Slightly off topic, but related :-) [Design Issues]

❝ But would we really need a mixed model ??

Hello, ElMaestro!

Look at residuals:

resid(M1)          1          2          3          4          5          6          7          8          9         10 -0.1540073  0.1540073 -0.4297153  0.4297153  0.1540073 -0.1540073 -1.1774560  1.1774560  1.6071713 -1.6071713 resid(M2)             1             2             3             4             5             6             8             9            10 -1.540073e-01  1.540073e-01 -1.018443e+00  1.018443e+00  1.540073e-01 -1.540073e-01 -3.608225e-16  1.018443e+00 -1.018443e+00

This is how I understand:

For observation 8 we have -3.608225e-16, I think, that mean, that this subject affect on "intra-variation" and make it less, and you can see SE is smaller. "Intra-individual part" went to coefficient and began part of inter-individual. Brr.. I don't know how to say with сlever words.

In lm / glm we see each observation as at statistically independent. And with lm we make smart trick when "storing" inter-individual variation in model coefficients, and exclude it from model error. Missing observation violate this system.

In mixed model we have another situation - all observation of subject is one statistically independent observation - realization of multidimentional variable. In the case of the ML / REML estimation, such a significant transition of one component of the variation to another does not occur in the case when the data contains missing values. ML and REML variation estimates all biased, but less biased than lm with missing data.