Best model for variable in range [-1,1]

[Ariel Soto-Caro]

Hello Everyone.

I need your advice about the proper model for my dependent variable.
This variable is a ratio that ranges in [-1,1].
My first thought was to use the fractional response model and run the function -fracglm-.
But then I realized that those models are meant for variables ranging in [0,1].
I guess that if I divide my dataset into 2 groups, one in [-1,0] and the other at [0,1] I'm losing information.
The other alternative is to use OLS, but that it would predict values lower than -1 or higher than 1.

There is a standard approach for these types of variables?
Thank you so much!

[Leonardo Guizzetti]

Can you say more about your dependent variable? What is it? Why is it restricted to a range of [-1, 1] ?

[Ariel Soto-Caro]

Can you say more about your dependent variable? What is it? Why is it restricted to a range of [-1, 1] ?

Hi Leonardo. This dependent variable can be constructed in the following way: For a certain geographic location and period, the net rate of change in its population can be defined as: (Joiners - Leavers)/Population.
Here, sometimes Joiners>Leavers, but sometimes Joiners<Leavers. But never (at least in this context) Joiners or leavers will be greater than Population.
I hope this helps.

[Ariel Soto-Caro]

Dear Dr. Jeff Wooldridge would it be possible to provide me your guidance in this matter, please? I even was thinking of using a Tobit approach, "limiting" the dataset into my range, but I know is not the nature of my dep variable. I will really appreciate your thoughts on this.

[Nick Cox]

The smallest your ratio can be is -1 if no one joins and everyone leaves in one year but otherwise the upper limit you mention is one of practice not principle. I don't see this as a Tobit problem.

The possibilities include

1. Keeping the response as it arrives and applying a plain linear regression might work well. I'd check with a plot of residual versus fitted and one of observed response versus fitted.

2. The lower bound bites in which case I might play with adding 1 to the response and then trying Poisson regression with robust standard errors.

This is as much about what works in practice as about what method respects the one bound you do have.

[Ariel Soto-Caro]

The smallest your ratio can be is -1 if no one joins and everyone leaves in one year but otherwise the upper limit you mention is one of practice not principle. I don't see this as a Tobit problem.

The possibilities include

1. Keeping the response as it arrives and applying a plain linear regression might work well. I'd check with a plot of residual versus fitted and one of observed response versus fitted.

2. The lower bound bites in which case I might play with adding 1 to the response and then trying Poisson regression with robust standard errors.

This is as much about what works in practice as about what method respects the one bound you do have.

Thank you so much, Dr. Cox. Has been really insightful.