# Can I fit a mixed model with subjects that only have 1 observation?

I have a very large dataset where I have repeated measurements over time for individual locations. Some locations might have 10 data points and some locations have only 1 data point. I fit a mixed model and use locations as random effects. My question is can I still use the location that only has 1 data point (since you can't make a regression line with just 1 data) or should I exclude those locations?

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You can keep them in the model. A more thorough answer will go into greater detail what exactly they contribute to the model though. –  Andy W Mar 8 '12 at 0:28

More specifically, let $\sigma^{2}_{1}$ be the location random effect variance and $\sigma^{2}_{2}$ the unexplained variance. The likelihood function for a location with only a single observation has no curvature in $\sigma^{2}_{1}$ as long as $\sigma^{2}_{1}+\sigma^{2}_{2}$ remains constant (i.e. the two variances are not identified from each other, but the total variance is identified). But, there is curvature in $\beta$, the regression coefficients.