Fitting proportion with respect to observations I have a dataset where the response variable is the proportion of land irrigated by a canal and the predictors are:

*

*the name of the village

*the total area in which the crop is sown

*the district name and

*the sub-district name.

Since proportion can take values only between 0 and 1, I fit $\log\left(\frac{p}{1-p}\right)$ on the predictors where $p$ denotes the proportion. The problem is, some of the proportions take values 1 and 0, and the corresponding $\log\left(\frac{p}{1-p}\right)$ takes values $\infty$ and $-\infty$.
How to deal with this problem?

To fit proportions I'd use a beta regression model, in which we model the expected value as a function of covariates. To do this in R you can use the betareg package.
If you really want to go with log-proportions, then one way to mitigate the boundary problem is to set $0\to\epsilon+0$ and $1\to 1-\epsilon$, for some small $\epsilon>0$, say, 0.001.
