5.13 (Morgan and Titterington, 1977.) The mover-stayer model has state transition probabilities of the form:

qij = (1 − si)pj (i = j = 1, 2,...,m), qii = (1 − si)pi + si (i = 1, 2,...,m), where {pk} is a probability distribution and 1 − si ≥ 0 ,

(1 − si)pi + si ≥ 0 , for i = 1, 2,...,m .

Show that conditional probabilities of state change are, for i = j, Pij = pj/(1 − pi) .

Consider how you would fit this model to data using the EM algorithm.