The Representation of Social Processes by Markov Models

In this paper we consider a class of issues which are central to modeling social phenomena by continuous-time Markov structures. In particular, we discuss (a) embeddability, or how to determine whether observations on an empirical process could have arisen via the evolution of a continuous-time Markov structure; and (b) identification, or what to do if the observations are consisten with more than one continuous-time Markov structure. With respect to the latter topic, we discuss how to select the specific structure from the list of alternatives which should be associated with the empirical process. We point out that the issues of embeddability and identification are especially pertinent to modeling empirical processes when one has available only fragmentary data and when the observations contain "noise" or other sources of error. These characteristics, of course, describe the typical work situation of sociologists. Finally, we note the type of situation in which a continuous-time model is the proper structure to employ and indicate that issues analogus to the ones we describe here apply to modeling social processes with discrete-time structure.