# Thread: Interpreting the coefficient in a NegBin regression

1. ## Interpreting the coefficient in a NegBin regression

Hi,

I am doing a regression on immigration in Denmark. My dependent variable is a count variable with the number of immigrants between two regions in Denmark. As one of my independent variables I use the number of divorces times 100 divided by total population, i.e. the unit of measurement should be in percentage. When I run the regression the divorce variabel has a coefficent on -6.92, what is the interpretation of this result?
Does it mean that a 1 percent increase in the divorce fraction decreases the number of immigrants by 6,92% or what?

Thanks

2. ## Re: Interpreting the coefficient in a NegBin regression

Originally Posted by Jeppe
Hi,

I am doing a regression on immigration in Denmark. My dependent variable is a count variable with the number of immigrants between two regions in Denmark. As one of my independent variables I use the number of divorces times 100 divided by total population, i.e. the unit of measurement should be in percentage. When I run the regression the divorce variabel has a coefficent on -6.92, what is the interpretation of this result?
Does it mean that a 1 percent increase in the divorce fraction decreases the number of immigrants by 6,92% or what?

Thanks
This page includes a nice explanation of how to interpret coefficients from negative binomial regression.

Negbin regression usually uses a log link and takes a multiplicative form, so on the face of it the coefficient indicates that the log count of the number of immigrants decreases by a factor of 6.92 for every 1% increase in the divorce fraction, when holding the value of all other IV's constant. I'm a little confused, because using the exponential form of the coefficient, exp(-6.92) = 0.0009878, this suggests that the expected count of immigrants reduces a thousandfold for every 1% increase in the divorce fraction. That doesn't make a whole lot of sense - perhaps I have this wrong, or perhaps the coefficient your software is outputting has already been put in the exponential form? It might be handy if you could post some output from your model. If I'm mucking something up, others please feel free to correct me!

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