful way to interpret the fit of a (multinomial) logistic regression model, and you should probably not attempt to interpret it. I think SPSS is the only software that produces that table.

Example: I want to develop a model that predicts if people will either go to prison for violent assault, or be a victim of assault. I don't have a computer, so I make up a model that just predicts "No" for everyone. Most people don't go to prison and are not violently assaulted, so my model is correct 99% of the time. But my model is also useless.

See also the case of John Gottman, who got famous by making the same mistake: http://www.slate.com/articles/double_x/doublex/2010/03/can_you_really_predict_the_success_of_a_marriage_in_15_minutes.html