# Possible regression models for a dependent variable that is a proportion

I am writing an applied econometrics paper. The dependent variable is a percentage of people who answered in the affirmative to a survey question asked in 60 different countries.

One possible model is a beta regression model for proportional dependent variables.

What are some other methods that are suitable for proportional dependent variable regression analysis?

Let $y$ be the proportion in $[0,1]$ instead of the percentage. I think the issues here are possible nonlinearity and censoring. You can try including quadratic terms on the right hand side. At the same time, you can try the following models.

I. Linear models: If no $y$ is exactly 0 or 1, linear models will be OK. The following four options come to my mind.

1. $y=\beta_0 + \beta_1 x + u$ if no $y$ is close to 0 or 1.

2. A log model $\ln y = \beta_0 + \beta_1 x + u$, which is helpful when some $y$ values are close to zero but all are far from one. Note that interpretation changes.

3. Transform the dependent variable to $-\ln (1-y)$. This is helpful if $y$ are all far from zero but some close to one. But this looks a bit unnatural to me, and I would consider the next logistic model instead.

4. The logistic model $\ln \frac{y}{1-y} = \beta_0 + \beta_1 x +u$. This usually helps if there are many $y\simeq 0$ and $y\simeq 1$. Interpretation is done in terms of logits.

II. Tobit models: If some $y$ are exactly 0 or 1, you can try Tobit models (help tobit in Stata). Remember that normality is assumed for the error term before censoring. Also, using Tobit models means that "I think $y$ could be bigger than 1 (smaller than 0) if not censored."