TRANSCENDING GENERAL LINEAR REALITYANDREW ABBOTT

Rutgers University

This paper argues that the dominance of linear models has led many sociologists to construethe social world in terms of a "general linear reality." This reality assumes (J) that thesocial world consists of fixed entities with variable attributes, (2) that cause cannot flowfrom "small" to "large" attributes/events, (3) that causal attributes have only one causalpattern at once, (4) that the sequence of events does not influence their outcome, (5) that the."careers" of entities are largely independent, and (6) that causal attributes are generallyindependent of each other. The paper discusses examples of these assumptions in empiricalwork, considers standard and new methods addressing them, and briefly explores alternativemodels for reality that employ demographic, sequential, and network perspectives.

A growing chasm divides sociological theoryand sociological research. While the generallinear model and other new techniques havereshaped empirical work, renewed acquaint-ance with the classics has transformed theory.These contradictory transformations havebred acrimony; Collins (1984) has sought toreduce social statistics to the status of asubstantive theory, while Blalock. (1984a:138ff.) accuses theorists of proliferatingvague alternatives. To a certain extent, oldand irremediable philosophical differencesseparate the two groups; the debate has beentaken up by interactionists (Blumer 1931,1940, 1956), macro-theorists (Coser 1975),and many others over the years. But the splitdid not assume its current proportions untilthe challenging and once-laborious mathemat-ics of linear and characteristic equationsbecame computerized. Quantitative work hassince come to dominate central disciplinaryjournals (Wilner 1985), while theoretical andqualitative work has increasingly founded itsown journals and/or chosen book form.'

* This paper was originally presented at the TenthAnnual Social Science History Association, Chicago, 23November 198S. I would like to thank Ron Angel, JoelDevine, Larry Griffin, Bill Gronfein, Erik Monkkonen,Doug Nelson, and Rob Paiker for comments.

' That commodification is central to methodologicalpreeminence is easily demonstrated. Blalock's text(1960) is the classic sociological source on regression andother methods currently commodified in SPSS andsimilar packages. A contrasting source on uncommodi-fied methods applying mathematical techniques tosociology is Coleman (1964). In the 1966-1970 period,Blalock had 162 citations to Coleman's 117 in ScienceCitation Index. The figures for later years are: 1971, 54to 39; 1975, 117 to 24; 1980, 121 to 24; 1984; 104 to 15.The very fact that Coleman's excellent book has neverbeen reprinted testifies to the same fact.

One caution should be raised concerning terminologythroughout the paper. The labels "theorist" and "empir-

In this paper I identify one intellectualsource for disagreement between theorists andempiricists. I shall argue that there is implicitin standard methods a "general linear reality"(GLR), a set of deep assumptions about howand why social events occur, and that theseassumptions prevent the analysis of manyproblems interesting to theorists and empiri-cists alike. In addition to delineating theseassumptions, I shall consider alternativemethods relaxing them. The paper closes witha brief discussion of three alternative sets ofmethodological presuppositions about socialreality. Through this analysis, I aim not torenew pointless controversies, for I believethe general linear model (GLM) is a formida-ble and effective method. But I argue that themodel has come to influence our actualconstruing of social reality, blinding us toimportant phenomena that can be rediscov-ered only by diversifying our formaltechniques.^

icist" (or "methodologist") are arbitrary polar termsdesigned to refer quickly to ideal-typical positions. Theydo not, obviously, embody a formal sociology ofsociology.

^ Much of theorists' disaffection with methods reflectsnot opposition to quantification, but to the common beliefthat standard linear models are the only possibleformalization for theories. Although there are otherapproaches, few have wide application (see Freese [1980]and Freese and Sell [1980] for reviews of formalsociological theorizing). Most classic work on theory andtheory construction (e.g., Hage 1972; Abell 1971; evenStinchcombe 1968) has employed the GLR view of socialreality. I should note that I iissume throughout that theoryexists to provide comprehensible and logically rigorousaccounts of facts. Definitions of comprehensibility,logicality, and facticity are of course debatable. Sometheorists believe that empiricists' "facts" are uninterest-ing or artifactual while some empiricists believe thattheorists' theories are incomprehensible and esthetic. Butdespite their disagreements about content, the two sides

Sociological Theory, 1988, Vol. 6 (Fall: 169-186) 169

170 SOCIOLOGICAL THEORYI. GENERAL LINEAR REALITYThe phrase "general linear reality" denotes away of thinking about how society works.This mentality arises through treating linearmodels as representations of the actual socialworld. This representational usage can beopposed to the more cautious use of linearmodels in which the analyst believes thatsome substantive causal process logicallyentails patterns of relations between variables,patterns which can then be tested by thatmodel to discover whether the actual state ofaffairs is consistent with the substantivemechanism proposed. These two uses will becalled the representational and entailmentuses, respectively. The discussion of sectionn will outline precisely what theoreticalassumptions are implicit in representationalusage. To begin the analysis, however, wemust first sketch the mathematics of themodel.

The general linear model makes somevariable dependent on a set of antecedentvariables up to an error term:

by problems of estimation. One can easilyconceive a general-form GLM:

y = Xb -I- u (1)

Lower case letters here represent vectors andupper case ones matrices. The row dimensionof y,u, and X is the number of cases observed(m), while the column dimension of X androw dimension of b is the number (n) ofantecedent variables. We can disregard theconstant term without loss. In formal terms,the model is a linear transformation from R(n)into R(l). The transformation itself makes noassumptions about causality or direction; anycolumn of X can be interchanged with y if theappropriate substitution in b is made. Usingthe transformation to represent social causal-ity, however, assumes that y occurs "after"everything in X. In cross-sectional applica-tion, use of the model postulates a "causaltime" that takes the place of actual time. (Foran elegant analysis of time in such models,see Robinson 1980).

That the range of the linear transformationhas but one dimension is a constraint imposed

agree that theory aims to explain why facts are what theyare. I shall also assume that the basic criterion of rigor islogical formalism. Although there are many types oflogic, I wish to exclude esthetics as the hasic criterion oftheory and the correlated notion that much theory is inprinciple unformalizable.

X(t) = X ( t - 1 ) B + U (2)Here the index embeds the variables in actualtime. Each succeeding value of each variablereflects a unique mix of all the antecedents. Bbecomes a square matrix of dimension n, andthe full transformation is thus from R(n) intoR(n). This more general GLM underlies mostpanel studies, although the relevant coeffi-cients can be estimated only by deleting ontheoretical grounds some fraction of thedependence this model postulates. Loosely,this second model envisions the situation as aschool of fish (the cases) swimming in someregular pattern (the transformation) through amultidimensional lake (the variable or at-tribute space).

To use such a model to actually representsocial reality one must map the processes ofsocial life onto the algebra of linear transfor-mations. This connection makes assumptionsabout social life: not the statistical assump-tions required to estimate the equations, butphilosophical assumptions about how thesocial world works. (For a polemical analysisof the statistical assumptions, see Leamer1983.) Such representational use assumes thatthe social world consists of fixed entities (theunits of analysis) that have attributes (thevariables). These attributes interact, in causalor actual time, to create outcomes, them-selves measurable as attributes of the fixedentities. The variable attributes have only onecausal meaning (one pattern of effects) in agiven study, although of course differentstudies make similar attributes mean differentthings. An attribute's causal meaning cannotdepend on the entity's location in the attributespace (its context), since the linear transfor-mation is the same throughout that space. Forsimilar reasons, the past path of an entitythrough the attribute space (its history) canhave no infiuence on its future path, nor canthe causal importance of an attribute changefrom one entity to the next. All must obey thesame transformation.

There are, of course, ways of relaxingsome of these assumptions within standardmethods, all of them at substantial cost ininterpretability. But it is striking how abso-lutely these assumptions contradict those ofthe major theoretical traditions of sociology.Symbolic interactionism rejects the assump-

GENERAL LINEAR REALITY 171tion of fixed entities and makes the meaningof a given occurrence depend on its loca-tionwithin an interaction, within an actor'sbiography, within a sequence of events. Boththe Marxian and Weberian traditions denyexplicitly that a given property of a socialactor has one and only one set of causalimplications. Marx's dialectical causalitymakes events produce an opposite as well as adirect outcome, while Weber and the varioushermeneutic schools treat attributes as infi-nitely nuanced and ambiguous. Marx, Weber,and work deriving from them in historicalsociology all approach social causality interms of stories, rather than in terms ofvariable attributes. To be sure, Marx andWeber discuss variable attributes in some oftheir purely conceptual writing, but their mostcurrently influential works are complex sto-ries in which attributes interact in uniquewaysthe Protestant Ethic, the GeneralEconomic History, the Eighteenth Brumaire,and even much of Capital.

The contrast between these assumptionsand those of GLR suggests that theorists mayreject empirical sociology because of thephilosophical approach implicit in representa-tional use of die GLM. In the rest of thispaper, I shall consider the assumptions of thatuse, drawing examples from work by some ofthe best exponents of the GLM. For eachassumption, I will discuss its nature, theattempts made to relax it within standardmethods, and the types of alternative methodsextant or possible. My focus throughout onthe problems with GLR and the potentialitiesof its alternatives does not imply anyderogation of its very great successes, and inparticular any derogation of the studies I useas examples. But by exploring the theoreticallimits of the GLM, I hope to suggest newlines of development in empirical sociology.

n . THE FUNDAMENTAL ASSUMPTIONSA. Fixed Entities with AttributesA central assumption of the GLM is that theworld consists of entities with attributes.Entities are fixed; attributes can change. Inpractice, standard empirical work overwhelm-ingly concerns biological individuals, govern-mental units, and other entities considered tobe "stable" by common cultural definitions.The GLM is less often applied to socialgroups like occupations, professions, and

social movements whose members and socialboundaries are continually changing.

The entities/attributes model for reality canbest be understood by contrasting it with itsmost common alternative, the central subject/event model. A historical narrative is orga-nized around a central subject (Hull 1975).This central subject may be a sequence ofevents (the coming of the Second WorldWar), a transformation of an entity or set ofentities into a new one (the making of theEnglish working class), or indeed a simpleentity (Britain between the wars). The centralsubject includes or endures a number ofevents, which may be large or small, directlyrelevant or tangential, specific or vague.Delineating a central subject and the relevanteventsthe task of colligation (McCullagh1978)is the fundamental problematic ofclassical historiography.

Precisely the same phenomena are orga-nized by the entities/attributes and central-subject/event approaches, but in differentways. Consider flie problem of the spread ofthe multidivisional form (MDF) among Amer-ican firms (see Fligstein 1985). There is a setof entitiesthe firmswhich at any givenmoment have fairly clear boundaries. Firmscan be thought of as having propertiessize,rate of asset increase, domination by- certainkinds of individuals, business strategies. Wecan imagine generalizing across the "cases"in terms of these "variables" and askingabout the relation of the variables to the use ofMDF. Yet we could also think about thehistory of a given "area" of firms, say theutilities area. We will see some entities in thatarea disappear through merger, others appearthrough internal differentiation and separa-tion. Firm sizes will fluctuate through thisappearance and disappearance as well asthrough variation in continuous entities. Somedominant individuals will control certainfirms continuously, while other leaders willmove from one firm to another through themergers and divisions. Strategies will comeand go, shaped by interfirm contagion and byperiod events like the depression. The histo-ries of individual firms will be seen to followunique paths shaped by the contingencies oftheir environments. In such a view, whatGLR saw as variables describing entitiesbecome events occurring to central subjects.

This example shows a profound difficultywith the fixed entities approach; it ignoresentity change through birth, death, amalgama-

172tion, and division. One way the MDF canarrive is through merger; yet merger removesentities from the sample and replaces themwith new ones. It is not merely a strategy(Fligstein 1985:383), but an event changingdie sample frame. The social science ofdemography does indeed deal with appear-ance and disappearance of entities, anddemographic models are now being applied toorganizations in the work of the Stanfordschool of organizational ecologists (for areview see Carroll 1984). Yet the eventhistory models so applied are essentiallysimple GLMs treating rates of change (usu-ally of organizational death) as dependentvariables and using a log-linear group ofindependent variables to predict them. Enti-ties are grouped in synthetic cohorts andexistence becomes yet another variable at-tribute to be predicted. Moreover, while suchdemographic methods address the appear-ance/disappearance problem, they do notaddress the merger/division problem in anyformal way.

Classical demography also provides prelim-inary models for the other major problem withtreating entities as fixed, the fact that namesoften stay the same while the things theydenote become different. This problem ismost evident in the situation of exchangebetween aggregate entities.

Consider the attempt of Simpson et al.(1982) to estimate the ability of occupationsto recruit and retain cohorts of workers. Theentities analyzed are occupations, character-ized by the attributes of 1) strength, skill, andeducational requirements, 2) product markets,industrial dispersion, and sex-specific growth,3) earnings and earning growth potential, and4) unionization or licensure. TTie dependentvariable is an occupation's relative retentionof a twenty-year age cohort, measured by theratio of the odds of a cohort member's beingin that occupation in the base year to thoseodds twenty years later, suitably standardizedfor death, relative occupational growth, andso on. Four twenty-year time-frames areanalyzed, starting in 1920, 1930, 1940, and1950.

There are two central problems with thisdaring design. First, the occupations them-selves do not denote a constant body of workor activities. Simpson et al. have addressedthis by excluding groups for which censusclassifications are not commensurate through-out the period. But this rules out, for

SOCIOLOGICAL THEORYexample, the occupations reshaped by technol-ogya substantial fraction of the occupa-tional structure, and a fraction that may infact be determining what happens to the rest.Yet even those remaining in the samplechanged drastically. Accounting, for exam-ple, began this period as a solo professiondoing public auditing and ended it as abureaucratized one doing nearly as muchwork in taxes and corporate planning as inauditing. The name stayed the same; the thingit denoted did not.

Second, the original cohort members presentin an occupation after twenty years are notnecessarily the same individuals who were init at the outset. Evans and Laumann (1983)have shown that even the professions haveextraordinarily high turnover and that theycontinue to recruit until well into middle age.Thus, the individuals aggregated under thelabels are not necessarily the same individualsat one time as at another. Retention isconfused with migration. Moreover, thecohort barriers are so wide that as each cohortages twenty years, some individuals go fromthe start of their careers to their careermidpoints, while others go from midpoint tonear retirement. The cohortsthemselvespresumed entities like the occupationsarethus no more coherent entities than are theoccupations themselves.

One might handle such problems bydisaggregation. But this is the counsel ofdespair. Both occupation and cohort do havesome sort of reality, some sort of causalpower. To disaggregate and model theoccupations as properties of individuals wouldforfeit any sense of occupations' reality asstructures. The classic answer to such multi-level problems is ecological regression (for areview see Blalock 1984b). But to assigncoherent group-level terms to individualsasis standard ecological practiceis completelyimpossible. The individuals don't stay in thesame aggregates over time, and the aggre-gates themselves changeboth by migrationof their members and by change in emergentproperties like type of work. These transfor-mations make ecological parameters meaning-less.

Some writers have noted the possibility ofcombining demographic and attribute meth-ods to deal with such problems. In suchmethods, underlying demographic dynamicsprovide memberswith their own at-tributesto an emergent level of aggregates.

GENERAL LINEAR REALITY 173which in tum have their own attributes (seee.g., Coleman 1964:162ff). Event historymethods (see Tuma and Hannan 1984) tosome extent so mix demographic and attributemodels. On the theoretical side, a number ofwriters have argued that iterative processes ofinteraction between micro-level units in factprovide the structure that is macrostructure(Cicourel 1981: Giddens 1984; Collins 1987).Thus, there are a variety of preliminaryattempts to address these issues, but clearlymuch workboth theoretical work on theformal structure of central-subject/event ap-proaches and mathematical work on how torealize themis required to develop this areafurther.

B. Monotonic Causal FlowBetween the various attributes of entities thatit analyzes, GLR assumes that causality flowseither from big to small (from the contextualto the specific) or between attributes ofequivalent "size." Cause can never fiow fromsmall to large, from the arbitrary to thegeneral, from the minor event to tfie majordevelopment. This assumption has severalconstituent parts.

The assumption of monotonic causal flowbegins with the assumption of "constantrelevance." A given cause is equally relevantat all times because the linear transformation,in most models, doesn't change over timeperiods (because the reestimation required isimpractical). Of course, the B matrix of thegeneral GLM can change, but GLR practition-ers seldom take the position, common inhistorical writing, that "at time t, x wasimportant, while later, the conjuncture ofthings made y more important." That kind ofthinkingin which B is mostly zeroes and thenon-zero elements differ from iteration toiterationis not common. The first constitu-ent of the monotonic causal fiow assumptionis thus the assumption, not necessary butnearly universal, of constant relevance.

Within this presumed constant relevancystructure, the GLM assumes necessarily thatif a cause changes, so does its effect. But thismeans that if a causal variable fiuctuates overa period of two weeks, a GLM cannot allow itto determine something that fiuctuates over aperiod of two years. It can study the"contextual" effect of the latter on theformer, using cross-sectional data to discoverhow different levels of "context" affected the

behavior of the more rapidly fiuctuatingvariable. But once context is removed, theuse of linear models implies the assumptionthat causes and effects have meaningfulfiuctuation over the same period. Thisassumption has in tum become a GLRassumption, a theoretical belief in what I shallcall the unity of time-horizon. ("Time-horizon" denotes the minimum length of timein which a meaningful change in a variablecan be observed.) GLR allows contextualeffects of various levels down to a uniform"basic" level for causal effects, but refiisesany reversal of this hierarchyany causing ofthe large by the small, the enduring by thefieeting.

The uniform time-horizons assumption canmost easily be seen in time series analyses,where a simple GLM is estimated on a singleentity using successive years as differentcases. Consider the problem of distinguishingthe effects of govemment revenue andexpenditure policies on the distribution ofincome in society. According to Devine(1983), neoconservatives see the state asreacting to the rising expectations of apluralist populace, while Marxists see thestate balancing between rewarding the domi-nant classes and purchasing the complaisanceof the dominated ones. Liberals by contrastview the state as technocratically motivatedand lacking any intent to redistribute income.Measuring income distribution with the capi-tal/labor income ratio, Devine predicts it withseveral prior attributes of the society: 1) theprior income ratio, 2) "controls" for infia-tion, unemployment, unionization, real GNPgrowth, and minimum wage, and 3) federalfiscal fiowsrevenue and expenditures formilitary personnel, for veterans benefits, for"technoscale" (military research and procap-ital infrastructure) and for "human scale"(transfer payments, education, and othercollective goods). The federal fiscal fiows aretaken to measure intent, operationalizing thethree theoretical frameworks of neoconservat-ism, Marxism, and liberalism. Devine'stemporal structure for estimation is quitecomplex: infiation, real GNP growth, andunemployment are measured contemporane-ously with the dependent variable: priorincome ratio is measured the year before:unionization, revenue, and expenditures formilitary personnel, veterans, and "techno-scale" are measured two years before."Human scale" is split; the transfer payments

174 SOCIOLOGICAL THEORYare measured contemporaneously, while thecollective goods are lagged two years. Devinespecifies this complex lag structure afterfinding that simpler versions (e.g., lagging allfiscal variables for one year) produced lessstable estimates. He justifies this choice withthe argument that the longer lag "allows foradequate diffusion of state spending andextractive capacity (614)," except in the caseof transfer payments, where the effect isimmediate.

The problem with the whole approach isthat the values of these measures at any giventime are not fteely variable. Annual inflationand GNP growth are linked in "recessions"that take several years to grow and die.Because laws link "human scale" paymentsto entitled populations, those payments fluc-tuate with demographic changes in age andother entitlement variables, which in turnreflect events ranging in size from thetwo-decade baby boom to much shorterfluctuations in unemployment. Military spend-ing reflects wars and other foreign policyventures again of widely varying durations.Thus, the observed values of the various"independent" variables at any given time(subject of course to the lag structure) arelinked in arbitrary ways to their values atother times, the linkage being provided by thestructure of what a historian would call"events." Because of this linkage, one cannotregard the independent variables as measuresof the state's various intents, nor thedependent variable as a measure of therealization of those intents. The independentvariables don't really stand for the state's freeexpression of its intents, but rather for what itcan intend given the various events it findsitself within. One could imagine measuringthese events with moving averages processes,but the "width" of the moving averageswould have to change with the temporalduration of the events involved. Thus thelinkages of various yearly levels of variablesinto larger "events" undermines studiesassuming uniform time-horizons, as do nearlyall empirical uses of the GLM. Events ofequivalent causal importance just don't al-ways take the same amount of time tohappen.

In fact, the problem is not limited to timeseries studies. Consider the cross-sectionalproblem of understanding the relation be-tween wife's outside employment and niaritalinstability. Booth et al. (1984) have studied

this process in 2034 married couples agedunder 55 years, measuring the followingattributes of the marriages:

1) "controls"husband education, wife edu-cation, years married, number of children under18.

2) roughly five "steps" to marital problems a)hours wife worked, b) other income and wife'income, c) marital division of labor and spousalinteraction, d) marital disagreement and maritalproblems, and e) marital happiness and maritalinstability.

Hours wife worked was (apparently) mea-sured over a three-year period, the incomevariables over a one-year period, and theremaining "process" variables by scales atthe time of study. The various "steps" in theprocess of marital instability are set up in aclassic path diagram (following the order justgiven), and are supported by causal narrativessuch as:

marital interaction may be decreased by wife'semployment. Household tasks that used to behandled by the wife while the husband was atwork may cut into time previously allotted tojoint activities. (Booth et al. 1984:569)

The model assumes that these various at-tributes of marriages fluctuate over equivalenttime periods, or that the attributes earlier inthe list fiuctuate more slowly than those later.Yet in fact there is no conceptual reason tothink that employment rates fluctuate moreslowly than do, for example, marital prob-lems or marital happiness. One can easilyimagine a long period of gradually increasingmarital instability in which episodes of wifeemployment punctuate attempts to reinstate atraditional division of labor. It is conceptuallyreasonable to expect wife employment tofluctuate at the same rate as wife income, butmany of the other time-horizon assumptionsin this "process" are erroneous. Theseproblems compound the sequence problems tobe discussed below. When attributes ofentities fluctuate over different periods, itbecomes impossible to specify the causal ortemporal order that they actually follow.Moreover, the act of aggregation in GLRstudy, further assumes that these attributeshave similar time-horizons in all casesforexample, that one marriage's instabilityfluctuates at the same rate as another's.^

' One consequence of the montonic causal flow

GENERAL LINEAR REALITY 175As a levels assumption, the time-horizon

assumption bears directly on the micro/macroissue. GLR requires all causes to lie either onone temporal level, or on levels that decreasein the same direction as causality flows.Recent theoretical writing on the micro/macroproblem objects strenuously to such a view(see various essays in Alexander et al. 1987).Collins (1981) has taken a basically aggregateapproach to the problem, but Giddens (1984)and others have emphasized the role ofmicro-iterations in creating macro entities. Itis clear that such relations can be formalizedonly within different methodological ap-proaches, as in the work of Heise (1979) or inthe work inspired by the dissipative structuretheory of Prigogine (see Schieve and Allen1982).

Not only do these causal flow assumptionsdisable GLR-type analysis of microgenerationof macrostructure, they also prevent GLRfrom recognizing small events that assumedecisive importance because of given struc-tural conditions. Pascal tells us that ifCleopatra's nose had been a little shorter, thewhole face of the earth would have changed.GLR cannot envision such occurrences. Afew models for addressing them are beingdeveloped, such as threshold models (Grano-vetter 1978). Attempts to treat sudden eventswithin a continuous-variable, GLR-type frame-work have had mixed success (for anexample, see Schieve and Allen 1982:c. 8)

C. Univocal MeaningTo its restrictions on the relations betweenvariable attributes GLR adds restrictions onthe individual attributes. For many theorists,the most problematic assumption of GLR-based empiricism is its insistence that a givenattribute have one and only one effect onanother attribute within a given study.Theorists commonly treat terms like anxietyor wealth as having multiple meanings withinthe same explanation. The recent renewal ofhermeneutic approaches in social theory givesthis reservoir of meaning infinite depth. Instrict contrast GLR restricts our attention to

assumptions is that every GLM study is implicitly a paneldesign. By modeling certain variables as causallysubordinate to others, cross-sectional GLMs assume thatthe subordinates have had time to equilibrate to changesin their causes. On the implicit stochastics of cross-sectional models, see Tuma and Hannan 1984:89ff.)

one causal meaning of a given variable onanother.

This contrast is well illustrated by Kohnand Schooler's (1982) work on the reciprocaleffects of job conditions and personality. Theauthors wish to show how flexibility andindependence on the job determine and aredetermined by personality flexibility andstrength, both at a given time, and (byassumption) over the individual's career.Kohn and Schooler's personality constructsare ideational flexibility (operationalized withan earlier-developed scale), self-directedness,and distress. The two latter constructs aredeveloped by factor analysis out of separateindicators as follows:

self-directedness is reflected in not havingauthoritarian conservative beliefs, in havingpersonally responsible standards of morality, inbeing trustful of others, in not being self-deprecatory, in not being conformist in one'sideas, and in not being fatalistic. . . . Distress isreflected in anxiety, self-deprecation, lack ofconfidence, nonconformity, and distrust (Kohnand Schooler 1982:1276)

The two factors have a mild negativecorrelation. Kohn and Schooler go on toapply full-information maximum-likelihoodmethods to estimate reciprocal causal linesbetween the two, estimating the path fromdistress to self-directedness at - . 0 8 , and itsreverse at - .25. They conclude that "If oneof the three dimensions of personality ispivotal, it is self-directedness" (1280).

Contrast with this Freud's analysis of therelation between anxiety (distress) and egoindependence (self-directedness). Freud ar-gued that anxiety symptoms signified dangerto the ego. In response to some danger, theego invoked repression to block dangerousinstinctual impulses. (In the Kohn andSchooler case, such an impulse might be rageagainst a constricting workplace.) For Freud,repression had two exactly contradictoryeffects; 1) it exercised and supported egocontrol by diverting the threatening feelingsinto symptom formation but 2) it forfeited egocontrol by placing the repressed materialsolely under the logic of the id. Since thatlogic decreed that subsequent impulses,responding to different situations, wouldnonetheless follow similar lines of develop-ment, new and different dangers (e.g., in theworkplace) would nonetheless lead to similarsymptomatic results, with a consequent loss

176 SOCIOLOGICAL THEORYof feeling of ego control. (Freud 1936:11-28;1963b; on contradictory instincts see 1963a:97ff.) The Freudian theory suggests simulta-neous and contradictory causal relations fromanxiety to self-dependence. No theorist wouldwant to forego the dual pathways, because thetwo contradictory effects will probably gener-ate two different causal sequences. Nonethe-less, summation is the standard methodologi-cal solution, a solution particularly problematicin the case of contradictory effects, wheresums are likely to be small and statisticallyinsigniflcant.

Michael Burawoy's (1979) trenchant Marx-ian analysis of the Kohn and Schoolersituation illustrates a different pair of simulta-neous, contradictory causal paths within it.

Thus, the intemal labor market bases itself in acomplex of rules, on the one hand, whileexpanding the number of choices on the other.Nor should these choices be belittled by sayingthat one boring, meaningless job is much thesame as any other. The choice gains itssignificance from the material power it gives towoikers in their attempts to protect themselvesfix)m managerial domination. Workers have avery defuiite interest in the preservation andexpansion of the intemal labor market, as themost casual observation of the shop floor woulddemonstrate. Moreover, it is precisely thatinterest that draws workers into the biddingsystem and generates consent to its rules and theconditions they represent, namely, a laborprocess that is being emptied of skill. (Burawoy1979:107-108.)

Here, the psychological attributes flexibilityand self-determination simultaneously in-crease both worker control and managementdominance. These two different effects canonly partially be separated by saying that theformer is short run and the latter long run, forin fact they are nearly simultaneous.

As these examples show, perhaps no otherassumption of the GLR seems as inimical toclassical theory as that of univocal meaning.Recognition of multiple meanings is centralfor sociological methodology because com-plexity of meaning is central for the qualita-tive theories currently dominant. (See, e.g.,Giddens 1982:c. 1.) Tlie most common empir-ical solution of the multivocality problem is todisaggregate by finding intervening indicatorsthat differentiate the causal paths. But notonly is this procedure not always possible, italso moves the causal focus from antecedentto intervening variables, a shift theorists mayreject.

There are several formal ways to addressthe problem .^ One might assume that eachvariable produces an ensemble of effects onanother and that some other process chooseswhich of these will obtain in the particularcase. (In the Freudian example, such a modelgoverns the choice of particular symptomformation.) If the determining process isendogenous, then the multiple meaning prob-lem becomes the interaction problem; somecombinations lead to one type of outcome,others to another (see sections E and Fbelow). If the determining process is exoge-nous, one can perhaps model it directly.

A second general approach insists onallowing more than one effect at once. Thereis some work relevant to this problem withinthe network framework. Several writers havecombined structural models based on differentrating methods into complex models forrelations between various units of analysis.This is, implicitly, a disaggregation strategy.(For an example, see Boorman and White1976.) Another disaggregation approach is toseparate the two effects temporally. Thus,Cantor and Land (1985) have recently concep-tualized the effects of unemployment oncrime as a negative effect through opportunity(more people are home to protect their goods)and a positive one through motivation (peoplewithout work must tum to crime). Theyseparate the effects by arguing that institu-tional support systems buffer the latter effect,which is thus estimated at a one-year timelag. Finally, certain forms of non-metricanalysis may support the direct inclusion ofmultiple effects (see Katzner 1983); thesemay be the only approaches that do notrequire disaggregation. A few authors, nota-bly Hayward Alker (Alker 1982, 1984; Alker,Bennett and Mefford 1980; Mefford 1982),have followed the lead of Schank andAbelson's (1977) artificial intelligence ap-proach to modeling processes of understand-ing, aiming directly at replicating complexunderstandings.

In defense of current methods, we shouldrecognize that the multiple meaning problemis in part a problem of presentation andemphasis. Even the most complex of multiplecausal relations (e.g., "determination in thelast instance" in the writings of Poulantzas[1975] and Althusser [Althusser and Balibar1970]) must in fact be disassembled intoconstituent relations to be logically inter-preted. The theorists' style with such con-

GENERAL LINEAR REALITY 177cepts is to retain their unity and treat them ascausally ambiguous or complex. The method-ologists' style is to disaggregate and treat thevariables indicating the various causal pathsas tbe independent variables of interest. Yetwhile methodologists need not recognize the"essentially subjectivist" position that humanaffairs are in principle non-fonnalizable, it isclear that serious work must be done on theproblem of univocality.

D. The Absence of Sequence EffectsThe preceding GLR assumptions, whichconcern causality as mediated through vari-able attributes of entities, are completed by aset of assumptions about independence be-tween entities, attributes, and time periods.These latter are not quite as inherent to theGLM itself as are the entity assumptions, butinsuperable difficulties of estimation andmodeling have made them, de facto, constitu-tive assumptions of the GLR way of thought.The first of these independence assumptionsconcerns sequence.

A fundamental assumption of GLR is thatthe order of things does not influence the waythey turn out. According to the general GLM,the state of entity x(l) at time t+ 1 (that is,the pattern of its attributes at t-l-1) isdetermined by applying the transformationmatrix B to its state at time t; how it got tothat present is not relevant to its currentfuture. Such an assumption challenges funda-mental theoretical intuitions about humanevents (see, e.g., Kamens 1985). The wholeidea of narrative history is that the order ofthings matters, an idea that undergirds theinteractionist and ethnomethodological para-digms as well (see Gallie 1968; Sacks,Schegloff, and Jefferson 1974; Sudnow 1971).

The sequence assumptions of GLR are infact quite complex, depending on whether weare concerned with the "causal" sequence ofthe variables within a cross-sectional applica-tion of the simple GLM or the temporalsequence of states of entities in the generalone. To see the assumptions about cross-sectional causal sequences, consider theproblem of relating the racial mix of anindustrial sector to its productivity (fordetails, see Galle, Wiswell, and Burr 1985).Each sector can be described by the followingproperties: 1) capital expenditures per worker,2) mean educational level of workers, 3)mean age of workers, 4) percent of blacks

among workers, and 5) productivity. Theseproperties are observed in the early 1960s andin 1972; annualized rates of change are thencreated for all but age. The cross-sectionalmodels treat the productivity rate as depend-ing on all the others within time period andthe over-time models use the change rates topredict both change in productivity andproductivity in 1972.

The authors believe their cross-sectionalGLM allows them to make conclusions aboutthe productivity of black workers; theyassume that black workers as individuals haveor lack productivity and that their beingrecruited to an industrial sector then affectsthe productivity of that sector. But it maywell be that in some cases more or lessproductive sectors needed labor when labormarket conditions favored hiring black work-ers, whether the latter have an inherentproductivity or not. In some sectors, that is,the causal arrow is undoubtedly reversed. Butthe GLM must assume that the sequence ofvariables is the same in every sector, (case).Here, that means assuming that the dependentvariable is dependent in every case. In morecomplex path models, it means assuming thatthe paths of causality are the same in everycase. Although carefully noted in the firstlarge-scale application of path analysis tosocial data (Blau and Duncan 1967:167), thisradical simplification has been ignored since.Worse yet, familiarity with the GLM has ledmany of us to believe that reality actuallyworks this way, that causality must always bein one direction across all cases.

The temporal situation is quite similar.Consider the problem of understanding therelation between personal unemployment andcriminal behavior (for details, see Thomberryand Christenson 1984). The entities areindividuals and their attributes are twovariables integrated over one year periodstheir percent of time unemployed and theirnumber of arrests. Data cover the years fromage 21 to age 24, and include someexogenous variables not of interest here. Theauthors take a general GLM approach,deleting a few coefficients to achieve identifi-cation. Each path is "justified" by a littlecausal story. For exainple:

1) Unemployment reduces commitment andinvolvement with conventional activities andhence leads to criminal activity. "A person maybe simply too busy doing conventional things tofind time to engage in deviant behavior."

178 SOCIOLOGICAL THEORY(Hirschi 1969, quoted in Thomberry andChristenson 1984:400)

2) Crime creates further bairiers to conven-tional means to success, among which isemployment. "Employers, for example, oughtto be less willing to provide jobs to current andformer offenders" (Thomberry and Christenson1984:401).These causal paths aggregate a set of

stories. Thus, individual A commits a firstcrime and goes on to a serious criminalcareer, never looking back, never botheringto seek legitimate work. Individual B spiralsin an ever deepening circle of greaterunemployment and more crime each year. Cgoes wrong at the start (perhaps because of arandom crime or perhaps because unemploy-ment drove him to crime), but is thenfiightened by the criminal justice system andnever errs again. Each of these storiescomprises several one-step theoretical ele-ments of. the kind just given, linked into asequential story. But aggregating these se-quences throws away the narrative patternsthat link the elements into individuals'stories. Suppose everyone who has twoconsecutive years of many crimes becomes apermanent criminal. A general GLM with aone-year transformation period cannot seethat, because the past at time t 1 is notrelevant to the future at t -f-1 except throughits influence on the present of time t.

A central assumption of GLR, then, is thatthe order of things does not make adifference. In the first place this meansassuming that the "more causally powerful"attributes are the same in every case. In thesecond, it means assuming diat the particularobserved sequence of attributes over timedoes not influence their ultimate result.Unlike most GLR assumptions, this sequenceassumption has seen some serious study(Abbott 1983; Abell 1987).

A number of methods permit specific formsof sequential dependence. ARIMA modelsallow a variable to depend on its own past aswell as on past random disturbances, althoughusually restricting attention to one entity andone variable (Box and Jenkins 1976. Revert-ing to my earlier metaphor, this is likefollowing one fish's complete path throughthe lake.) Markov models for sequential datadivide the attribute space into a limitednumber of states (parts of the lake) andspecify the likelihood of moves from eachstate to any other. If the number of states is

small, the future can be made to depend onthe sequence of n past states, although thenumber of transitions to be estimated for suchmodels rises with the nth power of theoriginal number of states (see Bishop, Fein-berg, and Holland 1975). Although such nthorder Markov processes operationalize theo-retically important concepts of time, they arein fact rare (but see Brent and Sykes 1979). Inparticular, the recent fiorescence of eventhistory modelswhich are discrete-state,continuous-time Markov modelshas not tomy knowledge involved use of information onthe exact sequence of past states to predictcurrent and future developments (for ageneral review see Tuma and Hannan 1984).^

Theorists and empirical workers alike havecalled for methods that can classify or clustersequential data, such as the Mstories ofindividuals, occupations, and revolutions (see,e.g., Stinchcombe 1978). For sequences ofunique events in continuous or discrete time,various forms of uni- and multi-dimensionalscaling have long been used (Hodson, Ken-dall, and Tautu 1971). Abbott (1985) hasapplied them to the sequence of events in thehistories of professions. Sequences of repeat-ing events may be analyzed by optimalmatching methods; Abbott and Forrest (1986)have recentiy applied them to sequentialcultural rituals and argued for their generalapplicability to social data. Although bothscaling and matching methods work withintercase distances and hence force smallsamples, they provide a serious start on theproblem of identifying common sequences.^

E. Casewise Independence andRelated AssumptionsOther independence assumptions of the GLRconcern cases and variables. Although com-

'* I have not mentioned another general sequencemethod, dynamic programming. Most solvable dynamicprogramming problems are handled by making Marko-vian assumptions for the back solutions. See Puterman(1978). I should also note that there are multivariateARIMA models (e.g., Tiao and Box 1981), althoughconsiderable interpretation is involved in their use.

' In addition to Abbott's sequence work (1983, 1984,Abbott and Forrest 1986), there is an alternative, moreformal analysis of sequences in Abell's recent work(1984, 1987, Proctor and Abell 1985), which employshomomorphisms to measure sequence resemblance.Demographers are generally handling sequencing byenumeration, rather than by the direct approachesadopted by Abbott and Abell (see, e.g., Hogan 1978;Alexander and Reilly 1981; Marini 1984). An interestingsequential formalism of interaction is Heise (1979).

GENERAL LINEAR REALITY 179monly seen as statistical assumptions, theseare also conceptual presuppositions. The firstis that there is not "excessive" dependencebetween elements in a given row of the datamatrix X. By increasing parameter variance,collinearity makes the GLM unable to distin-guish the effects of variables closely related toeach other. The GLR proscription of collinea-rity directly violates the view, commonamong theorists, that social determinants Hein closely related bundles; Weber's causalconcept of "elective affinity" (Howe 1978)and his related notion of ideal types (Weber1949:89-104) are the most obvious examples.Another celebrated bundling controversy pitselitists against pluralists over the degree towhich different bases of status tend to parallelone another.

In formal terms, the collinearity problemconcerns the "level" of variation. Highlycorrelated independent variables can be treatedas aspects of a single variable through factoranalysis and other forms of scale constnic-tion. But the GLM falters if variables likeincome have causal functions simultaneouslyas members of "emergent attributes" likegeneral status and as independent variables.Hence GLR as a view of reality tends to limitnot only entities (see section A), but alsovariables to one level, unlike many theoreticalconceptions.

Correlated error terms are a second statisti-cal problem with conceptual implications.Correlated errors usually arise through tempo-rally or spatially structured data. They can beremedied, up to a point, by the use of specialestimators. Behind the issue of error correla-tion, however, is a conceptual problem with along historyGalton's problem of distinguish-ing effects of diffusion between units fromeffects of similar mechanisms within units. Infact, the standard remedies for serial correla-tion require theoretically postulating its exactstructure; there are no purely statisticalgrounds (beyond the esthetic criterion ofparsimony) for distinguishing between differ-ent temporal autocorrelation models. As forspace, only now are substantial models forspatial autocorrelation combined with localcausation being developed (Loftin and Ward1981, 1983; Hubert, Golledge, and Costanzo1982). Spatial autocorrelation makes it even

more evident that the correlated error problemis ultimately conceptual, not statistical.^

Perhaps the most important independenceassumption of GLR, however, involves thecasewise independence of the dependentvariable, assumed in the assertion diat theindependent variables determine the depen-dent variable up to an error term. A widevariety of sociological theories treat depen-dent variables as structurally constrained. Insuch theories independent variables are suffi-cient to explain the dependent up to an errorterm only given the necessary conditionsspecified by the constraints.

Versions of the constrained-dependent-variable problem are common. Thus, Peter-son and Hagan (1984) study the effect ofrace, education, marital status, class, age,and a host of other factors on criminalsentencing, using simple GLM specificationsfor two dependent variables. The first is theprobability of sentencing (a probit model), thesecond the length of sentence. The units ofanalysis are drug offenders sentenced between1963 and 1976 in a particular Federal District.The constraint lies in the availability of prisoncells. The independent variables freely deter-mine sentence and length once availability istaken into account, availability being itself afunction of past sentencing procedures, amongother things. Availability may operate only asa general limit with a similar effect on allcases. But more often sentence severity willvary in different cases and at different timesbecause of varying likelihoods that certainsentences can actually be served.

Some of the many possible constraints ondependent variables have received seriousstudy. Most such study has separated theproblem of specifying constraint from that ofanalyzing causal mechanisms once the con-straint is given. For example, the structuraland exchange mobility literature specifyingthe constraints on occupational achievement

' The standard source on spatial autocorrelation is Cliffand Ord (1981). Methods that originated in the study ofatomic, unrelated individuals run an obvious risk ofignoring contagion, particularly spatial contagion. Whensociologists move from the realm of largely disconnectedindividuals to networks of actors (e.g., from estimatingthe effect of education on social status to analyzing thereasons for the survival of newspapers [Carroll andDelacroix 1982]), the newly central contagion effectsdisappear because the models hide them. Yet contagioneffects are among the central determinants of behavior, asnetwork studies (e.g., Coleman, Katz, and Menzel 1966)tell us.

180is generally separate from the status attain-ment literature describing achievement itself.(For summaries see Boudon [1972]; Sobel[1983]. The two topics are separate sectionsin Blau and Duncan [1967] and Feathermanand Hauser [1978]). Simply distinguishingthe constraints of structural mobility from thefree motion of exchange mobility has provedperplexing, and Sobel, Hout, and Duncan(1985) have recently proposed adding thethird concept of "unreciprocated mobility."Some have followed the reverse path ofspecifying constraiiied attributes influencingmobility (Yamaguchi 1983). A more detailedapproach to constraint has been taken inHarrison White's vacancy models and relatedMarkovian mobility models (for reviews seeStewman 1976; Tuma and Hannan 1984).

A considerable methodological literaturetreats social structure as itself causal, reason-ing that social causes must move along linesconnecting individuals. The network litera-ture takes this approach, as do a variety offormal mathematical modelsfor markets(White 1981), for justice systems (Padgett1985), and for power in general (Marsden1983). Methodologies addressing this prob-lem include blpckmodeling (White, Boor-man, and Breiger 1976; Boorman and White1976;), multidimensional scaling (Laumannand Pappi 1976), and other formal networkmodels (Burt 1982).

F. Independence of contextA fmal independence presupposition of GLRis that the causal meaning of a given attributecannot, in general, depend on its context ineither space or time. Its effect does notchange as other variables change around it,nor is its causal effect redefmed by its ownpast. Mathematically, this assumes that thematrix B of coefficients in the general GLMdoes not depend either on X(t) or onX( t - l ) ,X( t -2 ) , etc. In actual GLM prac-tice, this dependence is often allowed. Thecontemporaneous dependence is expressed byinteraction terms; the past dependence by lagterms and change scores. But these tech-niques have their drawbacks, as we shall see.The GLM can consider only a narrow rangeof such effects, and GLR as a way of thinkingabout the world does not really incorporatethem at all.

As an example, consider Bradshaw's (1985)analysis of dependent development in Africa.

SOCIOLOGICAL THEORYA series of GLMs are here used to investigatea recursive "story" of dependent developmentthat unfolds as follows:

Multinational firms ally with indigenous elites topromote economic growth (E) and the develop-ment of a modem sector (M). This alliance canbe seen in the impact of foreign investment (I),trade dependence (D), primary product special-ization (P),,and commodity concentration (C) onstate expansion (X). The combination of growthand development leads to economic inequality(Q), which in turn leads to social turmoil (T).

Eight linear models are runthree with Tas dependent, two each with E and M asdependent, and one with X as dependent. Eand M prove highly stable over the two timeperiods analyzed (1960 and 1977), while T isquite volatile. X has some (small) effect on E,M, and T in 1977, although this is probablydue to its dependence on E (and perhaps M)in 1960. It is clear that some of thesevariables receive their meaning from theircontext. Thus, as Bradshaw notes (1985:202),if the state is expanding (X) and has the(foreign) resources (I) to transform theeconomy in a way rewarding to itself and theinvestors who support it, then E, M, and Twill increase niore than they would if eitherconditionstate development or external in-vestmentwere absent. With either conditionabsent, the situation will not differ from thatwith both absent. One might alternativelytheorize, however, that strong state develop-ment (X) and external investment (I) wouldlead to strong police and military forces(unmeasured), which could prevent turmoil(T) by threat alonea suppressor effectcontrasting to the conduciveness effect previ-ously hypothesized. Such interactions arenormally handled with multiplier terms inGLMs, a practice that renders the lower-ordercoefficients in the equation completely arbi-trary, and that requires exceedingly delicatehandling (Allison 1977; Southwood 1978).

Although the GLM itself can handle a fewinteractive effects or temporal dependencieswhen used with suitable care, GLR as a wayof thinking has a harder time with them. In adetailed analysis of substantive models forinteraction, Southwood (1978) shows theextraordinary complexity of even two variableinteractions when they are envisioned withproper care. With nine variables involved,and even a few particular interactive specifi-cations considered, the models implied here

GENERAL LINEAR REALITY 181surpass visualization. They mean that thesixty points describing the thirty cases at thetwo points in time make a particular shape inthe nine-space of variables, with somespecific deviation from regularity in thatshape for each specific interaction. Howeverstraightforward the inclusion of multiplierterms in equations may be, the conceptualleap of imaging them is prodigious indeed.

Yet complex interactions permeate, indeedthey define any real historical process. For ahistorian wouJd define the place of, say,primary product specialization in any one ofthese countries in terms of the conjuncture ofother variables at the time. Thus, in describ-ing the impact of these variables on agricul-tural policya relative of Bradshaw's mod-em sector sizeBates (1981:128) says thefollowing:

Palm oil in Southern Nigeria in the 1960s wasproduced in a nation where marketing boardshad been set up by the government in associationwith merchant interests. Government revenuesderived from export agriculture, and populardemands for government services were strong;local processors consumed a growing share ofthe industry's output; fanners had few alterna-tive cash crops, and production was in the handsof small scale, village-level fanners. Theindustry was subject to a high level of taxation.Only when farmers began to abandon theproduction of palm oil for other crops, and whenthe government found different sources ofrevenue, did the government relent and offerhigher prices for the crop.

The production of wheat in Kenya offers a "striking contrast. Historically, the marketingboard for wheat had been set up by theproducers themselves, and prosperous indige-nous farmers had played a major role in thenationalist movement which seized power in thepost-independence period. The government de-rived a relatively small portion of its revenuesfrom agriculture; fanners had attractive alterna-tives to the production of wheat; consumers hada strong preference for wheat products andalternative sources of supply lay in far distantmarkets. Wheat production was dominated by arelatively small number of very large farmers;and elite-level figures had direct fmancialinterests in wheat farming. The result was a setof policies providing favorable prices for wheatproducts and extensive subsidies for farm inputs.

The attributes of Kenya and Nigeria cometogether in this discussion into two differentconjunctures that produce strikingly differentagricultural policies. It is the conjuncture thatproduces the results, not the superposition of

interaction effects on fundamental "main"effects of the independent attributes. Therereally is no general causal story that Brad-shaw can capture in a set of path models andthat can in turn be modified by particularinteractions. There are only the thirty particu-lar stories. Even though the passage abovedoes not give a particularly detailed or subtlehistorical account, it describes a situation thatcannot be envisioned in GLR terms. Themeanings of each attribute of each country aredetermined by thfe ensemble at the time. Toreturn to the analysis of section A above,social life happens in eventswhich can beseen as ensembles of particular values ofattributesrather than in a free play ofattributes on each other.'

m . TRANSCENDING GENERALLINEAR REALITYThe general linear model is a powerful toolfor empirical research. And effective usersrecognize that there is, in fact, no warrant fortreating it as a model for social causality.Rather, the GLM tests substantive models ofsocial reality on the assumption that thosemodels entail linear regularities in observeddata. The substantive models involved neednot take the point of view I have calledgeneral linear reality.

But in practice the GLM has generated atheoretical "back-formation." Many sociolo-gists treat the world as if social causalityactually obeyed the rules of linear transforma-tions. They do this by assuming, in thetheories that open their empirical articles, thatthe social world consists of fixed entities withvariable attributes; that these attributes haveonly one causal meaning at a time; that thiscausal meaning does not depend on otherattributes, on the past sequence of attributes,or on the context of other entities. Sodistinguished a writer as Blalock (1960:275)has written "These regression equations arethe 'laws' of a science." To say this is to reifyan entailed mathematics into a representationof reality.

Throughout this paper I have discussedsome alternative methods that deal with some

^ The fictitious character of main effects was wellunderstood during the creation of modem inferentialstatistics, but has been quite forgotten. For a soberingdiscussion, see Traxler (1976) concerning Neyman'sobjections to the idea of main effects.

182 SOCIOLOGICAL THEORYof the problems designated as interesting bytheorists but excluded by GLR. I would likehere to briefly present the theoretical posi-tions that underlie these alternative methods.Each of course makes assumptions about thefully complex reality of the theorists, but eachignores different things than does GLR. Allfollow the same general strategy of relaxingone or more of the stringent philosophicalassumptions here analyzed.

A. The Demographic Model of RealityThe demographic model principally relaxesthe first, fundamental assumption of GLR,that of fixed entities with variable attributes.It allows entities to appear, disappear, move,merge, and divide. Demographic methodseasily handle problems involving the appear-ance and disappearance of entities, and, as Inoted above, these methods can in principlebe combined with attribute-based methods tohandle some of the central difficulties ofentities/variables methods. Demographic meth-ods are weaker with merger and division,however; even marriage is classically treatednot as an amalgamation of two individuals,but as a state change in the life of one ofthem. Indeed, rather than presenting GLR-based methods with improved means formodeling the flow of entities, demographyseems to be moving towards use of GLRmodels for state changes under conditionswhen entities can be assumed fixed (e.g.,Rosenfeld 1983; Morgan and Rindfuss 1985).

In fact, to develop a general demographicreality that has strength comparable to that ofGLR requires extensive theoretical and meth-odological work. Methods that would sustaininquiry in this broad demographic senserequire the serious conceptualization andmeasurement of complex entity processes, ofwhat I earlier called "central subjects." Weneed rigorous concepts for how to delimit andmeasure social actorsho^ to separate socialnames and the things behind them; how tolimit central subjects to a single level ofinteraction; how to specify that level ofinteraction. We need to decide how to defineeventsnoi simple ones like organizationaldeath, but complex ones like organizationaltransformation, in which members of entitieschange even while the variable properties ofthe entity itself change. For once we relax thefixed entities assumption, adnnitting firstsimple events like appearance and disappear-

ance then complex ones like merger ortransformation, we advance directly towardsredefining the social world in terms of centralsubjects to which events happen. This movetowards a story-based model of the socialworld will ultimately force us to a sequentialview of reality.

B. The Sequential Model of RealityA sequence-based, central subject/event ap-proach reverses nearly all the GLR assump-tions. It assumes, first of all, that the socialworld consists of fluctuating entities, accept-ing the demographic model just outlined. Itdeliberately makes order and sequence effectscentral. Moreover, it emphasizes the transfor-mation of attributes into events. Thus, itinterprets "30% of the cohort recruited by acertain occupation is retained after 20 years"not by comparing it to retention rates in otheroccupations, but by comparing it to previousand later rates in the same one; meaning isdetermined by story, not by scales thatabstract across cases. The sequential modelalso avoids the assumptions about monotoniccausal level. Extremely minor events (e.g.,an assassination) can have large consequencesbecause of their location in a story.*

The central conceptual task of the sequenceapproach, cognate with the conceptualization/measurement task of standard methods, is thecolligation of events; how to separate hypo-thetical "events' (like hypothetical "con-cepts" in standard methods) from the occur-rences used to indicate them; how to chooseobserved occurrences so as to best indicatethe course of events. A large literature in thephilosophy of history deals with the problemof colligationthe problem of defining com-monly acceptable units and of groupingnumbers of occurrences under a singlegeneral action (for surveys see McCuUagh1978; Olafson 1978:c.3). But there is little insocial science beyond Abbott's (1984) brief

' In practical terms, methods studying sequentialrealities arise out of a common empirical situationparticularly difficult for the GLM: the situation in whichwe are interested in how a process unfolds over time andin which there are relatively few (from 20 to 200) cases,with a large and heterogeneous collection of dataavailable on them. Such situations include the compara-tive histories of organizations, of professions, ofrevolutions, of international policies, and dozens of other

GENERAL LINEAR REALITY 183study of the practical problems of measure-ment with social sequence data.

The sequence model of reality does makethe same kinds of assumptions about casewiseindependence as does GLR. Abbott's (1985)analyses of professionalization sequences, forexample, are flawed by the assumption thateach profession develops independently of theothers, a proposition he has vigorously deniedin other contexts (e.g., Abbott 1988). Perhapsthe lone form of sequential analysis address-ing the casewise dependence issue squarelyremains White's (1970) vacancy chain model.

C. The Network Model of RealityA third basic alternative to GLR emphasizesthe relaxation not of the entities and sequenceassumptions, but rather of the independenceassumptions. The network/structure litera-tures reject these assumptions, focusingdirectly on the lines along which causes mustflow rather than on the particular states andrelations of the various causes. Althoughnetwork models make the same kinds ofentity assumptions as GLR and lack in mostcases the historical structuring of the se-quence approach, they embrace syochroniccontingencies that GLR, as well as thedemographic and sequential approaches, mustignore. Since the network literature is largeand well-developed, my aim here is merely toidentify it as embodying an alternativeconception of social causality. The interestedreader can refer to numerous reviews of itelsewhere. (See, e.g., Marsden and Lin 1982;Knoke and Kuklinski 1982; Burt 1982.)

IV. CONCLUSIONThis paper has argued that sociological theoryand methods are divided by the unnecessarilynarrow approach to causality implicit in thedominant methods in the discipline. Althoughanalysts studying social structure throughnetwork data and workers studying entityprocesses through demographic methods havequietly developed alternatives, all too oftengeneral linear models have led to generallinear reality, to a limited way of imaginingthe social process. My aim in making thisargument, as I said at the outset, is notcontroversial. But since the paper has elicitedstrong and even hostile response, I shalladdress in closing some particular objections.

The chief objections of theorist colleagues

have been (1) these problems are well-knownand (2) even empirical work of the kind I hererecommend is not really possible within"human sciences." Although I have by nomeans read the entire theoretical literature,the rejections of empiricism I have seen donot in fact lay out the arguments I have madehere, but take objection 2 as their principalground (e.g., Giddens 1979, c. 7; 1982, c.1). The "human sciences" position is indeeda deeper objection, one that would requiremany pages to consider. My working answeris that (1) certain eminent and undeniablyinterpretive practitioners of the human sci-ences are ardent formalizers (e.g., Barthes1974) and (2) in fact interpretation andformalization interpenetrate in all parts of thisand other disciplines. After all, most of theformal work I have cited on social sequenceshas been largely inspired by history andliterary criticism.

Quantitative colleagues have also objected(1) that the philosophical assumptions ana-lyzed here are well known, but in addition (2)that my alternatives are limited in applicabil-ity, and (3) that I should not presentalternatives until they are better developed. Ithink all three of these judgments aremistaken. First, I have not seen these kinds ofdiscussions in standard methodologicalsources. Lieberson's brilliant book (1985)deals with some of these issues, but neverreally leaves the philosophical framework ofentities and variables. As for sequences,Abbott's (1983) review of prior sociologicalwork found virtually nothing and Abell(1987) has found little since. Careful practi-tioners of the GLM undoubtedly recognizethe problems I have written about; Liebersonis an example. But to say that any of theseproblems is in the active consciousness ofworking sociologists belies the plain evidenceof our major journals.

As for the limited applicability of myalternatives, that is only apparent. The wideapplicability of the GLM is itself an appear-ance, a consequence of the paradigm throughwhich quantitative sociology apprehends real-ity. Alternatives seem applicable only tospecial cases, as Kuhn says, because ourcurrent methods prevent our seeing themyriads of situations to which they apply. Itis not that "there are certain special kinds ofdata to which sequence methods are appropri-ate." On the contrary. One can argue on thetheoretical foundation of symbolic interaction-

184 SOCIOLOGICAL THEORYism that a sequence-based methodology is theonly one proper for the vast majority of socialexplanation.

Finally, one cannot require that alternativemethods should not be considered until fullydeveloped. The GLM did not emerge fullydeveloped in Blalock or Duncan, much less inSewall Wright; it became a full paradigmthrough a long process of development,criticism, and growth. To ask that alternativesachieve that development instantaneously isto deny the possibility of alternatives.

I have of course merely sketched the barestoutlines of those alternatives here. But I hopethereby to have begun a serious considerationof the relation between methods and theorythat can replace the shrill denunciations wesometimes hear.

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