A Two-State Markov Model for Behavioral Change
Mary H. Regier · Journal of the American Statistical Association · 1968
THIS paper is concerned with analyzing a particular aspect of behavior in a situation of the following type. A subject (usually a person) is observed and his behavior classified as falling into one or another of two mutually exclusive classes, or states. A sequence of such observations is made on the same subject at equal intervals of time, resulting in a sequence of classifications in the given states. We consider a probability model for a special case of this general situation, and our aim is to study the tendency of the subject to move from one state to another under generally stable environmental conditions. The observed subject may be an individual, or a group of individuals taken as a unit. Our basic assumption is that the sequence of observations is a Markov chain with stationary transition probabilities pij(i, j= 1, 2). A more general Markov model involving k states (k > 1) and with k2 parameters pij(i, j = 1, * , k) has been studied at length by Anderson [1] and Anderson and Goodman [2], who suggest inference procedures based on several sequences of independent observations. Bartlett [3] and Hoel [4], using a single sequence, give inference procedures on transition probabilities in higher order probability chains. The more restrictive model proposed in this paper, primarily designed for a single sequence, defines the unknown constants pij(i, j = 1, 2) as functions of a special parameter, q, which in a certain sense describes the tendency of the observed subject to move from state to state.