My independent variables were highly skewed, so to normalise the distribution they were log transformed. Also since there were zeros in the data, I've added + 1 to transform the variables. This is what the model looks like (negative binomial regression):
Dependant_var ~ log(Independent_var_1 + 1) + log(Independent_var_2 + 1)
Coefficients:
Est. Std. Err. z-value sig.
log(Independent_var_1 + 1) 0.031907 0.004701 6.787 1.14e-11 ***
log(Independent_var_2 + 1) -0.019007 0.004735 -4.015 5.96e-05 ***
IRRs:
log(Independent_var_1 + 1) 1.0324219
log(Independent_var_2 + 1) 0.9811724
Now, I'm having problems understanding how to interpret the results. If the data were not log transformed, I would interpret this as follows:
If everything else is held constant, a one unit increase in Independent_var_1
would result in the decrease by 0.031
units of Dependent_var
. And for IRRs – a one unit increase of Independent_var_1
will result in an expected increase of the Dependent_var
by a factor of 1.032 (everything else constant).
However, I'm confused since I don't have "units" anymore, but log transformed vars. Thanks.
[negative-binomial]
& included that in the title. The NB is a distribution of counts. Are your data counts? You state that your DV was skewed, but your example shows logs of your IVs. Which was skewed? The distribution (skewed or not) of your IVs doesn't matter, & the overall (ie, marginal) distribution of your DV doesn't matter, only the distribution of your residuals does & even then the NB is supposed to be skewed. Can you say more about your situation, your data & your goals? $\endgroup$ – gung - Reinstate Monica♦ Dec 20 '14 at 1:10