Multinomial logistic regression

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A multinomial logistic regression model is used to analyze the effect of predictors on a nominal outcome measure. The outcome measure thus consists of (more than two) categories that have no logical ordering, for example in a study on predictors of the chosen treatment in cardiac patients, where there are three options: 'PTCA', 'Bypass surgery' or 'Medication only'.

Do we need a multinomial logistic regression model?

We have an ordinal outcome measure (tumor grade 1, 2 or 3) and a linear continuous predictor (attenuation coefficient). We would like to develop a model to determine, based on the known attenuation coefficient, which category or grade this tumor will fall into. Our thought was that we should use a multinomial logistic regression for this. Is that correct, and are there other options as well?

It is indeed possible to use a multinomial logistic regression model to analyze the possible effect of a continuous predictor on an ordinal outcome measure. Do note the following: this model does not take the ordering of the categories into account. Tumor grade 1, 2, 3 could, so to speak, just as well be called red, green, blue, without a clear order. If the model predicts grade 2 instead of grade 3, this is "equally wrong" as predicting grade 1 instead of grade 3. To also take the ordering of the categories into account, you could perform an ordinal logistic regression.

In both models, however, the estimated parameters always remain somewhat removed from the "clinical interpretation" of the problem. You could therefore also consider reversing the axes and — for example in a (boxplot-like) graph — plotting the attenuation coefficient for the three different groups. You could then use an ANOVA / Kruskal Wallis to indicate the difference between the three groups. This approach in a sense reverses the relationship, since it calculates the difference caused by the tumor group in the outcome measure attenuation coefficient. However, the analysis method is a lot clearer/more familiar. Note: you will run into problems with this approach if you also want to include predictors other than the attenuation coefficient in the model.

Where do I find multinomial logistic regression in SPSS?

You will find multinomial logistic regression in SPSS under Analyze -> Regression -> Multinomial Logistic. See, for example, this annotated output from UCLA for an explanation of how to interpret the output of this procedure.

How do I perform multinomial logistic regression in R?

In R you can, for example, use the function 'multinom' in the package 'nnet' to perform a multinomial logistic regression.

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