Optional Factors in Regression

Question

I am working on a regression model (more specifically, the GLM). It has 6 factors that are always available and two factors that are only sometimes available. In other words, I have $y\sim x_1+x_2+...+x_6 + z_1 + z_2$, where $x_{1..6}$ are always available and $z_{1..2}$ are only available for certain data points.

I wonder how I would deal with this structure. One simple approach is to run many independent regressions. For example, I can do:

1. $y \sim x_1+...+x_6$ for all data points $y \sim x_1+...+x_6 + z_1$ for all data points where $z_1$ is available
2. $y \sim x_1+...+x_6 + z_2$ for all data points where $z_2$ is available
3. $y \sim x_1+...+x_6 + z_1+ z_2$ for all data points where $z_1$ and $z_2$ are both available.

The problem of this is that as the number of optional factors increase, the regressions I have to run increase exponentially. I wonder if there is any better way to deal with this.

Answer 1

Looks like you are dealing with the bane of every statistical analyses existence: missing data. You can either remove the missing values, impute them, or model them. Much of the time, missing data imputation is the best option. It can allow you to get reasonable results and keep all of your observations. There are several types of imputation that are dependent on the information you have about your missing values. For some information on missing data imputation and R code, refer to http://www.stat.columbia.edu/~gelman/arm/missing.pdf.