14.7. A survey of 20 graduates of a university class five years after graduation yielded the following results for the variables sex (1 ¼ male, 2 ¼ female), race (1 ¼ white, 2 ¼ other), and annual income, measured on a log scale (—denotes missing):

Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Sex 1 1 1 2 2 2 2 2 2 2 2 1 1 2 2 1 1 1 2 2 Race 1 1 1 1 1 1 1 1 1112222 ————— Income 25 46 31 5 16 26 8 10 2 — — 20 29 — 32 — — 38 15 —

(a) Compute ML estimates for the general location model applied to these data, based on complete cases only.

(b) Develop explicit formulas for the E and M steps (14.5) – (14.8) for these data, and carry out three steps of the EM algorithm, starting from estimates found in (a).