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Individuals in my dataset have unequal numbers of measurements; some have one annual measurement, others have four quarterly measurements. I want to estimate the mean of the population that these individuals were sampled from, assuming that time has no effect. Does the MLE for the overall mean of a mixed effects model with random intercepts and fixed slopes of zero boil down to something simple if I assume measurement error variance is identical across individuals? What if that measurement error has a constant coefficient of variance across individuals?

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    $\begingroup$ Check out stats.stackexchange.com/a/465652/87305. Note that $\gamma_{00}$ is the fixed effect "intercept" or "constant" reported in most mixed modeling software. $\endgroup$
    – Erik Ruzek
    Feb 9 at 15:27
  • $\begingroup$ What's the relationship between one annual measurement and four quarterly measurements? Presumably, that one annual measurement was taken during one of the quarters? Or is it an average of four measurements (that have now been lost)? $\endgroup$
    – dipetkov
    Feb 10 at 14:14
  • $\begingroup$ @dipetkov Most of the annual measurements will be contemporaneous, but not all of them. The annual measurements are not an average of other lost measurements. $\endgroup$
    – Jack Elsey
    Feb 10 at 15:07
  • $\begingroup$ I'm not sure what contemporaneous measurements means in this context. Anyway, if all data points correspond to a single observation then they would have the same variance, though I also think that describing measurements as "annual" and "quarterly" is somewhat misleading. $\endgroup$
    – dipetkov
    Feb 10 at 22:39

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