(This is a question about the case study on page 636 of the book Applied Longitudinal Analysis by Fitzmaurice, Laird and Ware)
The data consists of 1028 weights of mice fetuses, they are clustered in 94 mother mice. The mother mice were assigned to a dose of poison.
I am puzzled as I don't see the advantage of clustering the data. Can you help me comparing the following two approaches:
- Standard linear regression model of the weight against the treatment. (blue dashed line on the graph).
- Linear mixed model with a random intercept for mother mice. (red line on the graph, with the random intercept for one mother mice displayed next to the weights of the fetuses of that mother mice).
I thought the advantage would be that the standard errors of treatment effect of the clustered model would be a lot smaller than the one of a linear model, but the opposite is true (the standard errors are 10 times as large as the ones of the linear model)! So what is the true advantage of clustering the data and adding a random intercept?