SEQUENCE ANALYSIS

Annual Review of Sociology, 21: 93-113, 1995.
Andrew Abbott
Department of Sociology, University of Chicago

Introduction

Many apparently disparate developments in current sociology are avatars of one phenomenon: an emphasis on context. By context, I mean here simply the phenomena surrounding a case. I do not invoke the connotations of reflexivity that have become customary in the postmodernist usage of "context." I mean simply that sociologists seem less willing to detach cases from the network of other cases and prior times than they were heretofore.

For many years, our usual approach in sociology has been to think about cases independent of one another and, often, of the past. We characterize cases by properties like gender, race, totalitarianism, or bureaucratization and then ask how these properties are connected together in something we call a causal chain. Our methods are almost exclusively founded on such a model of social reality. And they have produced much interesting knowledge.

On the other hand, this model has major problems. It doesn't do very well by its own standards; variance explained is often small and effects are often substantively minimal despite their statistical significance. Rather than cumulation, we see diminishing returns. Moreover, the model's assumptions are embarassing at best (as was recognized by some of its founders, see Blau and Duncan 1967). We assume intercase independence even while our theorists focus on interaction. We talk about causality while our theorists emphasize social action. Our articles are filled with statements about race and bureaucratization "doing things," even while our theories concern people doing things. Between the two lie a cumbersome set of "just-so" stories specifying that if the people typically do such and such to each other, then the variables will be related as so and so. (Abbott 1992)

Meanwhile, there are areas of sociological research that clearly center on problems of events and actions in their temporal context, what we might call sequence problems. The various literatures related to the life course are probably the largest such area, but the tangle of literatures related to careers - occupational, criminal, organizational - runs a close second. Here the central problem has been reconciling the theoretical "sequentiality" of these literatures with the unrelentingly nonsequential character of sociologists' preferred methodologies.

Beyond sociology, surprisingly, the issue of sequence and temporality is much less of a problem. Sequences of events have a long research history in psychology and have enjoyed a recent renaissance in economics. Linguistics also has a tradition of sequence research, as does archeology.

Before considering the sequence literature, I give some basic concepts to set the stage. By sequence I mean an ordered list of elements. In the present paper the sequence will always be temporal, but mathematically the underlying property is order in one dimension, so spatial sequences (e.g., the arrangement of ethnic groups along transportation lines) would also fall under the term. However, there is no assumption of real time, as opposed to symbolic time, so "sequence" includes things like the order of steps in a manufacturing process or the successive parts of a ritual, where the time involved is "artificial" in some sense. Although the order of a sequence sometimes permits ties, as with parallel processes in a manufacturing process, most often we think of sequences as discrete, single lists, as in job careers. (To be sure, as moonlighting implies, even in careers we may not have a strong order, but rather simultaneous states.) The elements of a sequence are "events," drawn from a set of all possible events in a set of sequences, the "universe of events." We can conceptualize "ties," in fact, as conjunctural events drawn from the power set of the current universe (which includes all combination of basic events), so there is no real reason to worry about the idea of a single unilinear order.

A number of properties of sequences will be useful in the following discussion.

• First, events in a sequence can be unique or they can repeat. A sequence in which events cannot repeat, one that samples the universe without replacement, is "non-recurrent." The length of such a sequence cannot exceed the size of the universe; it will not equal that size if certain events do not happen. A sequence in which events can repeat - that is, a sequence that samples the universe of events with replacement - is a "recurrent sequence." The length of a recurrent sequence has no limit, but is typically set by some sampling frame - a lifetime, a wave of data collection, or something similar.
• Second, sequences can have dependence between their states. The most familiar examples of this are stochastic processes, in which the n+1th element of the sequence is some specified function of the nth or perhaps earlier elements. With a finite universe and a scalar probability of any given n+1th state after any given nth state, we have the simplest such case, the Markov process. There are of course many more complicated arrangements, particularly when the universe is infinite or continuous, as with interval-valued variables. There we may find higher-order autoregressive schemes, moving averages schemes, schemes introducing error, and so on. By contrast, there may on the other hand be minimal inter-state dependence, as in the example of the order of prayers in the Roman, Milanese, Syriac and other rites of the various Catholic churches.
• Third, there can be varying degrees of dependence between various whole sequences. As Harrison White noted in Chains of Opportunity (1970), we sometimes have sequences in which the occurrence of an event in any one sequence prevents that occurrence in any other; there can be only one Editor of the American Journal of Sociology at once, for example. This is true in a looser form for phemonena like "upper-classness" or "working in the farm sector" where larger constraints, usually conceptualized in sociology as "constraints on the marginals," limit possibilities across sequences.
• Fourth, sequence can be investigated either for itself or as an independent or dependent variable. Sometimes we are interested simply in the patterns in a collection of sequences. Other times we wish to know how prior event sequence affects the immediate future, as when we try to predict joblessness given prior sequence of job experiences. Still other times we wish to know what accounts for different sequences of behavior - what prior variables, for example, lead to descending spirals into criminality?

These four properties form a useful framework for analysis. In looking across the various sequence literatures, we shall see that some involve recurrent, others non-recurrent sequences. Some look for dependence within sequences, some between. Some consider sequence for itself, others for its origins, still others for its causal power.

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