Recall the open question asked at the end of Section 15.4 regarding the asymptotic distribution of MLE in GLMM with crossed random effects.

Consider the very simple example given there with only one unknown parameter, μ, and its MLE, ˆμ.

(i) Implement the MCEM procedure discussed in §15.4 to compute ˆμ.

(ii) Use simulated data to approximate the distribution of ˆμ. You may consider increasing sample sizes, m1 and m2, and observe change in the distribution of ˆμ as m1,m2 increases. Does the distribution look approximately normal as m1,m2 increase?