Interpretation of estimated coefficients if dependent variable is in per cent

[Lina Saltik]

Hello everyone,

I would be very happy if someone could tell me how you would interpret the estimated coefficients in a multiple regression analysis when your dependent variable (availability of medicines) is in percent. By percent I mean the ratio of e.g. 0.29 and not 29 %. Let me make this more clear: The data I have used for my dependent variable has been provided in a data bank in the form of 0.29 and not 29%, however, in order to make interpretations it would not make sense to speak about an increase in availability of 0.29 but rather to speak about an increase of 29% in medicine's availability.
Would you say it is correct for me to speak of the estimated effect (let the coefficient value of X be 0.29) of X on Y like this: A one unit increase in X on averages is expected to increase Y by 29 % (and not 0.29 %) holding everything else constant. Can I say it like this?

Many Greets,
Lina

[Richard Williams]

Consider using fracreg or some other program designed for the analysis of dependent variables that are proportions ranging between 0 and 1. For a brief overview, see

https://www3.nd.edu/~rwilliam/stats3...onseModels.pdf

[Lina Saltik]

Many thanks Richard. I have heard that it is not a problem and that one could just intrepret the coefficients as an increase/decrease in Y by e.g. 29 per cent. Dont you think that this is feasbile as well? Greets, Lina

[Richard Williams]

I don't agree, but some might. It is basically the same controversy as when using the Regression/Linear Probability Model with a binary dependent variable. For one of many discussions, see

https://statisticalhorizons.com/in-d...f-logit-part-2

My own harangue is at

https://www3.nd.edu/~rwilliam/stats3/Logit01.pdf

There is also the question of whether either fracreg or the LPM is appropriate. Something like the other programs my handout mentions may be best.

[Lina Saltik]

Alright. I will see what my supervisor will say about this issue. Many thanks once again!

[Richard Williams]

Several other sources debating the pros and cons of the LPM are listed on p. 2 of

https://www3.nd.edu/~rwilliam/stats3/L09.pdf

Me, I'm with Allison (see link above). "The upshot is that combining logistic regression [and fractional logistic regression] with the margins command gives you the best of both worlds. You get a model that is likely to be a more accurate description of the world than a linear regression model. It will always produce predicted probabilities within the allowable range, and its parameters will tend to be more stable over varying conditions. On the other hand, you can also get numerical estimates that are interpretable as probabilities. And you can see how those probability-based estimates vary under different conditions."