Is there any criterion about choosing reference factor in multinomial logistic regression?

Question

I have a dependent variable that includes four categories. I also have four continuous independent variables. The 3rd category covers the largest group in the sample. Is it important to choose the category covering largest group as a reference factor or can I choose another one that would make sense for comparisons?

Answer 1

You are free to choose any of the categories as the reference. From the viewpoint of overall statistical quality of prediction by the model, the choice is arbitrary. In terms of interpretation of individual IV's effects, it makes difference. The multinomial logistic model is:

$log(\frac{Prob(category_i)}{Prob(category_{ref})})=B_{i0}+B_{i1}X_1+B_{i2}X_2...+B_{ip}X_p$

So you interpret effects (regression coefficients) of independent variables for each category $i$ vis-a-vis your reference category $ref$. Namely, $exp(B_{i1})$, for example, is this odds ratio: by how many times the estimated odds $\frac{Prob(category_i)}{Prob(category_{ref})}$ increases in response relative to increasing $X_1$ by one unit.

This also implies that if you want to interpret the coefficients, you should not just look at whether they are significant or not. It matters if the independent variable $X$ is continuous or categorical. $exp(B)$ for a continuous predictor with wide scale (big variance) can be close to 1 even if the predictor is highly significant. So it is generally preferable to categorize continuous predictors into a small number of meaningful categories prior to doing the regression whenever you are going to interpret the coefficients. Also, categorization of a continuous predictor into equal subranges will allow you to check the linearity assumption.