# Interpreting mlogit coefficients in R - odds ratios and negative coefficients

I am struggling to understand how to interpret the output from my mlogit model. I am working with a dataset that is looking at where someone will get a tattoo (location, reference level = foot) depending on their age (continuous), sex (female or male), and year (2006 to 2015).

Running logistic regression in R I get the following summary output:

I then converted the coefficients to odds with:

Assuming the model I've made is not wrong and I have correctly extracted the odds from the coefficients, I have the following questions:

• For arm:age - Is it appropriate to say, "For a one unit increase in age, the odds of getting an arm tattoo over a foot tattoo increases by 1.04." Does this mean 1.04 is equivalent to an 104% increase?

• For lip:age - Does the negative coefficient change the odds? Would I state instead, "For every one unit increase in age, the odds of getting a lip tattoo over a foot tattoo decreases by 0.925."

• Am I actually extracting the odds or the odds ratio? Or, are they the same thing? I would like to report the odds ratio, ultimately.

• Lastly, is there a way to compare all the levels to each other instead of manually changing the reference level (to arm, then hand, then leg, then lip, etc.)?

Thank you in advance for your help. I've been trying to parse together answers from other users, but I can't seem to find clear answers to these questions for the mlogit function.

• You might want to re-parameterise your age variable so that zero lies within the range of your data as at the moment your intercepts are for someone aged zero which is giving you some values which are going to be hard to interpret. Commented Nov 20, 2016 at 15:25