-
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.
REFERENCESAbbott, A. 1983. "Sequences of Social Events."
Historical Methods 16:129-147.1984. "Event Sequence and Event
Duration."
Historical Methods 17:192-204.-. 198Sa. "Professionalization
Large and Small."
Unpublished manuscript. Department of Sociology,Rutgers
University.
-. 1988. The System of Professions. Chicago:University of
Chicago Press.
and J. Forrest. 1986. "Optimal MatchingTechniques for Historical
Data." Journal of Interdisci-plinary History 16:471-494.
Abell, P. 1971. Model Building in Sociology. New
York:Schocken.
1984. "Comparative Narratives." Journal forthe Theory of Social
Behavior 14:309-331.
-. 1987. The Syntax of Social Life. Oxford: OxfordUniversity
Press.
Alexander, J.C., B. Giesen, R. Munch, and N.J.Smelser., eds.
1987. The Micro/Macro Link. Berke-ley: University of California
Press.
Alexander, K.L., and T.W. Reilly, 1981. "Estimatingthe Effects
of Mairiage Timing on Education Attain-ment." American Journal of
Sociology 87:143-156.
Alker, H.R. 1982. "Logic, Dialectic, and Politics." Pp.65-94 in
same, ed.. Dialectical Logics for the PoliticalSciences. Poznan
Studies Vol 7. Amsterdam: Rodopi.
1984. "Historical Argumentation and StatisticalInference."
Historical Methods 17:164-173.
_, J.P. Bennett, and D. Mefford. 1980. "Gener-alized Precedent
Logics for Resolving Insecurities."International Interactions
7:165-206.
Allison. P.D. 1977. "Testing for Interaction in
MultipleRegression." American Journal of Sociology83:144-153.
Althusser, L., and E. Balibar. 1970. Reading Capital.New Yoik:
Pantheon.
Barthes, R. 1974. S/Z. New York: Hill and Wang.Bates, R. 1981.
Markets and States in Tropical Africa.
Berkeley: University of California Press.Bishop, Y.M.M., S.E.
Feinberg, and P.W. Holland.
1975. Discrete Multivariate Analysis. Cambridge MA:MIT
Press.
Blalock, H.M. 1960. Social Statistics. New York:McGraw-HiU.
1984a. Basic Dilemmas in the Social Sciences.Beverly Hills CA:
Sage.
1984b. "Contextual-Effects Models." AnnualReview of Sociology
10:353-372.
Blau, P.M., and O.D. Duncan. 1967. The AmericanOccupational
Structure. New York: Free Press.
Blumer, H. 1931. "Science without Concepts." Ameri-can Journal
of Sociology 36:515-533.
1940. "The Problem of the Concept in SocialPsychology." American
Journal of Sociology45:707-719.
1956. "Sociological Analysis and the'Variable.' " American
Sociological Review21:683-690.
Booth, A., D.R. Johnson, L. White, and J.N. Edward.1984.
"Women's Outside Employment and MaritalInstability." American
Journal of Sociology90:567-583.
Boorman, S.A., and H.C. White. 1977. "SocialStructure from
Multiple Networics 11: Role Structures."American Journal of
Sociology 81:1384-1446.
Box, G.E.P., and G.M. Jenkins. 1976. Time SeriesAnalysis. San
Francisco: Jossey-Bass.
Boudon, R. 1973. Mathematical Models of SocialMobility. San
Francisco: Jossey-Bass.
Bradshaw, Y.W. 1985. "Dependent Development inBlack Africa."
American Sociological Review50:195-207.
Brent, E.E., and R.E. Sykes. 1979. "A MathematicalModel of
Symbolic Interaction Between Police andSuspects." Behavioral
Science 24:388-402.
Burawoy, M. 1979. Manufacturing Consent. Chicago:University of
Chicago Press.
Burt, R. 1982. Towards a Structural Theory of Action.New York:
Academic.
Cantor, D., and K.C. Land. 1985. "Unemployment andCrime Rates in
the Post World War 11 United States."American Sociological Review
50:317-332.
Carroll, G. 1984. "Organizational Ecology." AnnualReview of
Sociology 10:71-93.
Carroll, G., and J. Delacroix. 1982. "OrganizationalMortality in
the Newspaper Industries of Argentina andIreland." Administrative
Science Quarterly 27:169-198.
Cicourel, A.V. 1981. "Notes on the Integration ofMicro- and
Macro-levels of Analysis." Pp. 51-80 inKnoir-Cetina and Cicourel
1981.
Cliff, A.D., and J.K. Ord. 1981. Spatial Processes.London:
Pion.
Coleman, J.S. 1964. Introduction to MathematicalSociology. New
York: Free Press.
Coleman, J.S., E. Katz, and H. Menzel. 1966. MedicalInnovation.
Indianapolis: Bobbs Merrill.
Collins, R. 1981. "The Microfoundations of Macroso-ciology."
American Journal of Sociology 86:984-1014.
1984. "Statistics Versus Words." Pp. 329-362in same, ed.
Sociological Theory 1984. San Francisco:Jossey-Bass.
-. 1987. "Interaction Ritual Chains, Power, andProperty." Pp.
193-206 in Alexander et al. 1987.
Coser, L. 1975. "Two Methods in Search of aSubstance." American
Sociological Review 40:691-700.
Devine, J.A. 1983. "Fiscal Policy and Class IncomeInequality."
American Sociological Review 48:606-622.
Evans, M.D., and E.O. Laumann. 1983. "ProfessionalCommitment."
Pp. 3-40 in Research in SocialStratification and Mobility.
Greenwich CN: JAI Press.
-
GENERAL LDffiAR REALITY 185Featherman, D.L., and R.M. Hauser.
1978. Opportunity
and Change. New York: Academic.Rigstein, N. 1985. "The Spread of
Multidivisional Form
Among Large Firms." American Sociological Review50:377-391.
Freese, L. 1980. "Formal Theorizing." Annual Review ofSociology
6:187-212.
, and J. Sell. 1980. "Constructing AxiomaticTheories in
Sociology." Pittsburgh: University ofPittsburgh Press.
Freud, S. 1936. The Problem of Anxiety. New Yoric:Norton.
[1915] 1963a. "Instincts and Their Vicissi-tudes." Pp. 88-103 in
General Psychological Theory.New York: Collier.
... [1915] 1963b. "Repression." Pp. 104-115 inGeneral
Psychological Theory. New York: Collier.
Galle, O.R., C.H. Wiswell, and J.A. Burr. 1985."Racial Mix and
Industrial Productivity." AmericanSociological Review 50:20-33.
Gallie, W.B. 1968. Philosophy and the HistoricalUnderstanding.
New York: Schocken.
Giddens, A. 1979. Central Problems in Social Theory.Berkeley:
University of California Press.
1982. Profiles and Critiques in Social Theory.Berkeley:
University of California Press.
_. 1984. The Constitution of Society. Berkeley:University of
California Press.
Granovetter, M. 1978. "Threshold Models of CollectiveBehavior."
American Journal of Sociology 83:1420-1443.
Hage, J. 1972. Techniques and Problems of TheoryConstruction in
Sociology. New York: Wiley.
Heise, D.R. 1979. Understanding Events. Cambridge:Cambridge
University Press.
Hirschi, T. 1969. Causes of Delinquency. Berkeley:University of
California Press.
Hogan, D.P. 1978. "The Variable Order of Events in theLife
Course." American Sociological Review43:573-586.
Hodson, F.R., D.G. Kendall, and P. Tautu. 1971..Mathematics in
the Historical and ArchaeologicalSciences. Edinburgh: University of
Edinburgh Press.
Howe, R.H. 1978. "Max Weber's Elective Affinities."American
Journal of Sociology. 84:366-385.
Hubert, L., R.G. Golledge, and CM. Costanzo. 1981."Generalized
Procedures for Evaluating Spatial Auto- .correlation." Geographical
Analysis 13:224-233.
Hull, D.L. 1975. "Central Subjects and HistoricalNarratives."
History and Theory 14:253-274.
Kamens, D.H. 1985. "The Importance of HistoricalSequencing."
Paper Presented at American Sociologi-cal Association, Washington,
DC. August 1985.
Katzner, D.W. 1983. Analysis without Measurement.Cambridge:
Cambridge University Press.
Knoke, D., and J.H. Kuklinski. 1982. Network Analysis.Beverly
Hills: Sage.
Knoir-Cetina, K., and A.V. Cicourel. 1981. Advances inSocial
Theory and Methodology. Boston: Routledge.
Kohn, M.L., and C. Schooler. 1982. "Job Conditions
andPersonality." American Journal of Sociology87:1257-1286.
Laumann, E.O., and F.U. Pappi. 1976. Networks ofCollective
Action. New York: Academic.
Leamer, E.E. 1983. "Let's Take the Con out ofEconometrics."
American Economic Review 73:31-43.
Lieberson, S. 1985. Making It Count. Berkeley:University of
California Press.
Loftin, C , and S.K. Ward. 1981. "Spatial Autocorrela-tion
Models for Galton's Problem." Behavior ScienceResearch
16:105-128.
1983. "A Spatial Autocorrelation Model of theEffects of
Population Density on Fertility." AmericanSociological Review
48:121-128.
Marini, M.M. 1984. "Women's Educational Attainmentand the Timing
of Entry into Parenthood." AmericanSociological Review
49:491-511.
Marsden, P.V. 1983. "Restricted Access in Networksand Models of
Power." American Journal of Sociology88.686-717.
Marsden, P.V., and N. Lin. 1982. Social Structure andNetwork
Analysis. Beverly Hills: Sage.
McCuUagh, C.B. 1978. "Colligation and Classificationin History."
History and Theory 17:267-284.
Mefford, D. 1982. "A Comparison of Dialectical andBoolean
Algebraic Models of the Genesis of Interper-sonal Relations." Pp.
31-47 in H. Alker, ed..Dialectical Logics for the Political
Sciences. PoznanStudies Vol. 7. Amsterdam: Rodopi.
Morgan, S.P., and R.R. Rindfuss. 1985. "MaritalDisruption."
American Journal of Sociology90:1055-1077.
Olafson, F.A. 1979. The Dialectic of Action. Chicago:University
of Chicago Press.
Padgett, J.F. 1985. "The Emergent Organization ofPlea
Bargaining." American Journal of Sociology90:753-800.
Peterson, R.D., and J. Hagan. 1984. "ChangingConceptions of
Race." American Sociological Review49:56-70.
Proctor, M., and P. Abell. 1985. Sequence Analysis.Aldershot,
Hants: Gower.
Poulantzas, N. 1978. Political Power and Social Classes.London:
Verso.
Puterman, M.L., ed. 1978. Dynamic Programming andIts
Applications. New York: Academic.
Rosenfeld, R.A. 1983. "Sex Segregation and Sectors."American
Sociological Review 48:637-655.
Robinson, J. 1980. "Time in Economic Theory." Pp.86-95 in same.
What are the Questions. Armonk, NY:M.E. Sharpe.
Sacks, H., E.A. Schegloff. and G. Jefferson. 1974. "ASimplest
Systematics for Tumtaking in Conversation."Language 50:696-735.
Schank, R., and R. Abelson. 1977. Scripts, Plans,Goals, and
Understanding. Hillsdale, NJ: LawrenceErlbaum Associates.
Schieve, W.C, and P.M. Allen. 1982. Self-Organizationand
Dissipative Structures. Austin: University ofTexas.
Simpson, I.H., R.L. Simpson, M. Evers, and S.S. Poss.1982.
"Occupational Recruitment, Retention andLabor Force Cohort
Representation." American Jour-nal of Sociology 87:1287-1313.
Sobel, M.E. 1983. "Structural Mobility, CireulationMobility and
the Analysis of Occupational Mobility."American Sociological Review
48:721-727.
; , M. Hout, andO.D. Duncan. 1985. "Exchange,Structure, and
Symmetry in Occupational Mobility."American Journal of Sociology
91:359-372.
Southwood, K.E. 1978. "Substantive Theory andStatistical
Interaction." American Journal of Sociology
83:1154-1203.Stewman, S. 1976. "Markov Models of
Occupational
Mobility." Journal of Mathematical Sociology4:201-245,
247-278.
-
186 SOCIOLOGICAL THEORYStinchcombe, A.L. 1968. Constructing
Social Theories.
New York: Harcourt Brace.1978. Theoretical Methods in Social
History.
New York: Academic.Sudnow, D. 1971. Studies in Social
Interaction. New
York: Free Press.Thombeny, T.P., and R.L. Christenson. 1984.
"Unem-
ployment and Criminal Involvement." AmericanSociological Review
49:398-411.
Tiao, G.C., and G.E.P. Box. "Modeling Multiple TimeSeries with
Applications." Journal of the AmericanStatistical Association
76:802-816.
Traxler, R.H. 1976. "A Snag in the History of
FactorialExperiments." Pp. 283-295 in D.B. Owen, ed. On theHistory
of Statistics and Probability. New York:Marcel Dekker.
Tuma, N.B., and M.T. Hannan. 1984. Social Dynamics.Orlando:
Academic.
Weber, M. 1949. The Methodology of the SocialSciences. New Yoik:
Free Press.
White, H.C. 1970. Chains of Opportunity. CambridgeMA:
Harvard.
1981. "Production Markets as Induced RoleStructures." Pp. 1-57
in S. Leinhardt, ed.. Socio-logical Methodology 1981. San
Francisco: Jossey-Bass.
.., S.A. Boonnan, and R.L. Breiger. 1976."Social Structure from
Multiple Networks I: Block-modeling of Roles and Positions."
American Journalof Sociology 81:730-780.
Wilner, P. 1985. "The Main Drift of Sociology Between1936 and
1984." History of Sociology 5:1-20.
Yamaguchi, K. 1983. "The Structure of Intergenera-tional
Occupational Mobility." American Journal ofSociology
88:718-745.