Consider the final model fitted to the osteoporosis data in Chapter 7, Section 7.2.

(a) When this model is fitted to these data, how many dimensions does each of the following have: (i) the data space? (ii) the fixed-effect subspace? (iii) the random-effect subspace?

(b) What is the relationship between the number of dimensions of the randomeffects subspace and the degrees of freedom of the deviance from this model?