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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
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up vote 11 down vote accepted

You should keep them in the model. They contribute nothing to estimating the location random effect variance, but you can use them to contribute to estimating the mean structure.

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.

Hopefully this isn't too common in your data set or you will have a very imprecise estimate of the random effect variance.

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