Negative Binomial regression

[komal Prakash]

I have number of children as count variable which I am regressing on the log of parent's income. How do I interpret the result of negative binomial considering that independent variable is a log transforamtion.


This forum has been a great help for me in the past. I appreciate the effort of people to help students like me who are new to this software. Thank you in advance

[Joao Santos Silva]

The coefficient on the log income is an elasticity. I suggest that, for robustness, you also try Poisson regression.

[komal Prakash]

Sir Joao Santos Silva, Thank you so much for input. I have looked everywhere for this answer. Though, intuitively I also figured out the same thing but could you explain why is it so ? I am using this for my dissertation and i need to explain the results.

[Joao Santos Silva]

Dear komal Prakash,

The NB and Poisson models assume an exponential functional form, and therefore the interpretation of the coefficients is as in a log-log model. Alternatively, think of a model like the Cobb-Douglas function; you can write it as y=exp(a*ln(K)+b*ln(L)) and therefore elasticities a and b are the coefficients in the model in its exponential form.

Best wishes,

Joao

[komal Prakash]

Thank you so much Joao Santos Silva Sir. It was really a great help.

[komal Prakash]

Sir Joao Santos Silva,
Could you help in one more query. My NB IRR coefficient is .98, which means one unit increase in independent variable increases the rate of dependent variable by 98%. But in case of log transformed independent variable, how do we interpret it?
1) 1 percent increase in independent variable increases the rate of dependent variable by .98% or 98%???
What will be the correct interpretation?
IF you could help, it would be great.

[Joao Santos Silva]

Sorry, I do not work with IRR and do not want to mislead you.