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I am researching whether female representation changes the innovation output of companies. I have panel data of 30 companies over 10 years and "diversity, sales, r&dbudget, #employees" as my independent variables and "# of product launches" as my dependent variable.

I want to control for the amount of employees in my regression, as they are going to have significant impact on the number of innovations. However, does it make more sense to just throw the employee number into the regression, or should I change my dependent variable from "product launches" to "product launches/employees" and not use the employees variable in the regression? The latter feels more correct, but I am no statistican.

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I would suspect in this case that the number of product launches is not directly related to the number of employees, simply because not all the employees are engaged in launching products. So my guess is that it makes sense to leave the dependent variable as the number of launches and to use measurements of company size as independent variables (number of employees, gross sales, etc.).

But, you should also be aware that models for count data, such as Poisson regression, can include an "offset", which weights the count observations. So in this case you could use log(Employees) as the offset if you want to adjust the number of launches for the number of employees.

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