Interpreting relative risk ratios after mlogit with categorical variables

[Hossein Jebeli]

I am using mlogit to estimate the relationship between a firm status (=1 active, =2 insolvent=3 exit) and deciles of lag of financial ratios such as cash ratio.

mlogit status i.L_cash_ratio_deciles, rrr

The following chart shows RRRs while I am using the deciles on the x-axis instead of i.L_cash_ratio_deciles categories which are 1 to 10.

I was wondering if the following interpretation of the relative risk ratios is correct: "For the firms in the 7th decile of cash ratio (i.e., between 1.95 and 3.08) relative to the firms in the first decile, the probability of going insolvent in the next year is about half of the probability of being active in the next year."

Interpreting relative to both the base group of outcome (i.e., active firms) and the base group of the categorical variable (first decile), makes the interpretation a bit more difficult to understand.

I know that marginal probability is a better approach, but the margins command takes for ever to give me results (since I need the CIs as well). Any suggestion is much appreciated!

Thanks,

[Maarten Buis]

I was wondering if the following interpretation of the relative risk ratios is correct: "For the firms in the 7th decile of cash ratio (i.e., between 1.95 and 3.08) relative to the firms in the first decile, the probability of going insolvent in the next year is about half of the probability of being active in the next year."

No, the unit of the dependent variable is a relative risk (I would say odds, but definitions differ) not a risk. So the risk of becoming insolvent relative to the risk of remaining active is halved. Or the expected number of firms who are insolvent per firm who remains active is halved. Usually I start with interpreting the constant, which establishes the unit of relative risk in detail, and than start discussing the parameters for other variables.

[Hossein Jebeli]

Thanks Maarten!

I am still not sure how I can use the constant in my interpretation.

I have other RHS variables (like firm size: small, medium, large):

 mlogit status i.L_cash_ratio_deciles i.size (and other controls), rrr

The constant for the insolvency outcome is 0.0008. This means "For the firms in the base category of all variables (i.e., are small and in the first decile of the cash ratio., etc.), the risk of going insolvent in the next year is about 0.0008 of the risk of remaining active in the next year."

Then for the firms outside of the base category, can I remove the comparison with the base category by adding up the RRR and the constant, like below?

"For the firms in the 7th decile of cash ratio, the risk of going insolvent in the next year is about (0.0008+0.5) of the risk of remaining active in the next year."