# Optional Factors in Regression

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.

• Why are all factors added? Can you write down your model specification? – Aksakal Dec 29 '15 at 18:54
• Because I want to use all available data. I noticed some format problems. Now I corrected them. – Tom Bennett Dec 29 '15 at 21:37