SEQUENCE ANALYSIS

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

Literatures

In focusing my prior reviews of sequence literatures (1983, 1990) on sociology alone, I have found readers befuddled by my forcing them to see familiar things like careers and school-work transitions through the unfamiliar lenses of sequence analysis. I therefore base my review on diverse sequence literatures around the social sciences, turning to sociology proper only at the end. In all areas, the review is selective, not exhaustive.

Psychology
Economics
Archeology
Linguistics
Political Science
Sociology

Psychology

The largest literature on sequences in social science is in psychology. This work is in three areas: cognition (broadly understood), interaction sequences, theories of developmental stages.

The first major cognitive sequence topic is perception. Typically, sequences here are sequences of stimuli, treated as independent variables that affect level of perception or discrimination. Thus Polich (1987) studies EEG responses to tone sequences, Baird et al. (1991) study verbal judgments of loudness in tone sequences, and Allik (1992) studies judgments of motion given random dot patterns with varying luminance. Occasionally this literature studies internal dependence, but only as an independent variable; French-St. George and Bregman (1989), for example, study the impact of predictability of tone sequences on ability to discriminate tones. This has been an area of considerable theoretical development, aimed at the general problem of how subjects distinguish "parameter" change from "noise" change in sequential perceptual stimuli. Treisman and Williams (1984) advanced the theory of criterion-setting for this problem, while for van Leeuwen et al. (1988) sequence influences are explained by a more general formal theory of perception.

Another sequence literature in studies of individual cognition concerns more general topics, particularly memory and learning. Here too sequence is sometimes an independent variable only. Thus, Park & Tennyson (1986) examine tailoring the sequence of assistance in a computer-based learning system to patterns of student error and Wold & Reinvang (1990) examine effects of sequence of information ability to recall it. Some studies focus on the effect of sequence on judgment. Thus Mullen et al (1989) and Davis et al (1989) investigate effects of polling sequences on estimates of consensus in groups and Peake & Cervone (1989) investigate "sequence anchoring," an extended form of primacy effect in which early judgments influence later ones. All of this work on judgment falls within study of internal sequence dependence.

Most of the cognitive psychology literature on sequence, however, concerns sequence as itself an object of learning or perception, often integrating that with a concern for the actual sequence of learning. For reasons that become clear on reflection, sequences of learning are best investigated empirically by studying the learning of sequences. In a typical study, Winn (1988) investigates whether students can remember the order in which concepts were presented. Sometimes studies concern the relation of sequence perception to sequence production or discrimination (Terrace 1986, Grenzebach & McDonald 1992), but the more characteristic study tries to embed learning of sequences in a more general theory of learning or encoding of information (Cohen et al 1990). Another interesting literature concerns the ability to reconstruct full sequences out of partial information (Oppenheimer & Lee 1983, Oppenheimer & Groot 1985, Wyer et al 1985), a topic that has also emerged in the "script" literature spawned by the work of Schank and Abelson (1977: e.g., Hue & Erickson 1991). Read et al (1989) show nicely how reordering can radically change subjects' understanding of the meaning of particular events.

A final cognitive literature concerns sequences of action. Here again, sequence is typically an independent variable, usually in the form of sequences of reinforcement (success of some sort). A substantial literature studies the effects of the "illusion of control," artificially high reinforcement early in a given experience (Burger 1986, Fleming & Darley 1990), but there is also longstanding and enormous literature on schedules of reinforcement (e.g., Pittenger et al. 1988). There are a few studies of mechanisms for generating sequences of action (e.g., Garcia-Colera & Semjen 1987 on finger movements and Inhoff 1986 on eye-movements).

Studies of individual sequences in psychology are supplemented by a second major literature, that on interaction. Once prominent in social psychology generally (e.g., in the Bales tradition), interaction sequences are now more common as topics in the therapy literature. Parker (1988) exemplifies the long-running literature on turn-taking in conversation. On a broader scale, Staw and Ross (1989) consider escalation situations, changing the reinforcement schedule of the classical experimental paradigm into a mutual reinforcement system and examining origins of such systems. Also common are studies of "sequence of sequences," that is, studies of the development over time of sequential interaction patterns. Mays (1986) examines this in small groups, while Ryle (1991) provides a Vygotskian theoretical analysis of counseling sequences. Ney (1987) gives a typical analysis of "the natural sequence of events" in counseling, in this case for treatment of child abuse. Mishler (see, e.g., 1986) has done much work on narrative sequences in counseling. Bakeman (e.g., Bakeman and Gottman 1986) has done a variety of interaction sequence studies.

Another interactional literature focuses on sequences of family interaction generally and mother-child interaction in particular. Cohn and Tronick (1987) examine developmental patterns in mother-child interaction, while Lamb and Malkin (1986) study such patterns when the child is seeking aid. Duncan and Farley (1990) consider the emergence of conventions in parent- child sequential interactions. Vucinich (1984) has looked more broadly at sequences in family conflict.

The final psychological sequence literature concerns developmental sequences. Such conceptions - known and despised in sociology as "stage theories" - are widespread in psychology. A good but dated review essay is Campbell and Richie (1983), which urges continuing use of developmental sequences despite arguments against them. Campbell and Richie were clearly preaching to the converted; the developmental literature continues to make sequence one of its fundamental concepts. Lister et al (1990) consider concept development in children and Berti et al (1986) focus on acquisition of economic ideas, on which there has been a substantial literature. Another literature continues the longstanding research on moral development sequences (Vasudev & Hummel 1987, Foster and Sprinthall 1992). A final literature considers sequences of diseases and treatments. For example, Faedda et al. (1991) consider response to lithium, Deltito et al. (1991) consider symptom change in panic disorder, and Ellickson et al (1992) study sequential patterns of drug use.

Overall, then, there is much writing on sequence in psychology. In most of it, however, the conceptualization of sequence is simple. Particularly when sequence is an independent variable, "sequence" is defined as simple reversal, or as monotonic ascent or descent, or some similarly regular pattern like alternation. Complex sequence patterns are never investigated except as tasks for tests of cognitive functioning or as linear sequences of nonrecurring states in developmental sequences. Even within the psychological literature on interaction, there is seldom a focus on serious contingency in sequence. When there is, it is usually seen in a stochastic process (usually Markovian) framework.

Economics

Economics, like psychology, features several disparate literatures on sequences. There is a longstanding literature on sequence problems in operations research proper that ties loosely to studies of sequential games. The games literature ties further to some papers on sequence problems in general economic theory. There is also a specific literature on sequences in markets. Finally, there is some writing on sequence effects in advertising and consumption, loosely related to the "sequence effects in perception" literature in psychology.

The operations research literature is highly technical. Most of it concerns scheduling problems where there are one or more machines capable of performing several tasks and the costs of setting up machines for new tasks are a function of the sequence in which the tasks are done. (A favorite example: making chocolate cake mix after white cake mix requires less set up than making white cake mix after chocolate! [Meier et al 1982 cited in Dilts & Ramsing 1989].) Exemplary papers are Chand & Chhajed (1992), Dilts & Ramsing (1989), Dobson (1992), and Gupta & Darrow (1986). Perhaps more interesting, for its practical utility, is Nakai's (1986) paper on another common problem, how to make a best selection of candidates interviewed sequentially, once known as "the classical secretary problem." (Nakai 1986:478). Although these papers seem technical, they concern problems central to daily social life and addressed by a variety of satisficing strategies. They provide important models for thinking about social processes. Because of its genesis in immediate application, operations research work on sequence and scheduling often makes a lot more practical sense than the more arcane flights of game theory.

In general economic theory, sequence concepts are uncommon, since the characteristic move of that area is to seek asymptotic distribution theory precisely in order to ignore the sequence of intermediate states. Nonetheless, sequential equilibrium (Kreps & Wilson 1982) is an important topic in game theoretic economic writing, see, e.g., Besanko & Spulber (1990). In sequential equilibria, game players' strategies respond to each others' given beliefs about the rest of the game and to information sets governing their knowledge of other players' behaviors. The central empirical questions involve the game's coming to rest in one or more equilibrium points. Hoel (1987) relaxes the customary game theoretic assumption of an exact alternating sequence of offers, allowing "plays" at random times by random players. Economists, like psychologists, have often used Markovian approaches to sequences, as in Hopp's (1987) study of investment decisions.

A related literature considers sequences within specific market contexts. Here, as in the psychological literature, sequence may be either central (as in studies of interaction) or simply used as an independent variable. The most common issue is reaction to certain kinds of sequence signals, as in psychology's sequence perception problem. Thus, Burgstahler & Noreen (1986) consider reactions of securities markets to sequences of related events (an independent variable model), while Vickers (1986) and later Delbono (1989) study markets where there is a sequence of innovations (that is, a sequence of opportunities to arbitrarily lower one's production costs over the next competition interval). In these two studies, the focus is on sequential decision-making. In both cases, the derived theory shows that crucial characteristics of the products, produced markets, or bidding games shape the unfolding of the observed sequence of dominance. A similar theme appears in other kinds of studies, as in Dewatripont's (1987) study of sequential models of spatial competition. Sequential game theory is related to other kinds of sequential social theories, like Fararo and Skvoretz's "production theory" (Fararo & Skvoretz 1984, Skvoretz & Fararo 1989). These are the coming formalizations of social action, and will replace the simple exchange theories of the Homans/Blau era. (Their equivalent in the area of cognition is the Schank/Abelson (1977) script tradition.)

Also to be considered under economics are stray articles in marketing which employ sequential ideas. Sequence effects for advertisements are tested by Aaker et al (1986) and Marks & Kamins (1988). Others have tested different orders in consumption decisions - does one first choose brand, store, store type, or location? (Stoltman et al 1990). I note these papers less to draw on their scientific content than to show that interest in decision sequences extends well beyond the pure psychology and economics community well into applied contexts.

Archeology

Archeology has long been interested in sequence analysis. The problem of ordering sequences of artifacts, using measurements provided either by resemblances between artifacts or by proximity in sites, provided the first impetus to many current methods in sequence analysis. Hodson et al's monumental collection (1971) collected many of these works in one place and provides an entry to the field. This literature continues to be large.

Although the theoretical question is nearly always the simple stage problem of what came before what, a variety of sequence methods are used in archeology, some reflecting modal charactersitics of artifacts, some reflecting more complicated statistical analysis. For an example employing several techniques, see Tolstoy & DeBoer (1989). Typically, profiles of sites in terms of different kinds of artifacts are used to sequence sites or industry types, if that is desired (McBrearty 1988). Sometimes the methods used are extremely ingenious and rely on knowledge of complex sequential constraints, as in tree-ring dating of rooms in pueblos (Crown 1991: these are analogous, formally, to the scheduling problems of operations research.) One worry in the archeological literature is the pervasive assumption that there is a single directional sequence without cycles. Bird & Frankel (1991) raise this problem in connection with Holocene Australia, showing the difficulties of dovetailing sequences at individual sites with those elsewhere, particularly in the case of random censoring and research-induced sampling biases.

Linguistics

A variety of sequence questions have been investigated in linguistics. As in psychology, sequence is here most often a straightforward and usually simple independent variable. Generally, studies transpose words, grammatical structures, or whole parts of texts, and investigate the disturbance of comprehension. The wide range of such studies is indicated by Gisiner & Schusterman's (1992) paper, which concerns sequence effects in a language- trained sea lion. Another illustrative paper is Jonz's (1989) investigation of scrambled texts with native and non-native English speakers. A central question here - one that derives from the work of Piaget and that is central for our understanding of time more broadly - is exactly how people construct their images of and words for temporal processes and sequences. Much work concerns acquisition of such conceptions in children; Natsopoulos and Abadzi (1986) exemplify this literature. As that example suggests, the issue of linear development - the stage theory question - is as important in linguistics as in psychology. In both cases we have sequences of sequences. Thus we find stage theory throughout language acquisition studies, not only for children, but increasingly for second language acquisition as well. Laufer (1990) studies stages in second language acquisition, and illustrates a common theoretical move among stage theorists - insisting on absolutely regular gross succession, but allowing a fair amount of inversion and irregularity in the details of acquisition within stage.

Political Science

In political science, sequences have played important roles as well. The modernization tradition was anchored in a stage theory hypothesis, which spread from its application to economic change by scholars like Rostow to applications to political devlopment in Huntington and his followers and to nationalism in the work of Deutsch and others. More recently, stage theories have been applied to the welfare state, a problem analyzed in detail by Abbott and Deviney (1992). In some political science discussions sequence means, as it usually does in sociology, essentially a sequence of variables (e.g., Carmines & Stimson 1986). At other times, sequence is conceived essentially as some form of autoregression (Waterman et al 1991). Or again, sequence can be conceived as simple transposition in order (economic liberalization before political versus the reverse in Weintraub & Baer 1992). Auten et al (1984) present such a one-step model of budgeting. A far more sophisticated sequential model of budgeting is Padgett's classic 1981 article, which remains one of few really serious multi-level stochastic models of sequences of events.

The various non-sociological sequence literatures share a number of characteristics. First, the most common sequence approaches in them are two: use of stage theories to comprehend patterns of development and analysis of the effects of fairly simple sequence effects (e.g., inversions) as independent variables. Stage theories with their assumption of nonrecurrence are widespread, being central in developmental psychology, archeology, and political science. Similarly, the limitation of "sequence effects" to simple reversal or, at most, variation of among the order of three events, is pretty universal across the psychological, political scientific, and linguistic literatures. Economics stands out for its formal approach to sequence issues, usually within a stochastic framework either in real time or in the "decision tree time" of game theory. The various Markovian studies scattered across linguistics, economics, and psychology also fit this one-step sequence format, focusing on internal interdependencies in sequences. No non-sociological work really addresses the contingencies between separable sequences, although one could think about the beliefs and strategies of participants in extensive games as separable but interdependent sequences.

Sociology

The two prinicipal sociological literatures involving sequential conceptions have both seen recent reviews in the Annual Review. The life cycle literatures were reviewed by O'Rand & Krecker in 1990. The careers literature was reviewed by Rosenfeld in 1992. I have little to add to those reviews in terms of coverage of the literature.

Although sequences have made many appearances in sociology, there are few formal theoretical analyses for them. I have already noted the Fararo/Skvoretz tradition. There was also early work by Mayhew and others (Mayhew et al 1971, Mayhew and Levinger 1976) and Abbott's (1983) attempt to characterize the theoretical and methodological literature on sequences. Beyond that the theoretical work in sociology is minimal. By far the most important theoretical literatures for understanding sequences of social events per se are the analytical philosophy of history (reviewed in Gardiner 1959 and monumentalized in Danto 1985) and the structuralist theory of narrative (reviewed in Chatman 1978 and epitomized in the astonishingly brilliant Barthes 1974). These are large literatures, not to be summarized sketchily. Nor have they been transcended by the culturalist muddles about history that dominate debates on historiography and narrative today. An attempt to reconcile all these literatures is Ricouer (1984-5: definitely not for the intellectually faint at heart).

There are really three levels of sequence conceptions in sociological writing. The simplest are linear stage theories. These are familiar not only in the life course literature, but also in the dozens of "-ization" literatures - professionalization, rationalization, modernization, and so on. In sociology, formal stage theories have long been common. One finds them in Marx, Michels, Bateson, Kuhn, Smelser, and many others. A particularly rich source are the "natural histories" of the Chicago School, Robert Park having seen stage theories nearly everywhere: in revolutions (Edwards 1927), gangs (Thrasher 1927), commercial organizations (Hughes 1928), criminal careers (Shaw 1930), dancers' careers (Cressey 1932), and so on. Another version of stage theories are theories about "short sequences" that must be negotiated in some order, typically the school-to-work transition, but often something more quirky like the transition to criminality (Sampson and Laub 1993). These are "turning points" theories.

The next level of sequence conception involves much more contingency and accident than do stage theories. Sequences here are often more subject to influence by other sequences or by marginal conditions. Most of the job careers literature takes this approach, probably because even at the simplest level - employment and unemployment - job histories are astonishingly erratic. I therefore call these "career" theories, bearing in mind that many theories about people's careers are actually stage theories, expecting regular development, usually of nonrecurrent events.

The most extreme form of sequence conception makes all sequences interdependent in a complex network. I have elsewhere (1992) called such theories "interactional field" theories. They are quite common. White's (1970) vacancy chain model is of this kind, but so also was my own theory of professions (1988a). Such theories require quite unusual methodological handling; White resorted to modeling sequences of holes in the system rather than sequences of jobs held by individuals (see Chase 1991 for a review of such models).

The sociological literature thus involves some of the same issues as do other literatures, but has different emphases. Stage theories dominate in the life course literature and in much of the "transitions" literature that is a part of it. But by contrast career theories dominate most job research, and the despair of discovering patterned sequences has forced that literature to focus on point outcomes or one-step stochastic models.

Contact Information:
Address: 1126 E 59th St. Chicago, IL 60637
Office: (773) 702-4545 Fax: (773) 702-4849
Email to: a-abbott@uchicago.edu