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I would like to comment on the estimation of the random effect with REML and without REML. This was my comment: "The variation between chicks for the model with REML is 545.70 and the variation between chicks for the model without REML is 498.0. Thus the size of the biological variation between chickens when REML is True is larger than the variation between chicks when REML is False." Is there anything that I am missing?

model2 <- lmer(weight~Time + Diet + Time*Diet + 
    (1|Chick), data=ChickWeight, REML = TRUE)
summary(model2)

model3 <- lmer(weight~Time + Diet + Time*Diet + 
    (1|Chick), data=ChickWeight, REML = FALSE)
summary(model3)
```
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  • The estimate of the variation in the intercept (baseline weight of chicks at Time=0) when using restricted maximum likelihood (REML) is 545.70
  • The estimate of the same variation using maximum likelihood (i.e., not REML) instead is 498.0.
  • The actual variation is the same no matter what estimation method we use; since REML (usually(1)) gives unbiased estimates, the larger REML estimate is in some sense a better estimate (although, for example, unbiased estimates are not always more accurate, and an unbiased estimate of the variance will not in general correspond to an unbiased estimate of the standard deviation ...)

Also note that although 545.7 vs. 498.0 looks like a big difference, on the standard-deviation scale this corresponds to a difference between a standard deviation of 23.4 vs 22.3 g (i.e., a 1-g or 4% difference in the SD).


(1) from http://nitro.biosci.arizona.edu/courses/eeb596-1999/handouts/reml.pdf:

REML does not always eliminate all of the bias in parameter estimation, since many methods for obtaining REML estimates cannot return negative estimates of a variance component.

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